Band parameters for III–V compound semiconductors and their alloys

JOURNAL OF APPLIED PHYSICSVOLUME 89, NUMBER 11 1 JUNE 2001 APPLIED PHYSICS REVIEW Band parameters for III–V compound semiconductors and their alloys I. Vurgaftmana) and J. R. Meyer Code 5613, Naval Research Laboratory, Washington, DC 20375 L. R. Ram-Mohan Worcester Polytechnic Institute, Worcester, Massachusetts 01609 Received 4 October 2000; accepted for publication 14 February 2001 We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other. © 2001 American Institute of Physics. DOI: 10.1063/1.1368156 TABLE OF CONTENTS I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Relation to band structure theory and general considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Multiband k"P method . . . . . . . . . . . . . . . . . . . . 1. Zinc blende materials . . . . . . . . . . . . . . . . . . 2. Nitrides with wurtzite structure . . . . . . . . . . 3. Strain in heterostructures . . . . . . . . . . . . . . . 4. Piezoelectric effect in III–V semiconductors . . . . . . . . . . . . . . . . . . . . . . . 5. Band structure in layered heterostructures . . . . . . . . . . . . . . . . . . . . . . . B. Relation of k"P to other band structure models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Empirical tight binding model . . . . . . . . . . . 2. Effective bond orbital model . . . . . . . . . . . . 3. Empirical pseudopotential model . . . . . . . . . III. Binary compounds . . . . . . . . . . . . . . . . . . . . . . . . . A. GaAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. AlAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. InAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. GaP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. AlP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. InP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. GaSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. AlSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. InSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. GaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Wurtzite GaN . . . . . . . . . . . . . . . . . . . . . . . . 2. Zinc blende GaN . . . . . . . . . . . . . . . . . . . . . . 0021-8979/2001/89(11)/5815/61/$18.00 5816 5817 5817 5818 5819 5821 5821 5822 5822 5822 5823 5823 5823 5823 5824 5826 5827 5828 5828 5829 5830 5831 5832 5832 5834 5815 K. AlN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. InN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Ternary alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Arsenides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. AlGaAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. GaInAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlInAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Phosphides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. GaInP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. AlInP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlGaP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Antimonides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. GaInSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. AlInSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlGaSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Arsenides antimonides . . . . . . . . . . . . . . . . . . . . 1. GaAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. InAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Arsenides phosphides . . . . . . . . . . . . . . . . . . . . . 1. GaAsP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. InAsP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlAsP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Phosphides antimonides . . . . . . . . . . . . . . . . . . . 1. GaPSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. InPSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlPSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. GaInN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. AlGaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlInN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5835 5836 5837 5838 5838 5839 5840 5840 5840 5841 5841 5842 5842 5842 5843 5843 5843 5844 5844 5844 5844 5845 5846 5846 5846 5846 5846 5846 5846 5847 5847 © 2001 American Institute of Physics Downloaded 05 Dec 2002 to 140.105.8.31. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 5816 J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Appl. Phys. Rev.: Vurgaftman, Meyer, and Ram-Mohan 4. GaAsN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. GaPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. InPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. InAsN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Quaternary alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Lattice matched to GaAs . . . . . . . . . . . . . . . . . . 1. AlGaInP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. GaInAsP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. AlGaInAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. GaInAsN . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Lattice matched to InP . . . . . . . . . . . . . . . . . . . . 1. GaInAsP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. AlGaInAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. GaInAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Lattice matched to InAs . . . . . . . . . . . . . . . . . . . 1. GaInAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. AlGaAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. InAsSbP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Lattice matched to GaSb . . . . . . . . . . . . . . . . . . . 1. GaInAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. AlGaAsSb . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Other substrates . . . . . . . . . . . . . . . . . . . . . . . . . . 1. AlGaAsP . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Nitride quaternaries . . . . . . . . . . . . . . . . . . . . . . . VI. Heterostructure band offsets . . . . . . . . . . . . . . . . . . A. GaAs/AlAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. GaInAs/AlInAs/InP . . . . . . . . . . . . . . . . . . . . . . . C. Strained InAs/GaAs/InP and related ternaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. GaInP/AlInP/GaAs . . . . . . . . . . . . . . . . . . . . . . . E. GaP and AlP . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. GaSb/InAs/AlSb . . . . . . . . . . . . . . . . . . . . . . . . . G. GaSb/InSb and InAs/InP . . . . . . . . . . . . . . . . . . . H. Quaternaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. GaN, InN, and AlN . . . . . . . . . . . . . . . . . . . . . . . VII. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5848 5849 5849 5849 5849 5850 5850 5850 5851 5851 5851 5851 5852 5852 5852 5852 5853 5853 5853 5853 5854 5854 5854 5854 5854 5855 5856 5856 5857 5858 5858 5860 5861 5861 5862 I. INTRODUCTION At present, III–V compound semiconductors provide the materials basis for a number of well-established commercial technologies, as well as new cutting-edge classes of electronic and optoelectronic devices. Just a few examples include high-electron-mobility and heterostructure bipolar transistors, diode lasers, light-emitting diodes, photodetectors, electro-optic modulators, and frequency-mixing components. The operating characteristics of these devices depend critically on the physical properties of the constituent materials, which are often combined in quantum heterostructures containing carriers confined to dimensions on the order of a nanometer. Because ternary and quaternary alloys may be included in addition to the binary compounds, and the materials may be layered in an almost endless variety of configurations, a seemingly limitless flexibility is now available to the quantum heterostructure device designer. a Author to whom correspondence should be addressed; electronic mail: [email protected] To fully exploit this flexibility, one clearly needs a reliable and up-to-date band parameter database for input to the electronic structure calculations and device simulations. However, after many years Volume 17 of the Landolt– Bornstein series1 remains the most frequently quoted source of III–V band parameters. Although that work contains much of the required data for a broad range of materials, it is nearly 20 yr old, lacks detailed descriptions of many of the important III–V alloys, and contains no information at all on the crucial band offset alignments for heterostructures. A popular compilation by Casey and Panish2 covers the band gaps for all III–V non-nitride binary materials and 12 ternary alloys, but the rapid progress in growth and characterization of many of those materials taking place since its publication in 1978 has decreased its usefulness. While a number of recent books and reviews on individual material systems are available,3–10 they are not necessarily complete or mutually consistent. A useful recent compilation of band structure parameters by Levinshtein et al.11 does not contain in-depth information on aluminum-containing elemental semiconductors, is often based on a limited number of original sources, and considers only six ternary and two quaternary alloys. The objective of the present work is to fill the gap in the existing literature by providing a comprehensive and mutually consistent source of the latest band parameters for all of the common III–V zinc blende and wurtzite semiconductors GaAs, AlAs, InAs, GaP, AlP, InP, GaSb, AlSb, InSb, GaN, AlN, and InN and their ternary and quaternary alloys. The reviewed parameters are the most critical for band structure calculations, the most commonly measured and calculated, and often the most controversial. They include: 1 direct and indirect energy gaps and their temperature dependences; 2 spin-orbit splitting; 3 crystal-field splitting for nitrides; 4 electron effective mass; 5 Luttinger parameters and splitoff hole mass; 6 interband matrix element E P and the associated F parameter which accounts for remote-band effects in eight-band k"P theory; 7 conduction and valence band deformation potentials that account for strain effects in pseudomorphic thin layers; and 8 band offsets on an absolute scale which allows the band alignments between any combination of materials to be determined. All parameter sets are fully consistent with each other and are intended to reproduce the most reliable data from the literature. For completeness, lattice constants and elastic moduli for each material will also be listed in the tables, but in most cases will not receive separate discussion in the text because they are generally well known and noncontroversial. As a complement to the band parameter compilations, which are the main focus of this work, we also provide an overview of band structure computations. The k"P method is outlined, followed by brief summaries of the tight-binding and pseudopotential approaches. The theoretical discussions provide a context for defining the various band parameters, and also illustrate their significance within each computational method. The tables provide all of the input parameters that are normally required for an eight-band k"P calculation. While we have not attempted to cover every parameter that may potentially be useful, most of those excluded e.g., the and q parameters necessary for structures in a magnetic field Downloaded 05 Dec 2002 to 140.105.8.31. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Appl. Phys. Rev.: Vurgaftman, Meyer, and Ram-Mohan 5817 and the inversion asymmetry parameter are either poorly characterized or have well-known best values that have not changed much over time and are easily obtained from other sources such as Landolt–Bornstein. To the extent possible, we have fully treated the 12 major III–V binaries and their alloys. Other nominal III–V materials that are not covered include BN and other boroncontaining compounds which are commonly considered to be insulators rather than semiconductors , as well as the narrow-gap InSbBi, InTlSb, InTlAs, and InTlP alloys, which up to now have not achieved technological importance. None of these materials has been integrated appreciably into any of the mainline systems, and in most cases a paucity of band structure information precludes the recommendation of definite parameter values. On the other hand, we attempt to provide a complete and up-to-date description of the nitride family of materials, including those with a wurtzite crystal lattice, in light of its increasing prominence and the numerous intense investigations currently being conducted. It is naturally impossible for us to universally cite every article that has ever provided information or given values for the relevant band parameters. The reference list for such a review would number in the 10’s of thousands, which would be impractical even for a book-length treatment. We have therefore judiciously selected those results that are most central to the purpose of the compilation. In some cases, wide agreement on the value of a given parameter already exists, and/or previous works have critically and comprehensively reviewed the available information. Under those circumstances, we have limited the discussion to a summary of the final conclusions, along with references to the earlier reviews where additional information may be found. In other cases, we discuss more recent data that have modified or altered the earlier findings. The most difficult topics are those for which there is substantial disagreement in the literature. In those instances, we summarize the divergent views, but nonetheless choose a particular result that is either judged to be the most reliable, or represents a composite combining a variety of experimental and/or theoretical findings. Although such selections are inevitably subjective, since they require an assessment of the relative merits and reliabilities, in each case we inform the reader of the basis for our judgment. A guiding principle has been the maintenance of full internal consistency, both in terms of temperature dependences of the parameters for a given material and with regard to variations with alloy composition. For example, composition-dependent parameter values for the Alx Ga1 x As alloy employ the best information at those intermediate compositions for which data are available, but also invariably agree with the results for GaAs and AlAs when evaluated at x 0 and x 1. In a few cases, this has required the introduction of additional bowing parameters in contexts where they are not usually applied. We have also been as complete as possible in gathering all available information on the less common ternary and quaternary alloy systems. The review is organized as follows. Discussions of the k"P, tight-binding, and pseudopotential band structure calculations are presented in Sec. II, along with some general considerations regarding the major band parameters. The main results for individual binary compounds, ternary alloys, and quaternary alloys are reviewed in Secs. III, IV, and V, respectively. A table summarizes the parameters recommended for each material, while the text provides justification for the choices. Section VI then reviews the band offsets that are needed to calculate energy bands in quantum heterostructure. Those results are presented in a format that references all offsets to the valence band maximum of InSb, which allows a determination of the relative band alignment for any possible combination of the materials covered in this work. II. RELATION TO BAND STRUCTURE THEORY AND GENERAL CONSIDERATIONS A number of excellent books and review articles have summarized the methods for calculating bulk12–14 and heterostructure15–20 band structures. Since the present review is intended to focus on band-parameter compilation rather than theoretical underpinnings, this survey is aimed primarily at providing a context for the definitions of the various parameters. The section is limited to a discussion of the bare essentials for treating heterostructures and a brief description of the practical approaches. A more detailed description of the theory will be presented elsewhere. A. Multiband k"P method The most economical description of the energy bands in semiconductors is the effective mass approximation, which is also known as the envelope function approximation or multiband k"P method. It uses a minimal set of parameters that are determined empirically from experiments. By means of a perturbative approach, it provides a continuation in the wave vector k of the energy bands in the vicinity of some special point in the Brillouin zone BZ . ¨ The electronic wave functions that satisfy the Schrodinger equation with a periodic lattice potential in a bulk crystal are given by Bloch’s theorem: r e ikr u nk r . 2.1 The cell-periodic Bloch functions u nk (r) depend on the band index n and the envelope function wave vector k. The wave functions (r) form a complete set of states as do the wave functions based on Bloch functions at any other wave vector, including the wave vectors at special points in the BZ.21 In treating the optical and electronic properties of direct gap semiconductors, it is natural to consider the zone-center -point Bloch functions u n0 (r) for our wave function expansions, and we drop the reference to the k 0 index for these functions. For our purposes here, the general form of the wave functions may be considered to be a linear combination of a finite number of band wave functions of the form r f n z e ik x x e ik y y u n r Fn r un r . 2.2 The envelope functions F n (r) are typically considered to be slowly varying, whereas the cell periodic and more oscilla¨ tory Bloch functions satisfy Schrodinger’s equation with band-edge energies. We distinguish envelope functions cor- Downloaded 05 Dec 2002 to 140.105.8.31. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 2. and Ram-Mohan responding to the 1 conduction c. . and 3: 1 2 3 1 2 L L L 4 4 . we have the usual 8 8 Hamiltonian with terms linear and quadratic in k.g. these terms correspond to the Kane model23. the additional contribution of the nearby c bands would enter the sum over intermediate states in the parameter. 2. Next. Rev. 11. with quadratic O(k 2 ) terms within the conduction and the valence bands24. We second-order perturbation theory for the denote this revised value as L : L 1 3m 0 1 c X px S E Ec 2 EP . and the energetically higher remote bands with an index r: F n F c . The second-order valence-band terms include those with possible intermediate r states that belong to energetically higher bands with the symmetry of s( 1 ). with being the Pauli spin matrices here H so 4m 2 c 2 0 V p" . 2.9 1. The matrix elements of the momentum operator between the conduction and valence bands can be expressed in terms of a single parameter P.org/japo/japcr.. the eight-band k"P model gives rise to eight coupled differential equations.: Vurgaftman. Zinc blende materials The zinc blende crystal consists of two interpenetrating face-centered-cubic lattices... and m 0 is the free electron mass.24 for the band structure.105. which define the ¨ Schrodinger eigenvalue problem for the energy bands near the center of the BZ. Its value in a given material is usually reported in energy units eV as: EP 2m 0 2 All of the terms appearing in the valence-band Hamiltonian may be cast in terms of the three quantities . whose values are reviewed in the subsequent sections: F 1 m0 S px ur Ec Er 2 4m 2 c 2 0 X V p x y V y px Y . 2.aip. see http://ojps. Alwhere though other. With the envelope functions represented by e ikr . 6E g 2. The spin-orbit interaction splits the sixfold degeneracy at the zone center into fourfold degenerate heavy-hole hh plus light-hole lh bands of 8 symmetry with total angular momentum J 3/2. the values of the so parameter are determined experimentally. Phys.6 . Redistribution subject to AIP license or copyright.g. Ga and the other a group-V element atom e. 15 valence .jsp . Phys.4 are parameterized by the quantity called the spin-orbit splitting 3 i so The E P matrix element is one of the band parameters that is extensively reviewed in the subsequent section. and parameter set is simply related to the standard definitions of the Luttinger parameters 1 . with the functional form often fitted to the empirical Varshni form27 Eg T Eg T 0 T2 T .10 2 . more physically justified and possibly quantitatively accurate.26 We define the following quantities in terms of matrix elements between p-like valence bands whose symmetry here and in the following is indicated as X. and . 89.8 If the conduction-band states were not included into our analysis explicitly.28.5818 J. and a doubly degenerate split-off so band of 7 symmetry with J 1/2. In a bulk semiconductor. one having a group-III element atom e. p( 12). 2 .7 r and are adjustable Varshni parameters.11 P2 .13 r 15 X px ur E Er X py ur E Er 2 . 2 2. Appl. Meyer. 1 June 2001 Appl.25 as well as the appropriate interband conduction-valence terms.3 Now. No. m0 2. . where S p x X is the momentum matrix element between the s-like conduction bands and p-like valence bands. For a bulk system. Z and remote bands: 1 3m 0 1 3m 0 1 The atomic potential V appears in the above expressions. 2. A zinc blende crystal is characterized by a single lattice constant a lc. originally defined by Kane: P i S px X . 2. and 1 6m 0 12 r X px ur E Er 2 . Lowdin’s perturbation theory22 is applied in order to eliminate the functions F r in favor of perturbation terms in the equations for the conduction and valence bands.29 Downloaded 05 Dec 2002 to 140. the L . In the bulk k"P theory. and d( 15) atomic orbitals. In practice.F r . 2. The matrix elements of the spin-orbit interaction. The remote bands are assumed to have bandEc E E g . the higherband contributions to the conduction band are parameterized by the Kane parameter F.5 r where S p x u r is the momentum matrix element between the s-like conduction bands and remote bands r.12 . functional forms have been proposed. The inclusion of electron spin and spin-orbit interaction effects are straightforward. .31. both direct and indirect energy gaps in semiconductor materials are temperature-dependent quantities.23 and we obtain a 6 6 valenceband Hamiltonian. Y. As .8. 2. where E g is the edge energies E r E c direct energy gap. Vol. Through second-order perturbation theory. or equivalently in terms of the Luttinger parameters.F . 16 * m hh 1 2 3.. 2. Fig. Note the anticrossing of the conduction band with a higher band along the – X direction. In this article.. 2.14 and m* lh m0 2 3 Using this procedure.J. Phys. In the context of heterostructures. 2. 1 2 3 3 . Rev. we derive consistent sets of F parameters from the best available experimental reports of electron effective masses. Phys.18 .aip. 2. That quantity exceeds the bare electron mass by 1%–2%. energy gaps.: Vurgaftman. The connecting curves represent band gaps for the random ternary alloys. For the non-nitride III–Vs. 2. being able to reproduce the correct effective masses at the center of the BZ ensures that the curvature of the energy bands is properly reproduced.8. 11.15 Both E P defined in Eq. 1 b . those remote bands are not necessarily the same ones that produce the largest correction to the electron mass. which means that the temperature variation of the effective mass arises only through the temperature dependences of the energy gaps as in Eq. There has been no previous attempt to compile reliable. which are not as physically meaningful but more convenient to work with theoretically. the hh effective masses in the different crystallographic directions are given by the relations m0 z 1 * m hh m0 110 2 1 2 2 2.g. 3 shows a similar plot of the lowest forbidden gap in each material. see http://ojps. However. One alternative experimental technique is to rely on measuring the effective g factor. respectively.31. 1 a the full-zone band structure in the vicinity of the energy gap obtained for GaAs using the pseudopotential method see Sec. Vol. the conduction band effective mass is given in terms of the band parameters m0 m* e 1 2F EP Eg 2 Eg Eg so/3 so * m so 1 EP 3E g E g so so . and extra bands may be included in order to improve the agreement. 2. At present. 2.g.. For thin-layer quantum structures..g. it is the nonresonant polaron31 mass that is actually measured. Redistribution subject to AIP license or copyright. we attempt to present the latter value and note the approximate magnitude of the polaronic correction whenever the information is available. to the hh effective masses that can typically be measured in a more direct manner. In this article. 2. since the band structure is governed by the bare electron mass. spin-orbit splittings.org/japo/japcr. depending on the strength of the electron–phonon interaction. and momentum matrix elements. 2 show -valley energy gaps as a function of lattice constant for zinc blende forms of the 12 binary III–V semiconductors reviewed in this work. which sets one limit on the accuracy of perturbative approaches. one having a group-III element atom e. No. should in principle contain an additional parameter to account for the effects of remote bands analogous to F . Unfortunately.105. A more detailed plot of the band structure near the BZ center in GaAs is given in Fig. Downloaded 05 Dec 2002 to 140. 2. Nitrides with wurtzite structure These expressions show the relationship of the Luttinger parameters. In polar semiconductors such as the III–V compounds. 2. with X-valley and L-valley indirect gaps indicated by the dashed and dotted lines. In any theoretical model. 1 June 2001 Appl. The filled points in Fig. although in a few cases e. Ga and the other a group-V element atom e.32. GaAsN and InPN the extrapolated dependences extend well beyond the regions that are reliably characterized.33 As an illustration. and Ram-Mohan 5819 they have yet to gain widespread acceptance. 89.17 111 k 2 k k 0 E En m* ..18 . The eight-band k"P model compares well with more rigorous calculations up to about a quarter of the way to the BZ boundary. Appl. Equation 2. * m hh m0 111 1 2 3 3 . using incorrect effective masses could lead to severe deviations from experiment. However. The lh and so hole effective masses are given by The wurtzite crystal consists of two interpenetrating hexagonal close-packed lattices.g. it is also important to have a good model for the nonparabolic dispersion away from the center of the BZ. The effective mass m * at the conduction and valence band edges can be obtained from the bulk energy dispersion (k) as30 2 2 m0 m* lh m0 m* lh m0 z 1 110 2 1 2 2 1 2. II B 3 . we show in Fig.15 are usually taken to be independent of temperature.5 appearing in Eq. which is not as influenced by remote bands as the effective mass. We also emphasize that the -valley direct gap is not necessarily the smallest. since the remote-band effects can be calculated but not directly measured. since several of the materials are indirect-gap semiconductors in which the X and L conduction-band valleys lie lower than the minimum. in the bound state spectrum of a quantum well. despite their importance E P and F are inherently difficult to determine accurately. At the valence-band edge.jsp . e.13 . self-consistent F parameters for such a broad range of materials. which relates the split-off hole mass to the Luttinger parameters. Meyer. we compile consistent sets of Varshni parameters for all materials.4 and F Eq. not enough data exist for any of the III–V materials to fix the effect of the interaction with remote bands on the split-off hole mass. InAsN. the arrows indicate the boundaries of the regions where the gap dependence on composition may be predicted with any accuracy. These are in practice derived from the anisotropic effective mass using expressions similar to Eq.31. Vol. The detailed definitions have appeared in the literature. The 1c conduction bands are s like at the center of the BZ. 81 . Although the different conduction-band energy contributions from the higher 6c X. and L-valley gaps are indicated by solid. 1. X-.5820 J. and GaPN are extended into regions where no experimental data have been reported. dotted.Y 1v: Z nearest higher-order conduction bands belong to the 6c states of X. defined by analogy with Eq.Y symmetry and the 3c states transforming like the Z representation. Rev. respectively. A wurtzite crystal is characterized by two lattice constants a lc and c lc.Y and 1 v : Z representations. Due to the anisotropy of the crystal. The materials with -. The procedure leads to six distinct A parameters. 2.15 assum- FIG. there are two distinct interband matrix elements arising from the 6 v : X. the wurtzite structure does not give a triply degenerate valence band FIG. 89. and Ram-Mohan FIG.aip. and dashed lines. Diagram of the band structure in the vicinity of the energy gap of GaAs: a throughout the first Brillouin zone reproduced with permission from Ref. A major difference between zinc blende and wurtzite structures is that the in-plane behavior of the bands in a wurtzite crystal is different from the behavior along the 0001 axis the c axis . The compilations in the following sections take the F parameters in the wurtzite nitrides to be zero.jsp . The energy gaps for certain ternaries such as AlAsP.Y and 3c Z intermediate states lead to two distinct F parameters. Lowest forbidden gap as a function of lattice constant for nonnitride III–V compound semiconductors points and their random ternary alloys lines at zero temperature. Direct -valley energy gap as a function of lattice constant for the zinc blende form of 12 III–V binary compound semiconductors points and some of their random ternary alloys curves at zero temperature.34–38 In contrast to the zinc blende materials. while the valence bands representations. The second-order valence-band terms in the Hamiltonian are evaluated in a manner similar to the earlier discussion for zinc blende structures. Downloaded 05 Dec 2002 to 140. No. N . no experiments that would enable us to establish independent values for the latter have been reported. see http://ojps. 2.. GaAsN.: Vurgaftman.105. 3. which are to a large extent analogous to the Luttinger parameters in zinc blende materials. Redistribution subject to AIP license or copyright. 2. ing negligible crystal-field and spin-orbit splittings .3 . The belong to the 6 v : X. InPN. Appl. 1 June 2001 Appl. For GaAsN and InPN. Phys. Phys.org/japo/japcr. 11.8. Meyer. b a magnified view near the zone center. the crystal-field splitting ( 1 ) is in general not related to the spin-orbit splitting. and crystal-hole CH valence bands explicitly identified. zzzz C33 . the elastic continuum theory is usually invoked. see http://ojps. light-hole LH . six deformation potential constants D i arise from a full treatment of the effect of strain on the six-band valence-band structure as shown by Bir and Pikus. From the Bir–Pikus strain interaction for the valence bands.21 Z ZH so y X i 3. Instead it is the deformation potential constant a. 89. we define the local 39. which parameterizes the shift of the valence-band edge E v a v ( xx xx xx ). and the datasets given below are widely accepted. Ignoring the quadratic term for small deformations. Unfortunately. xzxz C 44 . this parameter is difficult to isolate experimentally. at least for the non-nitride materials.43 The preceding discussion applies to the zinc blende crystal structure. quantum wire. Strain in heterostructures To model the strain in a pseudomorphically grown heterostructure such as a quantum well.jsp . the atomic displacements are represented by a local vector field. or quantum dot. the band gap increases for a compressive strain. This implies a negative value for a a c a v . For the growth of pseudomorphic layers along the 001 direction. which in turn affects the energy levels of the band electrons. there are only three linearly independent constants: xxxx C 11 .31. only the value of the potential b is relevant. In elastic continuum theory.aip. 4 a .. a Schematic illustration of the spin-orbit splitting and crystal-field splitting in wurtzite materials as compared to zinc blende materials. 2. III–V semiconductors develop an electric moment whose magnitude is propor- Downloaded 05 Dec 2002 to 140. Note that. i.105. negative strain. All of the deformation potentials are tabulated for each material in the sections that follow. In a wurtzite material. and Ram-Mohan 5821 FIG. In crystals with cubic symmetry. r r u(r). 4 b . Vol.42 The distribution of the hydrostatic pressure shift between the conduction and valence bands is generally based from theoretical predictions in this review. Ev 1. A typical valence band structure for a wurtzite material is shown in Fig. xxy y C 12 . The physical deformation of the crystal leads to a distortion of the atomic locations. the reader is referred to the textbooks by Bir and Pikus14 and by Chuang. associated with the change in band gap E g due to a hydrostatic deformation. 4. The cr 1 and so 3 2 parameters are tabulated for wurtzite materials in the following sections. 4. there is little controversy regarding their values. Two additional potentials b and d are necessary to describe the shear deformations terms that split the heavy/light-hole degeneracy. there are five linearly independent elastic constants xxxx C 11 . with most of the change being in the conduction band edge. It is generally believed that the conduction band edge moves upward in energy while the valence band moves downward..8. Appl.org/japo/japcr. 1 June 2001 Appl. Piezoelectric effect in III – V semiconductors Under an externally applied stress. For the wurtzite structure. Phys.J. The crystal-field splitting leads to the band-edge energies: X H cr X and Z H cr Z XH and Y H so x Y H cr Y Ev . The constant of proportionality is the empirical deformation potential constant a c . xxy y C 12 .19 2. The definition of the spin-orbit and crystal-field splitting in the wurtzite materials is further illustrated in Fig. edge.41 In the case of hydrostatic compression. Redistribution subject to AIP license or copyright. that is measured. Phys. the change in the conduction-band-edge energy E c due to the relative change in volume V/V ( xx yy zz ) can be parametrized by a linear relation between the change in energy and the hydrostatic strain. 3. No. For the 6 6 valence-band strain Hamiltonian that is not reproduced here. Due to the nature of the atomic bonding in III–V materials. Rev.14 These D i are tabulated for each nitride material in the following sections. is insufficient to describe the full effect of strain.e. b Schematic diagram of the valence band structure of a wurtzite material near the zone center with the heavy-hole HH . 11. that generates the above strain is given by the relation i j i jkl kl . the change in energy E g a( xx yy zz ) must be positive. Meyer. However.20 The spin-orbit splitting is parameterized by the relations so z 2. xyxy C 44 . xxzz C 13 . Furthermore.: Vurgaftman.14 it may be observed that the single deformation potential a v . Note that our sign convention for a v is different from many other works found in the literature.14 The procedure for generating additional terms due to the presence of the strain has been described in detail by Bir and Pikus14 and Bahder. Under positive hydrostatic pressure. two different spin-orbit splitting parameters arise. Y i 2. The values for the elastic constants will be included in our compilation of the band parameters for completeness.22 Although in principle. the crystal anisotropy leads to two distinct conduction-band deformation potentials.40 The stress tensor i j strain tensor i j via u i (r) i jr j . 2. although Wei and Zunger recently argued that this is not always the case. they are commonly assumed equal ( 2 3 ). Further details are available from the references cited above. 1.25 e im . 6 . No. the conduction band edge profile is V S (z) E g (z) E g (ref) V P (z).3. B. VII we will provide an updated review of the valence band offsets in zinc blende and wurtzite materials. 12 .jsp . 31 .) orbitals. On the theoretical side. 2.aip.64–69 These parameterizations are beyond the framework of the considerations presented here. However. With V P (z) 0 in the reference layer.105. Redistribution subject to AIP license or copyright. 33 . 32 . 5.70 the electronic states are considered to be linear combinations of atomic (s. 89. The Hamiltonian’s matrix elements between the atomic orbital states are not evaluated directly. where we have reverted to the tensor form for the strains i j . 11. the ETBM requires that the overlap integrals be determined in terms of the measured direct and indirect band gaps and/or effective masses in the Downloaded 05 Dec 2002 to 140. Phys. more phenomenologically. 2.26 In the zinc blende materials. only off-diagonal terms in the strain give rise to the electric polarization components P s i and P s e 14 i jk .24 and e im . electrical capacitance measurements. Vol. putting the main emphasis on the compilation of a fully consistent set of band offsets. but are instead introduced as free parameters to be determined by fitting the band gaps and band curvatures effective masses at critical points in the BZ. j k.45 The strain-induced polarization Ps can be related to the strain tensor i j using piezoelectric coefficients e i jk of the form P s e i jk i jk .5822 J.29 j k k j k d ik c k j j . for a more complete picture of the energy bands throughout the BZ. and other techniques. where it is standard practice to introduce the factor of 1/2 in front of the e im for m 4.: Vurgaftman.52 the transfer matrix method.51. 21 1..8. Converting from the tensor notation to the matrix notation we write 11 . we tabulate both piezoelectric coefficients and spontaneous polarizations for the wurtzite nitride materials. see http://ojps.28 e 31 22 So far we have considered the band parameters of individual materials in the presence of strain. In the empirical tight-binding model ETBM introduced by Slater and Koster. 13 . e 33 . Phys. Relation of k"P to other band structure models e 33 33 .23 The symmetry of the strain under interchange of its indices allows us to write e i jk in a more compact form.50 In Sec. and McGill. Meyer. Further details are available from recent publications46.d. McCaldin.5.2.org/japo/japcr. this potential energy is given as a function V P (z) of the coordinate in the growth direction and defines the band edge profile for the top of the valence band. 2. Band structure in layered heterostructures 2. 2. On the other hand. Rev. The k"P model has also been extended to include the intrinsic inversion asymmetry of the zinc blende structure.57–59 which is a variational approach that may be considered a discretization of the action integral itself. x-ray photoelectron spectroscopy.24 . e i jk 1 2 i 1. A critical review of valence band offset determinations was given by Yu. to include the effects of and X z valley mixing in order to include such effects in modeling resonant double-barrier tunneling. 12 .48.60–63 and.44.. and e 15 e 24 can be derived from symmetry considerations.5.3 . 2. with polarity specified by the terminating anion or cation at the layer surface.3. The misalignment of energy band gaps in adjacent layers of a quantum heterostructure is taken into account by specifying a reference layer and defining a band offset function relative to it. in a wurtzite crystal. Appl. 2. 5.2.53–56 or the finite element method. The nitrides also exhibit spontaneous polarization. where j and k are the components of the strain and stress tensors in simplified notation see Eq. respectively.31. 3. Valence band offsets have been determined experimentally by optical spectroscopy of quantum well structures. it is necessary to adopt another approach that requires additional information as input. 22 . The piezoelectric contribution to the total polarization may be specified alternatively in terms of matrix d related to matrix e via the elastic constants Pi Pi eij d ik j The k"P model is the most economical in terms of assuring agreement with the observed bulk energy band gaps and effective masses at the center of the BZ. The piezoelectric effect is negligible unless the epitaxial structure is grown along a less common direction such as 111 . this is supplemented by pseudopotential supercell calculations that include atomic layers on either side of a heterointerface. 11 2. The piezoelectric polarization is given in component form by P s e 15 x P s e 15 y s P z e 31 13 . 2. ¨ The coupled Schrodinger differential equations for a layered heterostructure may be solved using the finite-difference method.6 . Thus both diagonal and off-diagonal strain components can generate strong built-in fields in wurtzite materials that must be taken into account in any realistic band structure calculation. Empirical tight binding model .m 4.m 1. and Ram-Mohan tional to the stress.27 where e 14 is the one independent piezoelectric coefficient that survives due to the zinc blende symmetry. 23 ..47 and reviews. In general.49 In the sections that follow. 4. the three distinct piezoelectric coefficients are e 31 e 32 . i 1.2.p.6 in order to obtain the following form without factors of 1/2: P s e i1 i 1 e i2 2 e i3 3 e i4 4 e i5 5 e i6 6. 1 June 2001 Appl.. Depending on the number of orbitals and nearest neighbors used to represent the states. The resulting somewhat ad hoc formulation offers considerable computational savings in comparison with the ETBM.5405 meV/K and 204 K in Eq. the currently accepted value is 0. no envelope function approximation is made.3. the net ‘‘pseudopotential’’ nearly cancels79.0665m 0 and e 0. genetic algorithms. No.460 meV/K with g both cases. However.31. 538– 671 K. With atomic potentials as the essential input. In fact.87 The analysis by Thurmond88 indicated 0.g. the crystal potential is represented by a linear superposition of atomic potentials. 11.83 Ab initio approaches employ calculated band parameters e. 94 Electron effective masses of m * 0. The valence states are orthogonal to the core states. by Stradling and Wood95 using magnetophonon resonance experiments. X 0. the electronic properties of the heterostructure can be determined. In the empirical pseudopotential model. Rev.. However.11 which were compiled from a variety of measurements. e. Combinations of ab initio and empirical methods have been developed to a high level of sophistication. which can be fitted by trial and error or using. A more recent examination of a large number of samples by ellipsometry produced a very similar parameter set of E g (T 0) 0.06 meV/K. Meyer. and g 204 K in E X (T 0) 1.96–98 A low-temperature value of 0. the EBOM is considerably less efficient computationally than k"P.8.90 although somewhat different parameter sets have been proposed recently on the basis of photoluminescence measure0. BINARY COMPOUNDS A. Each lattice position must be represented in the supercell technique.86 III. 89 The two re1. Further details GaAs is the most technologically important and the most studied compound semiconductor material. the s p 3 s * basis with the second-nearest-neighbor scheme72 turns out to have 27 parameters for the zinc blende lattice structure. This is the value we adopt following the recommendation of Nakwaski in his comprehensive review. When this is added to the attractive ionic potential..93 who proposed on the basis of numerous earlier experiments the following sets: E L (T 0) 1.519 eV. Effective bond orbital model are presented by Cohen and Chelikowsky81 and in the reviews by Heine and Cohen. This allows the EBOM input parameters to be readily expressed in terms of the experimentally measured parameters. The relative merits of the k"P and pseudopotential approaches have been assessed.74. L 0.981 eV. In this review.jsp .105.067m 0 at the band edge. and the energies and effective masses obtained from the diagonalization of the Hamiltonian and the resulting energy bands are nonlinear functions of these parameters. especially for thicker superlattices. 2.17. GaAs While the inclusion of additional bands and overlaps of higher orbitals is a possible approach to improving the tightbinding modeling of energy bands in bulk semiconductors. i. we make no attempt to give a standardized set of tight-binding parameters..341 eV.75 2. 1 June 2001 Appl. the split-off gap.84 Extension of the pseudopotential method to heterostructures entails the construction of a supercell to assure the proper periodic boundary conditions..e.73 The lack of a transparent relationship between the input parameters and the experimentally determined quantities is probably the single greatest disadvantage of the tight-binding method in making complicated band structure calculations.J. the effective bond orbital model76–78 EBOM uses spindoubled s. and the zone-center mass of each band.605 meV/K. respectively. the main significance of the EBOM approach derives from the fact that the resulting secular matrix has a small-k expansion that exactly reproduces the form of the eight-band k"P Hamiltonian.105 We employ the effective masses for the L and X valleys given by Adachi3 and Levinshtein et al.104 which is based on reports employing a wide variety of different experimental techniques.3 Many band structure parameters for GaAs are known with a greater precision than for any other compound semiconductor.p x .0635m 0 . we may expect the EBOM to be more accurate than the k"P model for thin-layer structures. such as the band gap.. Empirical pseudopotential model The influence of core electrons in keeping the valence electrons outside of the core may be represented by an effective repulsive potential in the core region.p y . 3.82. The ETBM can also be applied to superlattice band structure calculations. Appl. sults are well within the quoted experimental uncertainty of each other and several other experimental determinations. Phys.07m 0 was derived theoretically in several ab initio and semiempirical band structure studies.815 eV.100–102 recent cyclotron resonance measurements103 indicate a low-temperature result of 0.g.0636m 0 were observed at T 60 and 290 K. the EBOM can be thought of as an extension of the k"P method to provide an approximate representation of the energy bands over the full BZ.13 .519 eV at 0 K.99 While a somewhat larger mass of 0.85. and ments: E g (T 0) 1. and 225 K. and Ram-Mohan 5823 bulk material. Downloaded 05 Dec 2002 to 140. A crucial difference between the EBOM and related tight-binding formulations is that the s and p orbitals are centered on the face-centered cubic lattice sites of the zinc blende crystal rather than on both of the two real atoms per lattice site. Since short-period superlattice bands sample wavevectors throughout the BZ. see http://ojps.71. Vol. although the required computational effort far exceeds the demands of the k"P method. by photoluminescence measurements.895– 1.p z orbitals to generate an 8 8 Hamiltonian.92 The original controversy87 about the ordering of the L and X-valley minima was resolved by Aspnes. which are modified to obtain good fits to the experimental direct and indirect band gaps and effective masses.72 For example. and the resulting band structure theory corresponds to the nearly free-electron model.065m 0 was determined for the bare electron mass once the polaronic correction was subtracted.aip. for example.517 eV. At room temperature. 89. as confirmed.org/japo/japcr. from the density-functional theory in lieu of experimental data.: Vurgaftman. Schottky-barrier electroreflectance measurements yielded the widely accepted value for the split-off energy gap in GaAs: so 0. Phys. 91.80 at short distances. Redistribution subject to AIP license or copyright.55 meV/K. which has not been accomplished using the more involved ETBM. This is especially true of the fundamental energy gap with a value of 1. appears to have internal consistency problems. AlAs Because of its frequent incorporation into GaAs-based heterostructures.10. Theoretical studies99. The total hydrostatic deformation potential a is proportional to the pressure coefficient of the direct band gap. Phys.0 eV and d 4. Shantharama et al.135 Garriga et al.8– 29. However.85. Whatever the direction of the valenceband maximum. AlAs is an indirect-gap semiconductor with the X – L – ordering of the conduction valley minima.42. A small 10 meV correction for the exciton binding energy is presumably necessary.5 eV. AlAs is also one of the most important electronic and optoelectronic materials. While two-photon magnetoabsorption measurements110 indicated very little warping in the valence band.70 meV/K and 530 K.9 eV.108 and 109 magnetoexciton experiments. and 3 2.23–2.124 using standard deformation-potential scattering models are consistent with a c falling in the range 6.0).3 eV.3. Phys.0.136 and Dumke et al.107 magnetoreflection.126.128–131 Moreover. Since the analysis by Shantharama et al. Rev. 2 2.115 and Hermann and Weisbuch. we adopt the Hermann and Weisbuch value implying F 1. and Ram-Mohan Many different sets of Luttinger parameters are available in the literature. InAs.165m 0 was derived by Adachi. A recent study of acoustic–phonon scattering in GaAs/AlGaAs quantum 11. Pseudopotential122 and linear-muffintin-orbital123 calculations yielded a c as large as 18.903.6. although it should be similar to that in GaAs. is in good agreement with early cyclotron resonance.117 suggested that those analyses overestimated the influence of remote bands outside of the 14-band k"P model and gave E P 25.120 The experimental hydrostatic pressure dependence of E g for GaAs implies a total deformation potential a a c a v 8.5 eV.106. No.104 1 6. where the constant of proportionality is approximately the bulk modulus.99 The most popular set: 1 6. 1 June 2001 Appl.119 The greatest uncertainty in the GaAs band structure parameters is associated with the deformation potentials. mend using the values a c which were derived from the ‘‘model-solid’’ formalism by Van de Walle. GaP. The shear deformation potentials b and d have been determined both experimentally and theoretically. which were reported by Chadi et al.17 eV and a v 1. 121 where the minus sign represents the fact that the band gap expands when the crystal is compressed note that our sign convention for a v is different from a large number of articles .0 0.5 eV. Some trends in the band gap pressure coefficients were noted by Wei et al. The temperature dependence of the direct energy gap. although recent results tend toward the lower end of that range.90 also given in Landolt–Bornstein1 .137.98.8 Unlike GaAs.139 but are more consistent with the experimental re0. We propose the following composite values: b 2. we will use a slightly different value.16 eV. Appl.jsp . and InSb. which are needed to calculate strain effects in pseudomorphically grown layers.5 0. 11. Heterolayer bandstructure calculations are relatively insensitive to the value of a v when it is close to zero. in order to provide self-consistency with the k"P expression in Eq. studies of the valence-band deformation potential3.8 eV.indirect gap in AlAs was measured to be 2.3 to 13.33 How* ever. we choose parameters that are consistent with the more readily available data on the AlGaAs alloy discussed in detail below as well as with the foregoing measurements on bulk AlAs. it is generally agreed that the conduction band moves much faster with pressure.25 eV.126. whereas it has the opposite sign in other materials.138 although better agreement with the results of Monemar133 can be obtained by increasing to 530 K.94 . see http://ojps. which was derived by Lawaetz106 on the basis of five-level 14-band k"P calculations.114 Here we prefer a composite data set. which are consistent with the vast majority of measurements and several calculations.105. In order to be consistent with the experimental hydrostatic pressure shift. m so 0. B. which are somewhat different from the empirical suggestion of Guzzi et al. which is similar to that for GaAs.31. InP.org/japo/japcr. GaSb. Redistribution subject to AIP license or copyright.03 eV at 4 and 300 K.18 . a ratio of the deformation potentials d/b 2..3 which is in excellent agreement with the recent calculation by Pfeffer and Zawadzki.96. the first-principles calculations of Wei and Zunger42 show that the energy of the valenceband maximum increases as the unit cell volume decreases for a number of III–V semiconductors including GaAs.129 However.: Vurgaftman. The X-valley minimum is located at a wave vector k (0.5 eV.0 eV. which has been used with some success in the literature to determine the optical gain in GaAs quantum-well lasers.93. respectively. 2.aip. the split-off hole mass in GaAs has also been measured and calculated using a va* riety of approaches.132 The various values for the deformation potential b varied between 1.133..118 have derived intermediate values.127 suggest a small a v .4 0. Not sults of Monemar:133 many data are available on the temperature variation of the L – gap. was given in an extrapolated form by Logothetidis et al.139 We suggest the following temperature-dependence parameters.8. Vol.116 yielded E P 28.66 and 3. All of the recommended parameters for GaAs are compiled in Table I.. 2 2. On the wells125 produced an estimate of a c other hand.113. At Downloaded 05 Dec 2002 to 140. While its value is usually less critical to the device design and band structure computations. we recom7.137 Since direct measurements on AlAs are difficult owing to its rapid oxidation upon exposure to air. we will consider only deformation potentials for the valley.5824 J. The exciton energies corresponding to the -valley energy gap were measured by Monemar133 to be 3. The first electron-spin-resonance measurements of the interband matrix element in GaAs.121. 89..172m 0 .1 was recently derived from studies of acceptor-bound excitons in biaxially and uniaxially strained GaAs epilayers.06. The conduction-band deformation potential a c corresponds to the shift of the conduction band edge with applied strain.111 A composite value m so 0.3.13 and 3. whereas various analyses of mobility data3. which is within the experimental error of all accurate determinations and reproduces well the measured hole masses and warping:99.134 Similar values were obtained by Onton. In this review. The low-temperature X. Meyer. and 3 2. those results are contradicted by optical spectroscopy111 and Raman scattering112 studies of GaAs quantum wells as well as by fits to the shallow acceptor spectra. Parameters a lc Å E g eV meV/K K E X eV g (X) meV/K (X) K E L eV g (L) meV/K (L) K so eV * me m l* (L) m t* (L) * m DOS(L) m l* (X) m t* (X) * m DOS(X) 1 2 3 Appl.142 and Wrobel et al. However.2– 1.137 Electron effective masses for the X valley with an ellipsoidal constant-energy surface were calculated using the pseudopotential method.aip.141 A split-off gap of 0.275 eV was measured by Onton.9 6.0 4.981 0.org/japo/japcr.065–0. and Ram-Mohan 5825 Recommended values 5.16 2.79–7.3 0. These values are quite similar to the composite parameters suggested by Adachi.32–0.0635–0.88 2.80 7. see http://ojps.07 0 K . Phys. it is impossible to maintain a -valley electron population in thermal equilibrium.76– 2 6. Phys. Most of the experimental values are in fact extrapolations from AlGaAs see below .5–29. the latter was obtained from a fit to measurements on GaAs/AlGaAs quantum wells.104. the agreement between different calculations of the hole masses is rather good.1 eV(F 0.0 0.133–0.172 28.148 The band edge hole masses in AlAs are also not known with a great degree of precision.23 0. 89. Both theoretical106. which had only limited sensitivity to the AlAs parameters.9 0.151 For reasons that are discussed in some detail by Nakwaski.815 0. we recommend using the values 5.124m 0 was inferred from a fit to absorption data.8 1.7 .82.17 1.3 Very few determinations of the electron and hole deformation potentials in AlAs exist. and 3 1..3– 0.47 eV derived from the modelac Downloaded 05 Dec 2002 to 140.067 1.3 2.2.519 0. 2 0. Unfortunately. Meyer.94 0. Vol.56 1.8 1221 566 600 5 Range 1.435 300 K 0.76. 11.65325 3. but are less trustworthy than the extrapolations from AlGaAs146.104. For the longitudinal and transverse effective masses of the L valley.105.jsp .51–1.460 204 1.681–3.64 eV and a v 2.3.28m 0 for consistency with the E P value of 21. A slightly e lower value of 0.31. and also because.98 2.20 1.9–2. 0.7– ¯ ¯ ¯ 18.106 This mass falls midway between the recommendations by Pavesi and Guzzi134 and Adachi.05 0.93 0. The -valley electron effective mass in AlAs is difficult to determine for the same reasons that the band gaps are uncertain.15m 0 .148 which indicate m * 0.148 and measured by Faraday rotation149 and cyclotron resonance.35 eV is generally adopted.140. As for the case of GaAs. Various calculations and measurements have been compiled by Adachi3 and Nakwaski. a gap of 2. in contrast to GaAs.06 190–671 ¯ ¯ ¯ ¯ ¯ ¯ 0. No. Appl.104 As pointed out by Adachi.104 it appears that the recent results by Goiran et al. Rev.48) given by Lawaetz.152 represent the most reliable values available at present.J.36 0.067 300 K ¯ ¯ ¯ ¯ ¯ ¯ 6.605 204 0.145 employing resonant tunneling diodes with AlAs barriers give an effective mass comparable to that in GaAs.147 and theoretical calculations100. we adopt a value of 0. 1 June 2001 TABLE I.66– 2. we employ the calculated results of Hess et al.0 (T 300) * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa room temperature.148 and experimental111 sets of Luttinger parameters have been published.88 10 1.0754 0. Band structure parameters for GaAs. Redistribution subject to AIP license or copyright.1 3. and there is some evidence that the assumed value for m l was inconsistent with other data. the indirect determinations144.150 The former experiment in fact measured only the ratio between the longitudinal and transverse masses of 5.388 25.3 For the split-off hole mass. We propose a composite Luttinger parameter set based on an averaging of the heavy-hole and light-hole masses from various sources and recommendations by Nakwaski:104 1 3.5405 204 1.: Vurgaftman.341 0.85 6.143 indicated higher values.8.42.420–1.06 2.135 although the extrapolations by Aubel et al. 09–0.13 0.14 ¯ ¯ 2.64 2.68 ¯ ¯ ¯ 0.2.28 21.6611 2.jsp .023–0.41–0.37–0.90 10 (T 300) 3.0 ¯ ¯ ¯ Parameters a lc Å E g eV meV/K K E X eV g (X) meV/K (X) K E L eV g (L) meV/K (L) K so eV * me ( ) m l* (L) m t* (L) * m DOS(L) m l* (X) m t* (X) * m DOS(X) 1 2 3 TABLE II.4 eV. Rev.8.276 93 1.42 0.104 many of the results supporting such a mass were in fact performed at room temperature.15 0.41 0.39 0. most of the data agree reasonably well with the values given by Fang et al.03m 0 .6 1.9–3.0215m 0 174 and 0.25 ¯ ¯ 2.aip. which also agrees well with the more recent experiments of Zverev et al. The vast majority of experimental low-temperature energy gaps fall in the 0. implies 0.11 extrapolated from room temperature to 0 K.32 0.9 452.79–7. 1 June 2001 Appl.24–0.39 eV.160. 171 Although a few theoretical and experimental studies have obtained low-temperature masses as high as 0. Band structure parameters for AlAs.3 eV153 and d ellipsometry measurements of the heavy-light hole exciton splittings in AlGaAs epitaxial layers. and band-toband transitions.417 0. Phys. Meyer.95.04 0.08– 11.15 21.175 ¯ ¯ 0.16 0.026m 0 . The experimental spin-orbit splittings given in Landolt–Bornstein1 fall in the 0. We take an average of 0.022m 0 at 300 K.105. considerable care must be taken to measure the mass at the band edge rather than at the Fermi level.5–22. InAs InAs has assumed increasing importance in recent years as the electron quantum well material for InAs/GaSb/AlSbbased electronic154 and long-wavelength optoelectronic155 devices.181 these values were most likely influenced by the strong nonparabolicity.15 ¯ ¯ ¯ ¯ 3.00 1.90 0.:164 0.97 0. Phys.29 1.7– 5.433 0.88 2.5826 J. Redistribution subject to AIP license or copyright.2– 2.00– 5.1 0.410–0. Since there are almost no credible reports of an effective mass lower than 0. whereas further experiments are necessary to confirm the latter.14 21.06–0.59 5.156–159 although somewhat higher values have also been reported.026m 0 which. and Ram-Mohan TABLE III.46 0.48 1. and band structure calculations.64 0.64 1.9 5 Range ¯ 0. Appl. cyclotron resonance.0 8.0215m 0 at any temperature. magnetoabsorption.9–2.70 530 2.276 meV/K and 93 K. since no determinations appear to be available.74 10 (T 300) 0.0583 2. While a value near the bottom of the reported range is usually recommended since the band edge mass represents a lower limit on the measured quantity.163–165 Although there is considerable variation in the proposed Varshni parameters.82 1. C.5 9.605 204 0.129 For the shear deformation potentials.76 0. 89. No.276 93 1.35–2.180 The majority of results at both low and high temperatures fall between 0.099 0. Parameters a lc Å E g eV meV/K K E X eV g (X) meV/K (X) K E L eV g (L) meV/K (L) K so eV * me ( ) m l* (L) m t* (L) m l* (X) m t* (X) 1 2 3 Recommended values 5.28 0.6 395. accounting for the shift of the energy gap.57 ¯ ¯ ¯ ¯ * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa solid formalism by Van de Walle.885 530 2.4 1250 534 542 5 Recommended values 6. see http://ojps.168–179 Owing to the strong conduction-band nonparabolicity in this narrow-gap semiconductor.33 5. All of the recommended parameters for AlAs are compiled in Table II.47 2.161 We adopt the value 0.104.15 1.64 20.27. Band structure parameters for InAs. Energies for the L and X conduction-band minima in InAs have not been studied experimentally.5 2.05 0.08 1.104. The temperature dependence of the band gap has also been reported by several authors. 11.104 our recommended lowtemperature value is 0. The temperature dependences of the indirect gaps are taken to be identical to the direct gap.8 3.133 0.20 1.2 0.162 in which it was possible to separate shallow impurity.417 eV that was obtained from recent measurements on a high-purity InAs sample. The small 1% polaronic correction is well within the experimental uncer- Downloaded 05 Dec 2002 to 140. Range ¯ 2.450 ¯ ¯ ¯ ¯ ¯ 1. Vol. Our recommended values are based on the suggestions by Adachi166 and Levinshtein et al.13–1. exciton.03 ¯ ¯ ¯ ¯ ¯ ¯ 6.05 0.9 2.3 3.22 3.7– 6.42–4.681–3.31 0.23 1.23–2.6 832.2 0– 2.: Vurgaftman.162.102.42 eV range.67–1.37–0.275–0.53 ¯ ¯ 0.276 93 0.7 1.24 0.2 8– 2.026 0.90 ¯ 5.57 0.17–1. 101.41 eV range. 3 The former is supported by 2.167 The electron effective mass in InAs has been determined by magnetophonon resonance..31.4– 3. the following values are suggested: b 3.org/japo/japcr. although the measurements are complicated by the camel’s back structure that makes the longitudinal mass highly nonparabolic. This nonparabolicity must be accounted for in any treatment of the density of electron states in GaP.11 By employing typical experimental m l /m t ratios for related III–V materials such as GaAs and GaSb corresponding longitudinal and transverse masses have been estimated and listed in Table III. Vol.159.9 eV.122 and Wei and Zunger.25.2 eV using a rather high theoretical estimate for the -valley effective mass in GaP.200 to be a 9. Meyer.5.23– 0. there is no a priori reason that an interband matrix element in GaP so much different from that in GaAs is unreasonable.45190 suggest an effective mass of 0.137. 1 June 2001 Appl. GaP Nitrogen-doped GaP has for a long time been used as the active material for visible light-emitting diodes LEDs . Phys.106.. 2 8.8.187 The most commonly employed Varshni parameters. The values of 1 and 3 given in that reference are very close to a previous determination of Pidgeon et al. these imply a 2.159 which also assumed a smaller low-temperature electron mass (0. and is in fact more crucial than the precise value of m l far above the camel’s back. We recommend his valence-band deformation potential.101 We use a slightly higher value of 0.129 who estimates that most of the energy shift occurs in the conduction band.101.157 A number of theoretical works104.200 A number of theoretical and experi- Downloaded 05 Dec 2002 to 140.25m 0 . which is in good agreement with tight-binding calculations by Shen and Fan. Redistribution subject to AIP license or copyright.5 eV has gained acceptance. 193 We have taken longitudinal and transverse effective masses for the L-valley minimum from Levinshtein et al.0). Effective masses of 5 – 7m 0 have been reported for the bottom of the camel’s back.189 An exciton binding energy of 20 meV is added to obtain the energy for interband transitions.122 Another set of deformation potentials has been calculated by Wang et al. Van de Walle129 estimated that the valence-band shift is small compared with the conduction-band shift.42 The shear deformation potentials adopted from Landolt–Bornstein1 are in good agreement with the calculations of Blacha et al. Lawaetz obtained E P 22.08 eV.org/japo/japcr.11 The Luttinger parameters for GaP were first calculated by Lawaetz.96 although higher values have also been reported. The hydrostatic deformation potential for the direct energy gap in GaP was measured by Mathieu et al.90. 195 although the present consensus puts the value at 0.194 Estimates for the transverse mass l range from 0.4 although its temperature dependence has not been determined. Phys.31.338–2.4 eV. 1 We take the conduction and valence-band deformation potentials of Van de Walle. 89. Street and Senske also determined Luttinger parameters from acceptor binding energies.86–2. Rev.116 more recently E P 21.14m 0 in InAs. with the X-valley minimum at k (0. although the precise value is not well known.13m 0 for GaP. Somewhat different values were calculated by Blacha et al. so that a calculated exciton binding energy which presumably has a weak temperature dependence must be added to the experimental results.106 Subsequent cyclotron resonance experiments refined the masses along the 111 196–198 and 100 198 directions. Almuch higher E P of 31.87 eV from absorption measurements.188 The L-valley minimum is located 0. see http://ojps.191 There have been a number of experimental determinations192 of the X-valley longitudinal and transverse masses.04.25m 0 in order to be consistent with the interband matrix element. Nakwaski104 concludes that further experimental work is needed to resolve the matter.2 are in excellent agreement with piezomodulation spectroscopy results by Auvergne et al.J.1. Whereas early studies suggested a value of 22.aip.24m 0 was calculated by Lawaetz106 and by Krijn. Surveying the data available to date. Noting the considerable uncertainty involved in this estimate.0.106 The diamagnetic shifts measured in magnetoluminescence experiments on GaAs1 x Px alloys with x 0. with the conduction-band contribution corrected to reproduce the result of Mathieu et al. and may be considered the most reliable: 1 4. 2 0. more accurate determinations of the interband matrix element in GaAsP have been published.86 Unfortunately.106.105. and Ram-Mohan 5827 tainty in this case. at present there exist little experimental data from which to judge the relative merits of the above calculations.184 We recommend this value. reported in Casey and Panish.350 eV have been reported.024m 0 ).2.193 whereas m * 2m 0 high above. Appl.0 eV.133. we suggest the following composite set: 1 20. 5 Indirect X – energy gaps of 2.2 eV. 11.185 GaP is the only indirect-gap with X – L – ordering of the conduction-band minima binary semiconductor we will consider that does not contain Al.187 The main uncertainty in determining the various energy gaps for GaP is that excitonic rather than band-to-band absorption lines typically dominate. Experimental studies183 have suggested a split-off mass of 0. The interband matrix element in InAs appears to have been determined relatively accurately owing to the large g factor in this narrow-gap semiconductor.190. and 3 9. GaP has a small spin-orbit splitting of 0..182 predict a much higher degree of anisotropy in the valence band. which leads to F though such an extrapolation from data on As-rich alloys is somewhat questionable.159 those parameters appear to disagree with the heavy-hole masses for various directions given in the same reference. A split-off hole mass of 0. No.106 Recently.186. This is somewhat larger than the effect predicted by other workers. and 3 1. The hydrostatic deformation potential in InAs was determined to be a 6.37 eV above the X valley.199 Those parameters as corrected in Landolt–Bornstein1 are in reasonably good agreement with cyclotron resonance results. The situation is further complicated by the camel’s back structure of the X-valley conductionband minimum. The density-of-states effective masses for the X and L valleys are taken from Levinshtein et al.49.95. The low-temperature value for the direct excitonic band gap was found to be 2.191 By analogy with the case of GaAs discussed above.19m 0 182 to 0.189 The electron effective mass in the valley is estimated from theory to be 0. All of the recommended parameters for InAs are compiled in Table III.jsp .275m 0 .09m 0 . which leads to F 2. The band structure is somewhat similar to that of AlAs. Although Luttinger parameters for InAs were determined experimentally by Kanskaya et al.: Vurgaftman.05. 11. D. 10 since it serves as the substrate for most optoelectronic devices operating at the communications wavelength of 1.155–0. Composite values for the Luttinger parameters and the split-off hole mass have been taken from various calculations.5771 372 2.4 0– 2.74 ¯ a c eV 5.31.205 obtained better agreement with photoluminescence results for AlP/ GaP heterostructures using a somewhat smaller X-valley mass.06–0.122 No values for the shear deformation potential d appear to have been reported.63 3. and Ram-Mohan TABLE V. A -valley mass of 0.6 eV.202 The direct gap of AlP was measured by Monemar133 to be 3.2 1.2– 2.4– 4. 1 June 2001 Appl.7– 6.04 ¯ 6.06–0. Parameters a lc Å E g eV E X eV g (X) meV/K (X) K E L eV g (L) meV/K (L) K so eV * me ( ) m l* (X) m t* (X) m l* (L) m t* (L) 1 2 3 Recommended values 5.350 ¯ ¯ ¯ ¯ ¯ 0. We suggest the following composite values: b 1.92 10 (T 300) 3.86–2. InP InP is a direct-gap semiconductor of great technological significance.155 0. It is unclear whether the conductionband minima follow the X – – L 201 or X – L – 182 ordering.68–3.62 77 K . Nevertheless.6 1405 620.30 0.7 ¯ E P eV F 0.275 ¯ ¯ 4.1 1.49–2. Band structure parameters for AlP.22m 0 was calculated using the augmented spherical wave approach.56 300 K E g eV meV/K 0.5828 J.6 eV and d 4.25 31. The indirect energy gap of 2. Range ¯ 2. A similar value has been obtained by extrapolation from AlGaP alloys by Alferov et al. 11.66– 3. F.2 0.0 ¯ ¯ ¯ Parameters Recommended values 5 TABLE IV.jsp . which are generally in good agreement with each other. We have adjusted the theoretical longitudinal and transverse masses by the same factor to conform to that fitting.206 We select b accordance with the calculations of O’Reilly130 and Krijn.0 3.4672 2.129 although a slight correction was found to be necessary when energy level alignments in a GaInP/ 1. Phys.22 ¯ me ( ) 2. see http://ojps.67m 0 and m * l t 0.09–0. Meyer. Almost no experimental data are available on the effective masses in AlP.6 ¯ c 11 GPa 1330 ¯ c 12 GPa 630 ¯ c 44 GPa 615 ¯ mental values have been reported130.65 ¯ VBO eV 1.65) is given by Lawaetz. Band structure parameters for GaP.101.54– 5. since no actual measurements of the L-valley position appear to have been performed.6 eV derived for GaP see previous subsection . while Bour et al. Rev.13 0.7 1.07 eV.93 0. Redistribution subject to AIP license or copyright. although further studies are clearly needed to confirm our projections.: Vurgaftman.05 0.1 d eV 4.34 m so 17.19–0.106. Vol.7 5.04–4. with the largest direct gap of the III–V compound semiconductors.338–2. In the absence of other information.4 2.212m 0 for the X valley.aip.67 m l* (X) 0.08–0. Phys. All of the band structure parameters for AlP are collected in Table V. we recommend the value of d 4.0– 3.27 8. Downloaded 05 Dec 2002 to 140. on the order of 0. 89.105.9 2.318 ¯ (L) K 588 ¯ 0.17 2–7 0.53 E X eV g (X) meV/K 0.56 eV.3 5 Range * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa a lc Å ¯ 5.106 The hydrostatic deformation potentials were calculated by Van de Walle.7 a v eV 3.182 An interband matrix element of 17.20 ¯ ¯ 0.2–31.203 obtained an extrapolation to 300 K of 3. All of the recommended parameters for GaP are compiled in Table IV.55 m.886 0.35 ¯ 1 0.23–0.3 703.25 22.5 eV and its temperature dependence are given in Casey and Panish2 with appropriate corrections to the original determinations.1081 1-coth(164/T) 2.253 camel back 1. Numerous studies of the band structure parameters for InP and its alloys have been carried out. No.13 2.204 although the actual value has apparently never been measured. E. AlP AlP.org/japo/japcr.101.52 2.5771 ¯ K 372 ¯ 2.35 0.15 b eV 1. although Issiki et al.07 0.0 camel back 0.200 for the shear deformation potentials.212 m t* (X) 3.71 ¯ 2 1.57 ¯ E L eV g (L) meV/K 0.49 2.3– 18.101 Another ab initio calculation182 yielded m * 3.62 eV at 77 K.63 eV at 4 K and 3.29–0.5771 372 0.68 2.4–7. Appl.318 ¯ (X) K 588 ¯ 3. is undoubtedly the most ‘‘exotic’’ and least studied.4505 2. The spin-orbit splitting in AlP should be small.6 4.04 1.72 0.15 4.07 so eV * 0.187.3 0.5 eV in AlGaInP laser structure were fit.5 1.92 10 (T 300) 2.895 2.23 ¯ 3 * 0.101 although higher values have been computed by Blacha et al. 3. The required correction of these results due to the exciton binding energy is unclear.. the essential characteristics have been known for some time.7 eV (F 0.8.08 0. 1.1.0 5.0 ¯ ¯ ¯ * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa Lawaetz106 and Gorczyca et al.aip. which is slightly smaller than the typically recommended values of 0. GaSb GaSb is often referred to an intermediate-gap semiconductor. 2 1. The difference between the results of Hermann and Weisbuch116 and Shantharama et al.213 although there is some controversy on this point and a different set of parameters was given by Levinshtein et al.0795 0.21 16. The resulting set of 1 5.420–1. magnetophonon resonance.08 1.1.084 0.219.223 This discrepancy is easily resolved once it is realized that the majority of references did not consider remote-band effects on the electron mass.12 ¯ ¯ 0.27 Casey and Panish.76 0.081m 0 . we obtain m * (T 0) e 0.173.363 162 0.0 1011 561 456 5 Range ¯ 1.7 eV above the -valley minimum.82–2. its gap of 0.210 When T .0 4.106 In arriving at our composite parameters.10 The effective masses for the L and X valleys are taken from Pitt. The temperature dependence is unclear.10 is in good agreement with all of the most reliable experimental results. Redistribution subject to AIP license or copyright. Appl.201 The – X separation has been studied more closely.37 meV/K.423 eV.2– 5.8 eV is neither as wide as in GaAs Downloaded 05 Dec 2002 to 140.32–0. using hot-carrier photoluminescence. and Ram-Mohan TABLE VI.1 1.7 1. Lautenschlager et al.207 and magnetoabsorption. with the most reliable values favoring an approximately 0.4– 7.7 10 4 T 2.79 10 (T 300) 1. We adopt the former value of E P 20.48–2.96. G.0 0. 97. We recommend using the Casey and Panish temperature dependence with a corrected value of E g at T 0 if one’s interest is primarily in the temperature range from 0 K to somewhat above room temperature.226 the piezomodulated photovoltaic effect.108–0.J.org/japo/japcr.230 All of the band structure parameters for InP are collected in Table VI.08 1.207. and magnetospectroscopy of donor transitions.108 eV by wavelengthmodulated reflection214 and photovoltaic effect207 measurements. with most other reports agreeing to within a few meV.6–20.215–225 if early and ambiguous determinations are excluded and the polaron correction is estimated to retrieve the bare mass.6 eV. a number of other experimental determinations have favored a value close to 16.31 0.: Vurgaftman.21m 0 .0– 2. In combination with the reported direct-gap deformation potential of 6.7 0.077– 0.212 forms are more appropriate at temperatures well above 300 K.101. Phys.31 ¯ 3.081m 0 . and 3 2.363 162 2.21 20.6 2.4–0. and Pavesi et al.04 eV . 11.080– 0. with dE – X /dT 0.88 4.4– 21 0. the gap decreases linearly with temperature and use of the Varshni expression is not necessary i.08.e. see http://ojps.068– 0. the binding energy of 5 meV has been added to the spectral position of the resonance. Recommended values 5.25–0. Phys.014 0.4 The most reliable values for the conduction-band deformation potential are probably those of Nolte et al. The spin-orbit splitting was determined as so 0. Averaging the e results from different groups.229 and theoretical calculations have also been performed. focused primarily on fitting higher-temperature band gaps up to 870 K.94 6... Parameters a lc Å E g eV meV/K K E X eV g E L eV g (L) meV/K (L) K so eV * me ( ) * m DOS(L) * m DOS(X) 1 2 3 5829 Rochon and Fortin207 found the low-temperature direct band gap to be 1.– 1. i.1 these values imply a rather small shift in the valence band.116 However.198 magnetoreflectance.117. did not use the Varshni functional form..118 calculated the interband matrix element E P in InP to be close to 20 eV. There are greater uncertainties in the positions of the X-valley and L-valley conduction-band minima in InP. which implies F 1. Rev.207 The temperature dependence of the direct band gap has been reported by Varshni.31 the latter result would imply F 0 .2 Lautenschlager et al.7 eV proposed by Hermann and Weisbuch.. While values have spanned the range 0..28 0.227 Furthermore.6 eV separation. Meyer.084m 0 .211 and Hang et al.108 0. although a more detailed examination of this issue is called for in view of the large divergence between the two results. The shear deformation potentials b and d have been determined by Camassel et al.1 Since exciton rather than interband transitions are usually observed in such absorption measurements.207. No.228.218 the reasonable range for m * (T 0) narrows to 0. The L-valley minimum is believed to lie 0.88 5. The -valley electron effective mass in InP has been investigated in great detail by cyclotron resonance. the valence-band warping was accurately determined by Alekseev et al.47 0.31. and Hang et al.5 eV.98.068–0.60.e.06 190–671 1.17–0.61–6.209 and Pavesi et al.94–2.13 0.1 and the different works have been compared in detail.96 has already been discussed in connection with the interband matrix element for GaAs.7 for InP. However. Vol.11. the Lautenschlager et al.384– 3. The split-off hole mass was measured by Rochon and Fortin207 to be 0.108.432 0.109.10 0.213 The inferred low-temperature value is 0.39 1.jsp .99.105. 89.8.4. There is a great deal of variation in the experimental and theoretical deformation potentials for InP as compiled by Adachi.96 eV.47 0.51–1.60 2.208 Hang et al.8697 2.4236 0.127 7 eV and Van de Walle129 5.214 and are in good agreement with exciton reflectance measurements. we follow the procedure of averaging the reported values for heavy-hole and light-hole masses along the 100 and 111 directions. Band structure parameters for InP.11 Luttinger parameters for InP have been measured using cyclotron resonance.0795m 0 . 0 .62–2. 1 June 2001 Appl. This result is in good agreement with the value of 20. 245 Effective masses for the X valley are taken from Levinshtein et al. 11. Band structure parameters for GaSb. The four results that fit the data to room temperature are in excellent agreement with each other.6 0. The temperature dependence of the L-valley minimum is known to be stronger than that of the valley. Somewhat higher values for the effective mass have been calculated theoretically.5830 J.1 and piezoresistance. Once again.106.116 we determine a composite value E P 27. Since GaSb forms an increasingly important component of mid-infrared optoelectronic devices.0 1.875 0. H.0 eV. Appl.11 The Luttinger parameters for GaSb have been determined using a number of experimental and theoretical approaches.: Vurgaftman. A large nont l parabolicity at the L point has also been reported.8.100–106 Owing to the small – L energy separation in GaSb and the much lower density of states at the minimum. which are weighted toward the more recent experiments.233 Bellani et al.243.4.597 140 0.239–243 Here the band structure is more sensitive to the adopted value of E P than in most materials.810 eV at 16 K.aip.76 0.4–6.1 with a value of 0.10m 0 and m * 1.243 An average value for the direct-gap deformation potential a 8..233.232 Correcting for the exciton binding energy and extrapolating the temperature.31.475 94 0. 231 . the L valley in GaSb is only 0.039 1. Therefore. appear to be the most reliable. Vol. but are also quite close to the ones typically used in the literature. 232 Ghezzi et al.812 eV.042 1.871–0.7 884.246.03 7.239–245 which produced low-temperature values in the rather narrow range of 0.239.1–1.238 although there was some spread in the earlier reports. see http://ojps. which is quite close to the results of Reine et al.239 The interband matrix element for GaSb has been estimated by several workers.245 Faraday rotation.749–0. Recommended values 6. Averaging produces a bare effective mass of m * e 0.247 On the basis of these results. have recently published a comprehensive review of the material and structural properties of GaSb. AlSb AlSb is an indirect-gap semiconductor with a lattice constant only slightly larger than that of GaSb.3 eV was determined for GaSb by uniaxial stress and transmission experiments.1 The spin-orbit splitting was measured by a number of techniques.105. which are complicated by the relatively strong conduction-band nonparabolicity in GaSb.1. Redistribution subject to AIP license or copyright. care must be taken to separate results for the polaron and bare effective masses.63.14 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa and 3 6. This composite implies F 1.2 402. 89. Phys. Effective masses for those states were measured by cyclotron resonance.12 27.244. which is within the experimental uncertainty of nearly all the reports.jsp . In recent years it Downloaded 05 Dec 2002 to 140.8 2.242. because the energy gap is nearly equal to the splitoff gap.239 and Roth and Fortin. Dutta et al.82 0.6 432.811–0.231.1 We adopt the Van de Walle129 suggestion for the valence-band potential of a v 0.7 6.12–1.233 Varshni parameters for the direct gap have been given by Casey and Panish.235 numerical values used in that work are given in Ref.11.236 The position and temperature dependence of the X-valley minimum were determined by Lee and Woolley. Parameters a lc Å E g eV meV/K K E X eV g (X) meV/K (X) K E L eV g (L) meV/K (L) K so eV * me ( ) m l* (L) m t* (L) m l* (X) m t* (X) 1 2 3 and InP nor as narrow as in InAs and InSb. which were oband modulation tained by electroreflectance235 236 spectroscopy.0959 4. instead of using the result of Hermann and Weisbuch.039–0.63 0. as summarized in Landolt–Bornstein.. we form composite values of m * 0.042m 0 .175. At low temperatures.22 13.0 4. and adjust his a c slightly to produce the consistent value of a.234 and Joullie et al.2 Wu and Chen (0 T 215 K).0 0.039m 0 at 0 K.1 All of the band structure parameters for GaSb are collected in Table VII.8 eV. which agrees to within 1 meV with earlier determinations1 and also with the recent transmission measurements of Ghezzi et al.3m 0 .org/japo/japcr.2 5 Range ¯ 0.76 eV236 being commonly accepted. 1 June 2001 Appl.10 1.4 0.72 10 (T 300) 0. Rev.4 4.92 ¯ ¯ 0. although as is often the case the polaron correction is no greater than the experimental uncertainty.812 0.116. we suggest the composite values 1 13.085–0. at room temperature a significant fraction of the electrons occupy L-valley states.11.3 4. we obtain E g (T 0) 0.240.248 The split-off hole mass in GaSb was measured by Reine et al. and Ram-Mohan TABLE VII.12–0.1 On the basis of these results.813 0.11. The -valley band-edge electron mass in GaSb has been studied by a variety of techniques.100 meV higher than the valley. No.417 140 1.0. 2 4.236.5 0.51 0. and recommended values have been obtained by simply averaging the Varshni parameters and .063–0. There is good agreement between various measurements of the shear deformation potentials in GaSb.231 Photoluminescence measurements on high-purity layers grown by liquid-phase epitaxy yielded a free exciton transition energy of 0.141 0.5 3–5. The smallness of the spread is rather surprising in consideration of the indirect nature of many of the determinations.235.7.039– 0. Phys.237 The values near the bottom of that range.14 ¯ ¯ 11–14.108–0. Meyer.155 its various alloys have been investigated in some detail..3 0.453 10–186 1.242 ¯ ¯ 0. .18 . and a T dependence similar to that in GaSb.161.259–264 While there is a broad consensus that E g (T 0) 0.4 1.166 The spin- orbit splitting energy was measured to be 0. On the other hand.260. 11.2 eV.19 1.1 along with composite Varshni parameters.5.183.31.32 meV/K and 170 K.70 ¯ ¯ 2.68–1. several different sets of Varshni parameters have been proposed.J.254 there appear to be no definitive measurements.171.118. The interband matrix element is taken from Lawaetz.329 ¯ ¯ ¯ 0. although it could be argued that both parameters have a high degree of uncertainty.236 which falls near the data compiled in Landolt–Bornstein. Little information is available on the hole masses in AlSb.164. and m hh(111). Phys.60 10 (T 300) 2. Appl.123 5. The primary technological importance of InSb arises from mid-infrared optoelectronics applications.260.258 Numerous studies of the fundamental energy gap and its temperature dependence have been conducted over the last 3 decades.11.276–282 By averaging the values for * * 1 .5.58 140 0. m hh(001). 106.42 140 1.357 0.329 0.106 and the split-off mass is taken to be consistent with Eq.235 eV.164.676 0.260 Our composite interband matrix element for InSb is 23.282.168.253.11m 0 .39 ¯ ¯ 1.236 spectroscopic ellipsometry by Zollner et al.: Vurgaftman. The indirect gap associated with the lowest X valley was investigated by Sirota and Lukomskii.255 We form our composite values of the Luttinger parameters on the basis of theoretical studies101.182.29 1.265–275 A bare effective mass of 0.. we take the valence-band hydrostatic deformation potential calculated by Van de Walle.168. we deduce the composite set: 34.25 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa I.35–2.org/japo/japcr. Recommended values 6.236 It has been suggested1 that early estimates of the band gap needed to be revised.1. Phys.09–0.105.256 Once again.0135m 0 at 0 K is in good agreement with a majority of the investigations.39 eV at liquid-helium temperature.243. 3 16.250 We employ the resulting lowtemperature value given in Landolt–Bornstein. and Ram-Mohan TABLE VIII.2. since the exciton binding energy is 19 meV252 instead of the assumed value of 10 meV. All of the band structure parameters for AlSb are collected in Table VIII.265.7 0.10– 0. Vol.260 Experimental and theoretical studies have found bandedge electron masses for InSb in the range 0.jsp . Band structure parameters for AlSb.2. with the L valley only 60–90 meV above the valley236 also quite similar to GaSb .81–0.249 and also using other methods.11 We have found no explicit theoretical or experimental results for the X-valley effective masses.1355 2.82 eV. The tain the composite set: L..75–2. 1 June 2001 Appl.and X-valley energies are taken from Adachi. 89.22 18.3 876.265.696 0.267. The spin-orbit splitting is taken from Alibert et al.106.41 4. 95.. Levinshtein et al.129 and make the rest of the results consistent with what appears to be the sole experimental determination.35–2.23 1. Parameters a lc Å E g eV meV/K K E X eV g (X) meV/K (X) K E L eV g (L) meV/K (L) K so eV * me ( ) m l* (L) m t* (L) m l* (X) m t* (X) 1 2 3 5831 has found considerable use as the barrier material in highmobility electronic154 and long-wavelength optoelectronic155 devices.015m 0 .269.160. The direct gap in AlSb was measured using modulation spectroscopy by Alibert et al. A wide variety of experimental and theoretical techniques such as magnetophonon resonance and other magneto-optical approaches have been employed to investigate the valence-band structure of InSb.8. Redistribution subject to AIP license or copyright. the light-hole effective mass in InSb is only slightly larger than the electron mass. No. These parameters are in good 1 agreement with the majority of the values found in the cited references.1 407.14 1.01–1. The deformation potentials in AlSb were measured at 77 K using a wavelength modulation technique.262.. 2 15.56 0.aip.283 The split-off hole mass is estimated to be 0.39 140 2. 2.284 A slightly higher value was deduced by Downloaded 05 Dec 2002 to 140.386 0. For many years it has been a touchstone for band structure computational methods. although in principle it should be possible to extract them from pseudopotential calculations that have already been performed for bulk InSb.254 in conjunction with literature values for the hole masses.18 ¯ ¯ ¯ ¯ 4.106.263. InSb InSb is the III–V binary semiconductor with the smallest band gap.8.250 Mathieu et al.18 1.264. It is likely that the X valley in AlSb exhibits a camel’s back structure by analogy with AlAs and GaP.168.259.1 Bulk AlSb samples were found to exhibit a gap of 2.012– 0.327–2. see http://ojps. Owing to the narrow energy gap.243.6 5 Range ¯ 2. The conduction-band minima ordering is believed to be the same as in GaP and AlAs: X – L – .97 0.1 The electron mass in the valley was measured using hot-electron luminescence.269.35 4. quotes a density-of-states effective mass of 0. Meyer.106.265 Averaging parameters from the most reliable references.266.253 While the L-valley and X-valley effective masses have been calculated.64 0. little information on the effective masses in the indirect valleys is available.25m 0 for the L valley.9 434.251 and Alibert et al.5 1.106.15–5. we ob0. Rev.1.257 partly because of the strong band mixing and nonparabolicity that result from the small gap.89 1. : Vurgaftman.285.63 0.289 The status of GaN work in the 1970’s was summarized in two reviews290.48 10 0.7 684.1. Vol.8–0.129 the valence-band deformation potential is rather small by analogy with the other III–V materials. 299 Petalas et al.4–18. Shan et al.306.290 All of these considerations contribute to the rather large experimental uncertainty in the bare direct energy gap at low temperatures. However.5 16. GaN and other nitrides experience a phase transition to the rocksalt lattice structure..508 meV/K and 996 K.156 meV/K and 738– 1187 K from absorption measurements on samples grown by MBE and metalorganic chemical vapor deposition.3 eV. as well as higherorder A(2s.832 meV/K and 836 K. While the signs of his Varshni coefficients are opposite to all of the other materials considered in this review.243. the wurtzite phase is implied. since what is usually measured at cryogenic temperatures are the energies for various pronounced exciton transitions. Numerous other PL and absorption studies were published in the 1990s. The temperature dependence of the GaN energy gap was first reported by Monemar.296.116 possibly due to an overestimate of the effective g factor.299–308 which broadened the range of reported A-exciton transition energies at 0 K to 3.1 15.2p) exciton transitions. We therefore average the most reliable experimental binding energies deduced from the difference between the ground-state and first-excited-state energies of the A exciton.939– 1. GaN GaN is a wide-gap semiconductor that usually crystallizes in the wurtzite lattice also known as hexagonal or -GaN . For example. Teisseyre et al.1 For a comprehensive recent review of the growth. which has led to its successful application in blue lasers and LEDs.aip.566– 1. which implies 3. and C exciton types related to the three valence bands can be resolved.11 23.288 If the crystal structure of a nitride semiconductor is not stated in what follows.316 obtained 700 K based on PL results. whereas the zinc blende phase is always explicitly specified.23 is close to other determinations.293 It has been known since the early 1970’s that the energy gap in wurtzite GaN is about 3. and Ram-Mohan TABLE IX. Rev. which are still the most frequently quoted in the nitride device literature.296.5 13.5 0.08 meV/K and 745– 772 K. 1 June 2001 Appl. For the temperature variation of the A exciton resonance.93 0. Meyer.732 meV/K and lipsometry. Early measurements of the temperature-dependent direct gap in wurtzite GaN.298.5 311.4–38.32 170 0. we refer the reader to the article by Jain et al. 89. a precise determination from luminescence experiments is not straightforward.291 as well as in Landolt-Bornstein.235 0.299–0.0 and d 4.jsp . and various properties of nitride materials.484 eV is obtained. see http://ojps.25 34.303.260 Our corresponding F parameter 0.298 Those experiments yielded a free-A-exciton transition energy of 3. Phys. Wurtzite GaN Range ¯ ¯ 0.7. Under very high pressure.1.474–3.294.012–0. an exciton transition energy of 3.6 106–500 ¯ ¯ 0. such as neutral donors.302.7 373. The identification of these closely spaced resonances is nontrivial. reported 0.858 meV/K using spectroscopic el0. Phys.31.307 led to 1.23 0 6.8 15. Redistribution subject to AIP license or copyright. under certain conditions zinc blende GaN sometimes referred to as cubic or -GaN can also be grown on zinc blende substrates under certain conditions.8.302.507 eV for the zerotemperature energy gap. Experimental binding energies for the A exciton range from 18 to 28 meV. GaN is a direct-gap material.28 meV/K and 1190 K Downloaded 05 Dec 2002 to 140.4794 3.1 5 (T 300) * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa Hermann and Weisbuch. Manasreh304 reported 0.org/japo/japcr.310–312 An accurate theoretical determination313 is out of reach at present owing to the large uncertainty in the reduced mass primarily associated with the poorly known hole effective mass .36 2.297. Salvador et al. 11.314 obtained 0.303.015 ¯ 32.298 who obtained 0. we take an average value of 7.286 For the total hydrostatic deformation potential. at very low temperatures.0135 0.315 fixed 700 K and found 0.243.3 0. Somewhat lower values for E P are also encountered in the literature. Band structures parameters for InSb. There appears to be a consensus on values for the shear deformation potentials in InSb: b 2.507 eV.105. Parameters a lc Å E g eV meV/K K E X eV g E L eV g so eV * me ( ) * m DOS(L) 1 2 3 1.310.296 The situation is further complicated by the excitons bound to various impurities.285–287 All of the recommended band structure parameters for InSb are given in Table IX. Appl. A review of the physical properties of GaN and other group-III nitride semiconductors up to 1994 was edited by Edgar.81 0.311 This gives 23 meV for the exciton binding energy.94 0. the lowest-order A. characterization.5 eV.295 However. J.308. B.15–18 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ Recommended values 6. were performed by Monemar.5832 J.9 0.292 Unlike any of the non-nitride wide-gap III–V semiconductors discussed above. From optical absorption measurements on bulk and epitaxial layers grown on sapphire. The contactless electroreflectance study of Li et al. According to the model-solid calculations of Van de Walle.306.475 eV and an estimate of 28 meV for the binding energy. It has been suggested that this spread is due to variations of the strain conditions present in the different experiments.296.284 The deformation potentials in InSb have been studied by various optical and electrical techniques.0 4.309 If we average all of the available experimental values. a large number of subsequent studies have derived less anomalous results. No. we do not recommended values for the wurtzite forms of the nitride materials.334 obtained similar results using infrared-reflectivity and Halleffect measurements. Other early values may be found in the reviews from the 1970s.317 suggested 0. although a slight anisotropy resulting from the reduced lattice symmetry is not ruled out.28m 0 . an infrared ellipsometric study by Kasic et al. yielded a hole mass of 1.2m 0 . these parameters may also be recast in terms of the Luttinger parameters familiar from the case of the zinc blende materials. Finally.1m 0 – 0.008m 0 along the two axes was obtained.2% . 4 b . Redistribution subject to AIP license or copyright. 308.346 Finally. Rev.291. Meyer et al.4m 0 for p-doped GaN.18m 0 to 0. whereas the latter report apparently corrected for that effect. 301 Reynolds et al.27m 0 from the Faraday rotation.909 meV/K and 830 K. Phys. Appl. obtained an isotropically averaged heavy-hole mass of 0.325 In order to derive the various parameters needed to characterize the valence band of a wurtzite material. Factors contributing to this uncertainty include strong nonparabolicity near the valence-band edge and the close proximity of heavy-. and Ram-Mohan 5833 for the A exciton transition energy. data and derived cr 16 meV and so 12 meV. we take 2 3 so/3 and 1 cr . A slightly higher dressed mass of 0. the excess-carrier lifetime measurements of Im et al..333 Perlin et al.jsp . 11. The bottom of the conduction band in GaN is well approximated by a parabolic dispersion relation. It was suggested338 that strain effects may have to some extent compromised the masses obtained by some of the other studies. An even smaller mass of 0. The experimental information presently available is sufficient only to suggest an approximate band-edge effective mass for the holes. 325 From a similar approach.31.228 0.222m 0 . Meyer. for which only the spin-orbit splitting must be specified. respectively.316 On the other hand..23m 0 from Shubnikov–de Haas oscillations in the twodimensional 2D electron gas at a GaN/AlGaN heterojunction. one must resort to theoretical projections. we averaged all of the reported values with the exception of those from the first-principles theory.3m 0 was obtained by Salvador et al. although various estimates of the critical points are available from theory and experiment.006m 0 and 0. and are much lower than Downloaded 05 Dec 2002 to 140.2m 0 .8m 0 . To obtain our recommended set of cr 19 meV and so 14 meV. 89.. see http://ojps.20m 0 from plasma reflection measurements. but tend to overestimate the crystalfield splitting.74 meV/K and 600 K based on exciton luminescence spectra.: Vurgaftman. and derived a bare mass of 0. Vol.9– 1. and Sidorov et al. indicated a very heavy hole mass of 2.54m 0 from luminescence data. Drechsler et al.335 and Knap et al. yielded the values cr 10 meV and so 18 meV.J. 1 June 2001 Appl.aip. The latter result has the smallest error bounds quoted in the literature 0.311 Using a more precise description of the strain variation of the valence band-edge energies.331 and Witowski et al. 305 Merz et al. obtained cr 25 meV and so 17 meV from a fit of their exciton data. which are in good agreement with the parameters suggested by absorption measurements on AlGaN a negligible composition dependence was reported . and additionally found the anisotropy to be less than 1%.298 This yields 0. An early study of Dingle et al.290 However.338 Saxler et al.344 consideration of the acceptor binding energies led Orton345 to suggest a much smaller value of 0.290.1.4m 0 . Finally.324 While early work suggested a GaN hole effective mass of 0. 294 A more recent and detailed analysis by Gil et al.327 In early studies. The former may require a slight downward revision because the electron gas was confined in a quantum well.337 in which a marginally anisotropic electron effective mass with the values of 0.342 In the cubic approximation.236m 0 and 0. Chuang and Chang reanalyzed the Gil et al. the precise choice of Varshni parameters has only a modest impact on the device characteristics. Ab initio theoretical calculations326 support a rather small value for the spin-orbit splitting 10 meV . Much of the difficulty stems from the fact that the resonances dominating the exciton spectra at low temperatures are not readily distinguishable at ambient temperature.237 0.319–323 Considering the huge uncertainties in the indirect gaps and their lack of importance to device applications. depending on what primary scattering channel was assumed. and crystal-hole bands see the schematic diagram in Fig. Elhamri et al. found 22 meV and cr so 11 meV.303 Fits of the exciton binding energies yielded hole masses in the range 0. because they are smaller and somewhat better known. obtained cr 22 meV and so 15 meV from their own data.20m 0 from cyclotron resonance measurements. Our recommended Varshni parameters represent a simple average of the various reported values except the anomalous results of Monemar. Few studies have attempted to resolve them. especially since in several cases considerably different values are inferred even in the same study.336 No appreciable correction appears to be necessary for the measurement by infrared ellipsometry on bulk n-doped GaN reported by Kasic et al. Our recommendation of 0. No. from fits to the thermoelectric power.332 used measurements of the shallow-donor transition energies to obtain masses of 0. light-.org/japo/japcr. from a fit to the PL results. The indirect energy gaps in GaN are much larger than the direct gap. Barker and Illegems328 obtained an effective mass of 0.339 Wong et al. Rheinlander and Neumann329 inferred 0. It is not obvious how to reconcile these diverse parameter sets.340 and Wang et al.. a considerable body of recent work has led to more precise evaluations of the effective mass.23m 0 was recently obtained by Wang et al. In contrast to most zinc blende materials.330 derived values of 0. pointed out the importance of the polaron correction in GaN since it is so strongly polar 10% . Phys. Shikanai et al.. II for details .105.327.343. and to the average from the studies of 2D electrons. Zubrilov et al. in wurtzite materials the crystal-field splitting is at least as important and cannot be ignored if one wishes to recover a realistic description of the valence-band states see Sec.20m 0 for the bare mass is close to the consensus from the investigations of bulk materials.327 which are commonly used in band structure calculations.8.324 In the following. however.318 It is fortunate that owing to the small relative change in the band gap energy only 72 meV between 0 and 300 K .337 It should be pointed out that most of these experimental values are somewhat lower than the theoretical masses derived by Suzuki et al. 290.341 determined masses ranging from 0. Zinc blende indirect gaps are specified in the tables.. However. We form our composite set of deformation potentials by selecting those values that seem to be most representative of the majority of results: 3.349 noted that the hydrostatic deformation potential should be anisotropic due to the reduced symmetry of the wurtzite crystal. and C 44 105 GPa. the parameters are different.363–371 Some works rely on an explicit comparison with the better understood case of wurtzite GaN. there are significant disagreements be- tween the various experimental results. and d potentials.5 eV and a 2 11.27 C/m2.367.368 and Petalas et al. although the most reliable values fall approximately midway.351 who compared the results of a number of experiments352–355 with two calculations. theory agrees best with the data of Polian et al. Six distinct valence-band deformation potentials.353 who obtained the recommended values: C 11 390 GPa.350 and fits to experimental data. 306 D 4 D1 4. Phys. that interaction is neglected.org/japo/japcr.368 We recommend a value of 3. 350 D 2 3.6 eV..593 meV/K. Redistribution subject to AIP license or copyright. 315 .38 That work succeeded in theoretically extracting the inversion parameter A 7 93. it was noted that the computed spontaneous polarization is highly sensitive to the values of the internal structure parameters such as the lengths of the atomic bonds. which is estimated to be 26. the assumption that the electron mass anisotropy is small implies that these are nearly equal. and Ram-Mohan the pseudopotential results of Yeo et al.13 pm/V.8. Yet another parameter set was extracted from empirical pseudopotential calculations by Ren et al. In principle.315 Although the 600 K using the more relitwo studies obtain the same able model 1 in Ref.6m 0 .365. Very few measurements of the piezoelectric coefficients in GaN have been reported.43 C/m2. We recommend using the d coefficients from the experimental study of Guy et al.0 eV.342. and we recommend using an average value of 0.301 A somewhat lower a 6. No.2 to 3. a Downloaded 05 Dec 2002 to 140.7 eV in wurtzite GaN.5 eV. 362 In one of the papers. While there is one report305 of E P 7.105.362 Very different values of P sp 0. these can be re-expressed in terms of the more familiar a v .5 meV below the energy gap. 8. e 31 employed a first-principles calculation to derive e 31 0.73 C/m2.1 eV derived by adopting the cubic approximation325 .029 C/m2 and P sp 0. C 33 398 GPa. which pointed out the differences between the coefficients in a bulk material versus a strained thin film.306. the low-temperature energy gaps range from 3. These are our recommended values.35 eV. Numerous sets of valence-band deformation potentials have been derived from both first-principles calculations325. Using the cubic approximation. 89.348. 2. 302 An alternative set of effective-mass parameters was recently calculated from a pseudopotential model by Dugdale et al. b. However.351 Overall.323 On the other hand. 1 June 2001 Appl.8 eV for the two components.jsp .16 eV . that would imply a unrealistic positive F parameter.7 meV/Å from a comparison with empirical pseudopotential calculations. attempted to derive the e 31 and e 33 coefficients from the e 14 coefficient in zinc blende GaN. Guy et al. Bykhovski et al. which is in good agreement with fits to the data of Gil et al.41 eV.327 which imply an average hole mass approximately equal to the free electron value (m 0 ). the result is E P 14 eV(F 0). C 13 106 GPa.. Meyer. with variations of nearly a factor of 6 in some cases.349 There are considerable discrepancies between the reported data.31.357 performed a careful study. This consideration may prevent an accurate theoretical evaluation of the spontaneous polarization for realistic nitride structures. which turn out to be somewhat different from those calculated in the original report. and gave the values: a 1 6.299 eV obtained from averaging the results of the luminescence measurements.35 C/m2 and e 33 1. Appl. C 12 145 GPa.348 Shan et al. It is hoped that a theoretical band structure picture that is fully consistent with the recent experimental results will be developed in the near future. 360 A calculation of Shimada et al. Coefficients of d 33 3. 306 D 5 4. yielded values of e 31 0.82 eV.356. Rev. there are two independent momentum matrix elements in wurtzite GaN.324 Christensen and Gorczyca319 reported a hydrostatic deformation potential a 7. are necessary to describe the band structure of GaN under strain. Our recommendation is to use the effective-mass parameters of Suzuki et al.63 C/m . which may indicate lower accuracy of the A parameters.357 Only two first-principles calculations of the spontaneous polarization in GaN are available.9 pm/V were deduced for the bulk GaN from the single-crystal thin-film d 33/2. produced a smaller density-of-states effective mass of 0. The temperature dependence of the energy gap was studied in detail by Ramirez-Flores et al. The determination of elastic constants for wurtzite GaN has been reviewed by Wright.: Vurgaftman.8 eV. Vol.360. Another value d 33 2. so that in contrast to the zinc blende materials the elastic constants for GaN remain somewhat controversial. 350 D 3 8. If one then derives an interband matrix element directly from the electron effective mass. we defer a full discussion of the experimental probes of the spontaneous polarization in GaN/AlGaN quantum wells until the AlN section. between 3. Since only differences in the spontaneous polarization are important in heterostructure band calculations. whereas the most accurate appear to come from low-temperature luminescence measurements372–374 of the free-exciton peak. Insofar as no information is available on the effects of remote bands on the wurtzite GaN band structure. Although the indirect-gap energies have not been measured.5834 J.301.aip. see http://ojps.32 C/m2 and e 33 2 361 0. 358 The latter measurement had the inherent uncertainty of an AlN buffer layer being present. and use the assumed elastic constants to obtain the e coefficients: e 31 0. Phys.8 pm/V and the relation d 13 measurement by Lueng et al.315.347 Their electron mass is lower than the experimental results. The band structure parameters for wurtzite GaN are compiled in Table X.29 and 3. first-principles calculations by Chen et al.074 C/m2 were reported. yielded a thin-film value d 33 2. obtaining values of 0. 11.22 C/m2 and e 33 0.49 C/m2 and e 33 0. Obviously. further work is needed to resolve this controversy. in addition to the strain tensor and the overall hydrostatic deformation potential. 359 Bernardini et al.9 eV was derived from an ab initio calculation by Kim et al. Zinc blende GaN A number of theoretical and experimental studies of the energy gap for the zinc blende phase of GaN have been reported.. Experimentally.7 pm/V and d 13 1. 350 and D 6 5.0 eV. C 12 159 GPa.41 4.017 0.10 0. Downloaded 05 Dec 2002 to 140. a number of theoretical sets of Luttinger parameters are available.65 2.38 1.369–378 In order to derive our recommended values. This results in the following parameter set: 1 2.25 0.12 8. which in turn implies F 0.5 0 3.8.75.57 5.27 3.369 The convergence of results from two different studies allows us to adopt these as our recommended values.4 eV.189 5. Two theoretical values for E P in zinc blende GaN have been reported in the literature.380 We choose an average value of a 7.019 0.370 which are similar to values obtained by Fan et al.5 11.362 The band structure parameters for zinc blende GaN are compiled in Table XI.6 8.105.4 293 159 155 AlN 4.15m 0 in zinc blende GaN.019 0.376 and Fan et al.6 9.13 4.28 0.47 0.96 14.41 4.1 390 145 106 398 105 0.92 2.21 0. Recommended band structure parameters for zinc blende nitride binaries.26 eV above the valley.10.0 0.51 0.3 0.2 3.0 0.029 AlN 3.593 600 9.26 1.593 600 6.379 split-off masses are averaged.0 5. both wurtzite and zinc blende forms of AlN can in principle be grown.92 0. Redistribution subject to AIP license or copyright.63 0.94 0.799 1462 0.6 8. Electron spin resonance measurements indicated an electron effective mass of 0.44 9. Phys.507 0.112 4. it represents the end point for the technologically important AlGaN alloy. 89.12 0.84 1.001 0. A note of caution is that these values have not been verified experimentally.2 5.91 14.: Vurgaftman.164 0.56 0.19 and 2.5 3.0 3.9 0. Recommended band structure parameters for wurtzite nitride binaries.48 0.379 An average of the two yields E P 25.909 830 0.35 1.6 4.545 5.382 and Bechstedt et al.369 Ramirez-Flores et al.381 No experimental confirmations of any of these deformation potentials for zinc blende GaN appear to exist. Elastic constants of C 11 293 GPa.11 5. Phys. we obtain * m so 0. puts the X-valley and L-valley minima at 1.org/japo/japcr.29m 0 . and 3 1.20 0. Appl.245 624 2.5 0.380 and Van de Walle and Neugebauer.23 1.3 2. and Ram-Mohan 5835 TABLE XI.3 187 125 86 * m so E P eV F VBO eV a c eV a v eV b eV d eV c 11 GPa c 12 GPa c 44 GPa recent calculation of Fan et al.J. As in the case of GaN. Parameters a lc Å at T 300 K E g eV meV/K K E X eV g (X) K (X) meV/K E L eV g (L) K (L) meV/K so eV * me ( ) m l* (X) m t* (X) 1 2 3 GaN 4.5m 0 and m * l t 0.47 27.6 0 1. Rev.91 5.jsp .31.82 4.27 0. The value of d 3.1 396 137 108 373 116 0. we average the heavy-hole and lighthole masses along 001 as well as the degree of anisotropy 3 – 2 . Various calculations put the hydrostatic deformation potential for zinc blende GaN in the range between 6.69 to 13.369 Effective masses of m * 0.92.52 0.aip.982 6. Wurtzite AlN has the distinction of being the only Al-containing III–V semiconductor compound with a direct energy gap. Similar -valley effective masses were derived from first-principles calculations by Chow et al.041 0.79 0.3m 0 were recently calculated for the X valley in GaN. and C 44 155 GPa are taken from the theoretical analysis of Wright.375 Since this appears to be the only experimental result.376.245 624 0.5 3.371. 1 June 2001 TABLE X.83 3. No.014 0. AlN Although binary AlN is rarely used in practical devices. 2 0.593 600 4.593 600 0.593 600 5.95 0.68 7. Parameters a lc Å at T 300 K c lc Å at T 300 K E g eV meV/K K cr eV so eV me me A1 A2 A3 A4 A5 A6 E P eV F VBO eV a 1 eV a 2 eV D 1 eV D 2 eV D 3 eV D 4 eV D 5 eV D 6 eV c 11 GPa c 12 GPa c 13 GPa c 33 GPa c 44 GPa e 13 C/m2 e 33 C/m2 P sp C/m2 GaN 3.0 3.4 and 8. Meyer.185 3.006 0. we adopt it as our recommendation. respectively.019 0.50 3. The same procedure is followed in obtaining 5.75 1.032 Appl.38 4.245 624 5.6 the recommended values of a v eV range and b 2.0 3.32 3.82 0.23 5.593 600 0.15 0.44 6.994 0. K.2 9. see http://ojps.368 have measured the spin-orbit splitting in zinc blende GaN to be 17 meV.42.12 0.8 4.86 14.59 3.29 25.50 1.92 2..68 1.3 25.59 0.4 eV is an average between the only published values from Ohtoshi et al.245 624 0. Although the hole effective masses in zinc blende GaN have not been measured.0 9.370.319.64 2.82 4.9 10 304 160 193 InN 4.64 6.2 eV 0.67.2 eV 1.20 6. Vol.0 3.081 InN 3.0 0. 11.5 1.5 eV.85 1.369.0 eV.53 0.8 3.27 3.97 0.0 5.95 2.2 2. although the growth of zinc blende AlN has not been reported.6 eV range .1 223 115 92 224 48 0.299 0.98 1.57 0.76 3. When all of the reported369–371.31 1.85 0.4 1.0 0 2.351 Very similar sets were calculated by Kim et al.0 5.6 to 3.1 0.72 1.67 0.0 3.703 1. 387 resolved at 300 K what they believed to be the free or shallow-impurity-bound exciton.jsp . Zinc blende AlN is projected to be an indirect-band gap material.11 eV. InN Although InN is rarely if ever used in devices in its binary form.362 of the spontaneous polarization in AlN have been performed with 0. C 12 160 GPa.369. since only absolute values of these parameters enter the Hamiltonian. Tang et al.347 The apparent disagreement in signs in various papers for A 5 and A 6 is ignored.12 C/m . respectively.388 1 2 3 0.051 P sp 0.362.371. 0. due to either bowing or long-range ordering.92.1 and 9.8 eV . it is important to emphasize that our recommendations for the crystal-field and spin-orbit splittings in AlN have only provisional status. It may be possible to explain the remaining discrepancy between the majority of the experimental investigations and the Bernardini et al.388 The hydrostatic deformation potential for wurtzite AlN is believed to lie in the range between 7. the finding of no significant differences from GaN for the entire composition range of the AlGaN alloy may indicate that their results are somewhat less reliable. 357.327 The recommended values of m e 0.799 meV/K and 1462 K were reported by Guo and Yoshida.327. Phys.1 eV (F 0.5836 J.47. We recommend the valence-band effective mass parameters of Suzuki et al.395.371. Meyer.371 The spin-orbit splitting is believed to be the same as in wurtzite AlN 19 meV .371 cited values of 104 and 169 meV from firstprinciples and semiempirical pseudopotential calculations.47m 0 ). The longitudinal and transverse masses for the X valley are predicted to be 0.382.383 and Perry and Rutz384 indicate that the energy gap in wurtzite AlN varies from 6. and Kim et al.25m 0 .351 Several early measurements392. Rev. C 33 373 GPa. The available calculations360.351 Similar sets were quoted in other theoretical works.379 E P 27.390 and McNeil et al.0 eV.398 Park and Chuang399 required P sp 0.378.9 eV.397 Hogg et al. Vol.105.385 Although Brunner et al. we obtain our recommended value of cr 164 meV. 369.348 We select a median value of 9. Cingolani et al.0. which is consistent with the observation that the band gap pressure coefficients in AlGaN alloys have little dependence on composition.369. and parameters:369. Averaging all of the available theoretical crystal-field splittings. and C 44 193 GPa are adopted from the calculations of Wright. The recommended band structure parameters for wurtzite AlN are compiled in Table X.327 An alternative set of A parameters was recently published by Dugdale et al.391 We recommend the values C 11 396 GPa. 11.394 are in reasonable agreement with the experimental values. 6.379.369 The same procedure employed for GaN yields the recommended Luttinger 1.31.326 Averaging the theoretical results from different sources. see http://ojps.0 eV319 and 9..aip. Suzuki et al.85 (m so 0.401 The recommended band structure parameters for zinc blende AlN are compiled in Table XI. L. Varshni parameters of 1. Our recommended values for the deformation potentials are a 9.371.378.381 The elastic constants of C 11 304 GPa. since it appears that no experimental data exist. On the other hand. Appl.386 With the aid of cathodoluminescence experiments.8 pm/V. -.400 The magnitude of the estimated spontaneous polarization is dependent on the assumed piezoelectric coefficients. 89.6 pm/V and d 13 rather similar to the previous determinations. That reference 2. Redistribution subject to AIP license or copyright.4 eV. calculation if a linear interpolation of P sp is invalid for the AlGaN alloy. The crystal-field splitting in AlN is believed to be negative.326 Again.388 A greater anisotropy than in wurtzite GaN is predicted. No. which were obtained d 33 5.28 eV at 5 K to 6. The effect of the spontaneous polarization on the optical properties of GaN/AlGaN quantum wells was observed by Leroux et al. with X-. The momentum matrix element is taken to be an average of the reported values:371.388 obtained cr 215 meV.2 eV at room temperature.361.081 C/m2 and P sp the reported results of P sp 2 0.4 eV. D 4 4. We recommend an intermediate value of 6.319. it forms an alloy with GaN that is at the core of the blue diode laser. who also found the low-temperature gap to be 6. respectively. 42.319.036 C/m2).360 calculation. it was found that the results were consistent with a lower value for the spontaneous polarization in AlN( 0. respectively.76). we recommend the calculated value and note that the controversy will likely be resolved in future work.3 eV. The absorption measurements of Yim et al. We adopt the value of 19 meV suggested by Wei and Zunger.371. Hydrostatic deformation potentials of 9. At this juncture.388 we obtain the recommended -valley effective mass of 0. at an energy of 6.5 eV.385 A similar energy gap was reported by Vispute et al.040 C/m2 to reproduce their GaN/AlGaN quantumwell data.318 also reported Varshni parameters. and C 44 116 GPa suggested by Wright. although it is again noted that experimental studies are needed to verify these calculations. it is the largest-gap material that is still commonly considered to be a semiconductor.23 eV for the low-temperature band gap.org/japo/japcr.396 However.327 calculated 58 meV.381 and d 348. reported good agreement with experiment using the original Bernardini et al.8.13 eV. Spin-orbit splittings ranging from 11371 to 20 meV327 have been cited in the literature. C 13 108 GPa. C 12 137 GPa. and 9.31m 0 .0 eV. which implies that the topmost valence band is crystal hole-like.53m 0 and 0. were able to fit their luminescence data by assuming negligible spontaneous polarization.293 Especially since some degree of seg- Downloaded 05 Dec 2002 to 140.32m 0 were obtained by averaging all available theoretical masses. Phys. Two rigorous calculations360.393 of the piezoelectric coefficient in AlN were compiled in Ref.348 The elastic constants in wurtzite AlN were measured by Tsubouchi et al. 1 June 2001 Appl.28m 0 and m e 0. Pugh et al.369 b 1. who provides a detailed discussion of their expected accuracy.6 eV. and L-valley gaps of 4. A number of calculations are available for the electron effective mass in AlN.379.: Vurgaftman. cr whereas Wei and Zunger326 obtained cr 217 meV.8 eV369 have been reported.389 Theoretical values are also available for a few of the valence-band deformation potentials D 3 9. a v 3. 10. A study of the charging of GaN/AlGaN field-effect transistors led to similar conclusions.9. and Ram-Mohan Furthermore. in conjunction with the Varshni parameters of Guo and Yoshida. 370 and Van de Walle and Neugebauer:381 a v 1.371. respectively. it assures self-consistency and in all of the cases that we are aware of it appears to be reliable.21 and 2.321 Valence-band effective-mass parameters were calculated by Yeo et al. 0. which found values of 0. is often quoted in the literature.. which in some cases may be attributable to specific physical mechanisms but in others simply represent empirical fits to the experimental data. and 371 and the split3 1.12m 0 .351 Similar sets were derived from other calculations. E P .48m 0 and 0. 89. the alloy band gap is smaller than the linear interpolation result and can in principle be a function of temperature.362. 2. static deformation potential.42 Kim et al. We also point out that since the -valley electron mass * m e can be obtained from Eq.85 eV is recommended.31.348.371 * For the hydrooff mass is chosen to be m so 0. with -. a different gap was stated in the abstract of that article .12m 0 .347 using essentially the same techniques.5 eV. C 12 125 GPa..26.409 only theoretical estimates are available for any of its band parameters. it is important to understand the properties of bulk InN in its wurtzite phase.3 eV. Phys. C 12 115 GPa. The results of the first two studies are quite similar. In compiling the tables for binaries.370 range of 2. are taken from the calculation of Wei and Zunger.371 Christensen and Gorczyca predicted a hydrostatic deformation potential of 4.15 . Simpler approximations are naturally Downloaded 05 Dec 2002 to 140.10– 0. respectively. It is predicted to be a direct-gap material.97 eV. and F.348 We recommend the average of a 3.8 eV was calculated by Kim et al. and C 44 86 GPa have been adopted from the calculations of Wright. along with low-temperature and room-temperature gaps of 1. and Ram-Mohan 5837 regation is believed to occur when that alloy is grown. 408 We recommend the latter. and we recommend the parameters derived by Pugh et al.1 eV for wurtzite InN. 2.35 eV from the theoretical319.63 is from the results of Pugh et al. X-.05 eV at 300 K.245 meV/K and 624 K were reported by Guo and Yoshida385 for wurtzite InN. While this procedure yields a complex dependence of the effective mass on composition. The absorption measurements of Puychevrier and Menoret403 on polycrystalline InN indicated gaps of 2. It is judged more reliable than earlier experiments performed on samples with high electron densities. with minor exceptions.371 and Dugdale et al. Varshni parameters of 0.14m 0 that has been calculated. the suggested approach is to: 1 interpolate linearly the E P and F parameters. 4. The result of Tansley and Foley. respectively. and note that the end points may be found in the tables corresponding to the relevant binaries. 4. respectively.410 A rough proportionality to the lattice mismatch between the end-point binaries has also been noted.407 represent our recommended temperature dependence. Phys.51. While elastic constants were measured by Sheleg and Savastenko.2 to 4. The bowing parameter for III–V alloys is typically positive i. we recommend appropriating the set specified above for GaN. Vol. since it closely matches the theoretical projection. respectively. Elastic constants of C 11 187 GPa.89 eV at 300 K for high-purity InN thin films. 2 1. b 1.e.aip. An even lower gap was obtained by Westra and Brett.8.360 The recommended band structure parameters for wurtzite InN are compiled in Table X. Meyer.370.3m 0 .201 In what follows.1 . by Pugh et al. and 5.404 yielded E g 2.11m 0 404 and 0.402 measured the energy gap at 78 K to be 2. Valence-band deformation potentials are taken from a combination of the calculations of Wei and Zunger. which is in the middle of the range 0. see http://ojps. it is not an independent quantity. C 13 92 GPa. These values. For alloys. the dependence of the energy gap on alloy composition is assumed to fit a simple quadratic form:410 Eg A1 xB x 1 x Eg A xE g B x 1 x C. we will give only bowing parameters for the alloy properties. so . Although the growth of zinc blende InN has been reported.379 The longitudinal and transverse masses for the X valley are predicted to be 0. The piezoelectric coefficients and spontaneous polarization for InN are taken from the calculation by Bernardini et al. 1 June 2001 Appl.326 We recommend an electron effective mass identical to that in wurtzite InN.72. and 3 obtain the temperature-dependent electron mass in the alloy from Eq. Redistribution subject to AIP license or copyright.370 The spin-orbit splitting is projected to be 6 meV. Since full selfconsistency has been imposed upon all of the recommended parameter sets.115 2 use the bowing parameter specified for the alloy to derive E g (T) and so(T) from Eq.org/japo/japcr.jsp . which closely resemble a previous result from the same group. Another set of absorption measurements by Tyagai et al.. The recommended crystal-field and spin-orbit splittings of 41 and 1 meV. the bowing concept has been generalized to include quadratic terms in the alloy-composition series expansions for several other band parameters as well.: Vurgaftman.994 and 1.326 There appear to be only two measurements of the electron mass in InN. We will employ the above functional form for all parameters and.1 where the so-called bowing parameter C accounts for the deviation from a linear interpolation virtual-crystal approximation between the two binaries A and B.5 eV. 2. an average of 3.. 370. we have assured that the values given for the mass and the other parameters are consistent with Eq. TERNARY ALLOYS For all of the ternary alloys discussed below.09 eV at 77 and 300 K. Osamura et al. and d 9.15 . Appl. Since apparently there have been no calculations of the valence-band deformation potentials.94.0 eV although for the purposes of the quadratic fit for GaInN.323 using the empirical pseudopotential method. The physical origin of the band gap bowing can be traced to disorder effects created by the presence of different cations anions .82 eV. C 33 224 GPa. No. IV. which became approximately 60 meV lower at room temperature. 11.352 we recommend the improved set of Wright:351 C 11 223 GPa.2 eV. neglect higher-order terms in the expansions.27m 0 . Rev.405 E g 1.370 The rec- ommended Luttinger parameter set: 1 3.15 in conjunction with the specified values for E g .105. 2. and C 44 48 GPa.406 although in their case a high electron density was also present.J.319 although a smaller value of 2. and L-valley gaps of 1.382 The recommended band structure parameters for zinc blende InN are compiled in Table XI. Bowing parameters for the X-valley and L-valley gaps in AlGaAs were determined using electrical measurements in combination with a theoretical model by Lee et al.147 Since the effective mass in AlAs was chosen to be consistent with the results in AlGaAs.33. Several studies of the composition dependence of the -valley electron mass have been reported for x 0.142 cannot be considered fully reliable. and heavy-hole and light-hole masses along the 001 direction. Nonzero bowing parameters for AlGaAs. Particular attention has been devoted to the crossover point.055 eV obtained from photoluminescence g measurements.92.3.183 0. Rev. a zero bowing parameter is recommended and gives good agreement with the interpolation procedures discussed at the beginning of Sec. in the present case it appears that much more accurate results can be obtained by using the cubic form of Aspnes et al.27.6 eV for x 0. Phys. Varshni parameters for Alx Ga1 x As have been obtained from photoluminescence.147 eV derived by Aubel et al.310x 0. dotted.245 0–0.138.419 These are in reasonable agreement with our recommended assumption that the bowing parameter is independent of temperature.143.140. have derived a hydrostatic deformation potential of a 10.14 to 0.1 is used for all compositions of Alx Ga1 x As. obtained a composition-dependent bowing parameter: C ( 0. result. 416 A small bowing parameter was favored on theoretical grounds.421 The points have been fit to a quadratic dependence. and spectroscopic ellipsometry studies. Linear interpolations are suggested for the electron masses in the X and L valleys. Most studies find that the split-off gap can be fit quite well by linear interpolation. Parameters eV Eg EX g EL g so Recommended values 0.134.410 although a more recent treatment by Magri and Zunger417. Investigations are complicated by the fact that whereas GaAs is a direct-gap material with – L – X valley ordering. The same procedures should be used to obtain the X-valley and L-valley electron masses.38 at low temperatures and 0.146. Phys.2 These results and photoluminescence excitation spectroscopy data420 support a C(E L ) almost equal to zero.3 eV.147.147 Downloaded 05 Dec 2002 to 140.104. Qiang et al. Its key role in a variety of transistor and optoelectronic devices has necessitated a precise knowledge of the fundamental energy gap as well as the alignment of the three main conduction-band valleys. 5. 8. X-. 89.310x) eV. 5. AlGaAs AlGaAs is the most important and the most studied III–V semiconductor alloy. split-off hole mass. The latter result is in good agreement with a linear interpolation between the GaAs and AlAs values a 8.31. reliable. see http://ojps.127 1. 4. Direct interpolation of the individual Luttinger parameters is not recommended. and dashed curves. 11. the same authors obtained a much smaller value of a 8. since most of the determinations were performed either at room temperature or at liquid-helium temperature.421 although owing to the narrow composition range and spread in the data points. 1 June 2001 Appl. it is difficult to judge the accuracy of such a scheme. it appears that the linear approximation gives adequate results for small x. Luttinger parameters.055–0.146.8. we attempt to give electron mass bowing parameters that are consistent with the above procedure. A. Appl.127 1.418 gave a complex fourth-order dependence reminiscent of the Aspnes et al.39 at 300 K .146 In order to estimate the valence-band warping. AlAs is an indirect material with exactly the reverse ordering.055 0 0 Range 0.85 eV for x 0. We select g C(E X ) 0.140 and Saxena141 as well as empirically by Casey and Panish. which agrees with the trend in the table compiled by Adachi.org/japo/japcr.422 However.411 Casey and Panish suggested a linear x dependence in the range 0 x 0.101. the suggested procedure is to interpolate the 3 – 2 difference. A linear dependence of the shear deformation potentials on composition was suggested by the ellipsometry study of exciton splittings and TABLE XII. -. There is insufficient data to determine the temperature dependence of the bowing parameter.138. Aspnes et al. Arsenides 1. respectively . In the tables. Redistribution subject to AIP license or copyright.6 to 10. No. and hole masses. at which the and X valley minima have the same energies. Lattice constants and elastic moduli may also be linearly interpolated.45 also supported by other data 412–415 and a quadratic dependence when 0.105. Bowing parameters from 0.jsp .22.139 which is near the bottom of the earlier range of values but is the most recent and seems the most FIG.: Vurgaftman. photoreflectance. Although the bowing parameters that we recommend in all other cases with the exception of the direct gap in AlGaSb are not a function of composition.66 eV have been proposed for the -valley energy gap when Eq.142.aip. V. since it was based on data points in a rather narrow composition range..90.055 0–0. Meyer. Vol.140.45 x 1.143 A value of C( so) 0. in this case .127–1. and L-valley gaps for the AlGaAs alloy at T 0 K solid. and Ram-Mohan sometimes possible.3 Composition dependences for all three of the direct and indirect gaps in Alx Ga1 x As are plotted in Fig. 2 Using spectroscopic ellipsometry to derive the positions of the critical points.5838 J. From other reports. This result implies a – X crossover composition of x 0. 430. 2 4.438..61 Range 0. Since no reliable data on the bowing parameters for the X.15 0. and imply C( so) 0.org/japo/japcr. 447. see http://ojps.446 These are in reasonably good agreement with the electroreflectance measurement of Perea et al.486 eV .434 because the room-temperature gap implied by that C(T) is higher than nearly all experimental values. The bowing of F is then obtained using the already-derived relations for the energy gap and the effective mass.8.84.041m 0 .201. These results indicate some bowing in the hydrostatic deformation poten- Downloaded 05 Dec 2002 to 140. Phys.443 for Ga0.53As437.459 although Zielinski et al.01.53As.431 Karachevtseva et al.08 eV and g C(E L ) 0. the most reliable data are for Ga0.448.79 eV. For Ga0. we have fixed our recommended Ga1 x Inx As bowing parameter by emphasizing the fit at the important x 0.31.4 0.425 It remains a direct-gap material over its entire composition range.aip.45–0.438.436 derived a much smaller value from an analysis of absorption spectra. Nonzero bowing parameters for GaInAs. e.440 That agrees with modeling of the diamagnetic shift of the exciton absorption peaks in Ga0. 0. The electron effective mass in GaInAs has been studied both theoretically and experimentally.53 alloy that is lattice matched to InP.437 The split-off hole mass should be interpolated linearly.439. Redistribution subject to AIP license or copyright.47In0.15 in conjunction with interpolated values for the interband matrix element and the F parameter is discussed below.454.433 and Jensen et al.171.and L-valley electron masses appear to exist. we suggest linear interpolation. we choose a composite average of E g (T 0) 816 meV.462 in a study of GaInAs strained to a GaAs substrate.435. evidence has accumulated favoring a low-temperature value of m* e 0.20 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ The GaInAs alloy is a key component in the active regions of high-speed electronic devices.47In0.424 and long-wavelength quantum cascade lasers.53As.3 eV for Ga0.436 magnetoabsorption.: Vurgaftman. 2.043m 0 .481 1.5 eV.15 eV. Meyer.32–0. 166 Tiwari g g and Frank432 give a much different set: C(E X ) 0. although with considerable spread in the results. Phys..4 eV) and E L (0.437 suggested the set of Luttinger parameters: 1 11.423 infrared lasers. Vol. The fundamental energy gap of Ga0.18. 2.08–1.4 0.426 Van Vechten et al.455 In recent years. Parameters E g eV E X eV g E L eV g so eV * me ( ) m * (001) hh m * (001) lh 3 2 5839 shifts by Logothetidis et al. and implies only a small E P bowing parameter.441 This bowing parameter also agrees well with photoreflectance measurements on GaAs-rich GaInAs by Hang et al.47In0.72 eV).431 in disagreement with Karachevtseva et al.443 The composition dependence of the Varshni parameters obtained in this manner is in good agreement with the functional form of Karachevtseva et al.145 0. Most studies have employed an interband matrix element of E P 25.47In0.461 to be a duction in a was also observed by Wilkinson et al.455 obtained a much larger light-hole mass.477 eV.448–452 and even smaller values. No.48 1.426–434 the most recent and seemingly most reliable values lie within the more restricted vicinity of 0.. GaInAs Recommended values 0.479 eV . Sugawara et al.447 As in the E P eV F VBO eV a c eV case of the energy gap. While early studies * proposed m e 0.J. It has also been proposed that the bowing depends on temperature.475 eV .g.0202 0.53As 7. which in turn implies a bowing parameter C 0.1 . Application of the more general approach using Eq.410.jsp .77 0.166. Appl. The experimental and theoretical bowing parameters for the splitoff gap have been reported by Vishnubhatla et al.459 and with cyclotron resonance experiments.47In0. Rev.46 0. 1 June 2001 Appl. 443. being almost flat below 100 K and decreasing rapidly at higher temperatures. namely its excellent lattice match to GaAs that renders strain effects on the band structure rather insignificant. A rewas measured by People et al. The recommended bowing parameters for AlGaAs are collected in Table XII. Alavi et al. 4.53As has been studied extensively.15–0. 11.101. 3 4.437 photoluminescence.47In0.477 1. While bowing parameters spanning the wide range 0.445 and Berolo et al.434 Bowing parameters for the indirect energy gaps were calculated by Porod and Ferry428 using a modified virtual crystal approximation. 0.456–458 This result implies the presence of bowing if the electron mass is interpolated directly using an expression similar to Eq.33–0. This is quite close to the recent determinations of Paul et al. 89.446. The only reliable experimental result apg pears to be a determination of E L in Ga0..72 0.38 2. We suggest that the bowing parameters for the hole effective masses should be consistent with the results of Alavi et al. In those cases where no value is listed.53As lattice matched to InP.440 On the basis of low-temperature results ranging from 810 to 821 meV.105.33 0. linear variation should be assumed. The former value is much more consistent with the matrix elements employed for GaAs and InAs see above . The relative paucity of deformationpotential data for this important alloy is due in no small part to the very property that is one of its greatest attractions.442 We choose to assume that the bowing is temperature independent. 0.6 eV have been reported.434 Kim et al.47In0.0091 0.453 more recent experiments in strong magnetic fields have suggested that the polaron effective mass is in fact higher.32–0.460 On the other hand. and Ram-Mohan TABLE XIII. 444 That g study supports a lower value for the bowing parameter. The hydrostatic deformation potential in Ga0.5 eV.47In0.434 Owing to the spread in values.453. by absorption. Those values are in good agreement with the light-hole masses derived from spin-polarized photoluminescence measurements by Hermann and Pearsall..53As. That study predicts large bowing parameters for both E X (1.439 and photoconductivity experiments.53As/InP quantum wells.153 although their best fit was obtained for a slightly smaller value of b in GaAs than we recommend in Table I..172. 488–494 Using the result of Emanuelsson et al.70 eV to reflect the majority of these results.10 0.201. at 0 K .38 and 2.52 composition. Meyer.410.101.496.24–0.51In0.482 with the most reliable results clustered around 0. Furthermore.483–486 The ordering-induced reduction of the direct energy gap can be on the order of 100 meV. Linear interpolations are usually employed to obtain the X-valley and L-valley minima in AlInAs.35 eV. the temperature-dependent band gap of Al0. and by long-range ordering of the group-III atoms which can take the form of a monolayer InP–GaP superlattice along the 111 direction.9 eV at 300 K is lattice matched to GaAs.70 0 0.418 Wakefield et al. we recommend C 0. Cury et al. which makes it an attractive material for wide-gap GaAs-based quantum well devices such as red diode lasers.5–0.39 to 0..01m 0 for Al0.15 0.51In0. Vol.487 Low-temperature band gaps of 1.48In0.5–0 ¯ ¯ ¯ ¯ ¯ ¯ tial.5840 J. Unfortunately.467. 468 On the other hand. Yeh et al. implies a bowing parameter of 0.org/japo/japcr. On the other hand.46In0. This value of E P requires F 0.81 4. although it should be noted that the results depend sensitively on the electron effective mass adopted for Al0. Phys. which is equal to the GaInAs value adopted in the previous subsection. respectively. We have derived bowing parameters for AlInAs employing this system of values.474–478 Subsequent electroreflectance and modulation spectroscopy studies favored a value near the higher end of that range.418. 11.465 The smaller result is supported by the cyclotron-resonance measurements of Chen et al. Krijn101 gave a bowing parameter of 0. 1 June 2001 Appl.54As on InP reported by Abraham et al. we recommend linear interpolation for the other masses in the AlInAs alloy.479 Although early work usually assumed a linear Downloaded 05 Dec 2002 to 140.469 Calculations by Shen and Fan470 also indicate an effective mass of 0. For the -valley band gap.75 eV. They found that an interband matrix element of 22.24 eV for x 0. The recommended nonzero bowing parameters for AlInAs are collected in Table XIV. it is useful to consider the Ga0.66 eV. That approximation implies that the X and valleys should cross at a composition of x 0.47In0.1 eV .74 0. Similar results were recently obtained by Kopf et al.969–2. GaInP The GaInP alloy exhibits some of the largest direct gaps among the non-nitride III–V semiconductors.069m 0 .7 on the basis of absorption measurements. B. Ga0. In view of the lack of hard data. the most precise band gap determinations are available for Al1 x Inx As with the x 0.129 That result would imply a considerable bowing parameter even within the a v theory presented by Wei and Zunger.52 was measured by Ferguson et al..049 4.42 Pending further confirmation.63 for consistency. Phys. the X conduction valley is lower than the valley in AlAs-rich Alx In1 x As.465 and were also recommended in several compilations of bowing parameters. and Ram-Mohan TABLE XIV. which we ascribe to a nonlinear shift of the conduction band edge.497 The X-valley gap energies in InP and GaP are nearly equal 2.8.4 The recommended nonzero bowing parameters for GaInAs are collected in Table XIII.018 eV have been reported for random GaInP alloys that are nominally lattice matched to GaAs.aip.4 Range 0.471 to be a 6.52As heterostructure system that is lattice matched to InP.31.201.473 This application has spurred extensive studies of the band structure characteristics of GaInP.1 eV and AlAs 8.472 obtained a valence-band deformation potential opposite in sign from the trend predicted by the model-solid theory of Van de Walle.456.457 obtained a much smaller mass of 0.105. Fan and Chen introduced a disorderinduced conduction-valence band mixing.101. see http://ojps. 3. Phosphides 1.5 eV was necessary to account for the experimental results. Rev.74 eV based on cathodoluminescence spectroscopy data. Nonzero bowing parameters for AlInAs.075m 0 .: Vurgaftman.432 With the inclusion of strain effects. In order to explain the electron effective mass in AlGaInAs quaternaries. Appl.466 We select a composite value of C 0. For this reason.64. By analogy to GaInAs and AlInAs.52As. 89.jsp . 458 The hydrostatic deformation potential for x 0.479–481 Theoretical studies have also produced a wide range of bowing parameters. Parameters E g eV E X eV g so eV * me ( ) E P eV F VBO eV a c eV Recommended values 0. which falls between the values adopted for InAs 6.15 eV for the spin-orbit splitting.464 reported a value of 0.52As.493 we obtain a recommended bowing parameter of C 0.48In0.7. and the – X crossover composition in GaInP is believed to be close to x 0. which is slightly lower than the early experimental result of x 0.7 eV.48In0. Redistribution subject to AIP license or copyright. a precise measurement for this lattice-matched alloy is somewhat complicated by its proximity to the indirect crossover point.65 eV.463 theoretical work indicated that it should be larger. The reasonably good agreement of all but one result allows us to suggest a -valley effective mass bowing parameter for AlInAs.495 corrected for the exciton binding energy of 8 meV.49P alloy for which the most extensive data are available. AlInAs AlInAs serves as the barrier layer in the important Ga0.49P E g 1.467 Since the larger crossover composition would require a negative bowing parameter for the X-valley gap. we recommend linear interpolation.. In contrast to GaInAs. Optically detected cyclotron resonance measurements * have yielded m e 0.64 1.68 by Lorenz and Onton.53As/Al0. which are at present rather well known. which is only a little lower than extrapolations from GaInAs-rich AlGaInAs. No. While Matyas reported a -valley bowing parameter of 0. That value is consistent with recent data for nonlattice-matched compositions. early photoluminescence and cathodoluminescence determinations yielded bowing parameters ranging from 0.76 eV.44 0. which favors a small L-valley bowing. However.502 and Schubert et al. Nonzero bowing parameters for AllnP. The shear deformation potential d was measured for GaInP grown on GaAs 111 B substrates. have more recently suggested C(E X ) 0.509 which translates into an upward bowing of 0. the large uncertainties in existing determinations make it difficult to conclusively prefer this value over a linear interpolation. a direct gap of 2. although a roomtemperature value of E L 2.5In0. No.38 eV for the direct-gap bowing parameter from relatively early electroreflectance measurements.4 eV.63 eV gap for AlP see above . 89. Auvergne et al.5P is thought to be 135 meV. we recommend using a negative bowing parameter of C 0. Linear interpolation of the indirect X-valley gap was found to give good agreement with photoluminesTABLE XVII.11m 0 . The electron effective mass in a random alloy with x 0.76 0–0. 11.22 5841 Range 0.67.48P.5P at 300 K.490 Similar results were obtained by Wong et al. and at the crossover composition the -valley value of E g 2. However. This result was supported by the work of Dawson et al. Appl.092m 0 . Nonzero bowing parameters for AlGaP. Phys. With a linearly interpolated value of E P 26 eV for the interband matrix element in Ga0.479 with recent results502 implying a linear interpolation to within experimental uncertainty.5In0.48 eV. alg though that article assumed L-valley indirect band gaps in the end-point binaries that are considerably different from the ones adopted here. Parameters E g eV E X eV g E L eV g so eV * me F d eV Recommended values 0.500 yielded E L g 2.19 0.506.500.86 0. Meyer.510 The recommended nonzero bowing parameters for AlInP are collected in Table XVI.67.482. although various estimates put the -valley electron mass close to 0.502. In deriving our recommended bowing parameter.05–0 ¯ ¯ 0–2. Mowbray et al.482 The – L crossover most likely occurs at x slightly smaller than the – X crossover point. Bour et al.38 0. No direct experimental determinations of the effective masses in AlInP appear available. which implies a negative C. Few data are available for the g position of the L-valley minimum in AlInP. indirect X-valley gaps of 2.496 and Meney et al..39 0.org/japo/japcr. Parameters E g eV E X eV g so eV * me Recommended values 0.38 eV is deduced.jsp . 2. AlInP semiconductor.13 Range 0. we derive an F parameter of 1.35 0. Rev. 1 June 2001 TABLE XV.505 reported a low-temperature direct excitonic gap of 2. linear interpolation is advised using the scheme outlined above.48 0.48. linear interpolation is recommended.147 eV on the basis of piezoreg flectance spectroscopy in the composition range near the crossover point. a bowing parameter C(E X ) 0.202 The lowest-energy optical transitions are typically associated with donor or acceptor impurities. the inherent difficulty of experimentally determining E g in close proximity to the indirect-gap transition caused underestimates by some workers.203 obtained 0.446.5In0.J.051 0.504 While the results imply a bowing parameter of 2.473.505.499 suggested C(E L ) 0.508 In fact.: Vurgaftman.5 was measured by Emanuelsson et al.507 Taking into account the correction for the exciton binding energy a rough estimate insofar as precise values have not been calculated . and from it the corresponding bowing. The recommended nonzero bowing parameters for GaInP are collected in Table XV.503 In the absence of reliable data for the other electron and hole masses.4 eV is the largest of any non-nitride direct-gap III–V Downloaded 05 Dec 2002 to 140.501 The bowing of the spin-orbit splitting in GaInP is known to be very small.4 Appl.48–0. 509.105.31.19 eV.8. and Ram-Mohan TABLE XVI.48P.495 to be m * e 0. Vol. instead of extrapolating the AlInP gap to the AlP binary.7 eV is given by Ozaki et al.680 eV for the lattice-matched composition.20 1.69 eV for Al0.34–2.52In0. Somewhat larger bowing parameters are implied by the pressure experiments of Goni et al. Parameters eV Eg EX g Recommended values 0 0. it is convenient to consider compositions close to Al0. see http://ojps.2 eV g agrees with other experimental and theoretical results. The spin-orbit splitting in Al0.25 eV in Ga0.2 For a precise determination of the bowing parameter. Nonzero bowing parameters for GalnP.52In0. Phys.500 g Since that implies at most a very small bowing parameter. Redistribution subject to AIP license or copyright.36 eV have been deduced from a variety of optical measurements.482 Early experimental and theoretical determinations of the bowing parameter for the L-valley gap were summarized by Bugajski et al. For Al0.0–0.23–0.71 eV. Modeling of the ellipsometric and thermoreflectance data of Ozaki et al.38 ¯ ¯ ¯ variation of the X-valley gap.498 Our recommended value of C(E X ) 0.44. while noting that considerable uncertainty exists for large x.507 and by the ellipsometry experiments of Adachi et al.480 which makes L the lowest conduction valley for x greater than 0. which is lattice-matched to GaAs.49 0–0. which is somewhat lower than the linearly interpolated values quoted in other papers. Krutogolov et al.48P at 0 K corrected for the exciton binding energy must be considered a better-established value than the 3.78 0 Range 0. AlGaP The ‘‘exotic’’ AlGaP alloy has an indirect band gap throughout its composition range.5P.03 0 0.aip. 3. we employed the – L crossover point of x 0.13 Alx In1 x P has a direct energy gap for x 0.476.52In0.499 which was confirmed recently by Interholzinger et al.65 0. 523 which is in good agreement with the empirical curve charting the increase of the bowing parameter with lattice mismatch between the binary constituents. Nonzero bowing parameters for GaInSb. we recommend use of the bowing parameter determined by Isomura et al.524 recently found a linear variation of the direct energy gap with alloy lattice constant i.260. Phys. We recommend using bowing parameters of 0.514 We recommend that a linear variation be assumed for all other band structure parameters of AlGaP see Table XVII .243. once impurity and phonon band transitions were carefully separated from the interband transitions. Also.43 ¯ Downloaded 05 Dec 2002 to 140. The pseudopotential calculations of Bouarissa et al. which are generally in excellent agreement with each other.72 ¯ ¯ ¯ cence spectra.33 and 0.11 deduced a bowing parameter of 0. 11.25 Range 0–0. A number of experimental243.8. Levinshtein et al. Since the electroreflectance measurements should have been more precise than the absorption experiments of Agaev and Bekmedova. the authors concluded that either a linear variation or a quadratic variation with a bowing parameter of 0.202.14–0.201 While Dai et al.259 whereas the pseudopotential calculations of Bouarissa and Aourag517 suggested a slow variation from 0. respectively..519 which cover only part of the composition range.260 A small bowing of the electron effective mass in the valley has been determined both experimentally and theoretically.4 eV for the X-valley and L-valley gaps. those results were confined to a relatively small range of compositions and as such were conceivably not sensitive enough to the quadratic bowing term.5842 J. it serves as the hole quantum well material in type-II infrared lasers155 and photodetectors515 with strain-balanced active regions.011 6. 2.31. While considerably larger masses were reported by Barjon et al.415 at room temperature. from which Levinshtein et al. 89. in that an average of the bowing for two direct critical points is used to represent the bowing of the indirect gap.jsp .49 eV were consistent with the data.33 0.11 give a large bowing of the lighthole mass. Vol. indicate appreciable bowing for both the X and L valleys. Meyer. As in the case of AlInP. This finding is in apparent contradiction with the limited data of Lorenz et al. and Ram-Mohan TABLE XVIII. 1 June 2001 Appl.516 yielded very weak bowing of the two indirect gaps. the bowing parameter for light holes is chosen to be consistent with the results of Roth and Fortin.105.201 The method employed by Adachi is rather indirect. which are near the top of the reported range. TABLE XIX.43 0.: Vurgaftman.446 Roth and Fortin243 compiled results from a number of references.43 eV by Isomura et al.415 0.243 The recommended nonzero bowing parameters for GaInSb are collected in Table XVIII. Isomura et al. in agreement with the band structure model of Auvergne et al..36–0. Nonzero bowing parameters for AlInSb.093–0. it follows that the bowing should be similar in the two cases.426 and theoretical410. AlInSb provides a convenient strain-compensating barrier material for mid-IR interband cascade lasers521 and other antimonide device structures. Recent cathodoluminescence experiments support a small bowing of 0.06–0. AlInSb While not widely used.260 Since the light-hole masses in InSb and GaSb are only a little larger than the electron masses.and L-valley gaps were estimated by Adachi166 and Glisson et al.516 studies of the direct band gap in GaInSb have been published.513 Using a limited number of data points.6 0. composition for InSb-rich AlInSb.e. Early absorption measurements of Agaev and Bekmedova522 yielded a linear variation of the direct energy gap with composition.aip.43 at 0 K to 0. However.523 deduced a relatively strong bowing of C 0.415 eV.0092 0. Phys. Nonetheless.. GaInSb Although GaInSb cannot by itself be lattice matched to any of the readily available substrates. in the absence of experimental data for the X-valley gap. Appl. that result was discounted1.0092m 0 . Rev. Parameters eV Eg so Recommended values 0.43 0. Bowing parameters for the X. support a bowing parameter of 0.512. The recommended nonzero bowing parameters for AlInSb are collected in Table XIX. the data presented in clear form by Zitouni et al.25 eV in the split-off gap. We assume a linear variation of the interband matrix element and determine the F bowing parameter from that assumption. extrapolation to AlP gives a value for E g that is somewhat higher than the value listed in Table V for the binary also based on limited data .520 on the basis of a model of their galvanomagnetic measurements. No. so the article assumed a linear variation with composition . Redistribution subject to AIP license or copyright.518 which suggest a smaller L-valley gap for GaInSb than that for GaSb no estimate of the L-valley gap in InSb was available at the time.4 0. Linear interpolation is also suggested for the heavy-hole and split-off hole masses..523 The only other band structure parameter whose composition dependence has been studied is the spin-orbit splitting. Negligible dependence of the bowing parameter on temperature was obtained using the photovoltaic effect.511 The direct gap in AlGaP was studied by Rodriguez et al. it appears to be the best available approximation.13 eV for the lowest X-valley gap in AlGaP.260. A small bowing parameter of 0.1 eV was found for the spin-orbit splitting in GaInSb. see http://ojps. The different reports.1 0. Antimonides 1..org/japo/japcr.2 in favor of the electroreflectance determination of C 0. We conclude that the considerable uncertainty for the indirect gaps in GaSb and especially InSb translates into a poor understanding of the indirect-gap bowing in GaInSb. Parameters E g eV E X eV g E L eV g so eV * me * m lh 001 F Recommended values 0. C.33 0.84 Range 0. 537–539 Recently.43 eV.2. Nonzero bowing parameters for AlGaSb.22x 0 0 0. see http://ojps. 11.43 1.236 L-valley gap bowing parameters ranging from 0. the evidence for ordering is inconclusive at present.166 We recommend slightly higher values.0–1. They obtained direct-gap bowing parameters of 0. Apart from a considerably larger lattice mismatch.527 This is expected to give better results than using the Landolt–Bornstein bowing parameter1 or interpolating linearly between the masses in GaSb and AlSb.48 0.2 0.6 1. which produces little deviation from linearity at small x but also bowing parameters in the range suggested by Mathieu et al.543 from ellipsometry and photoreflectance studies. we recommend C(E L ) 0 and note that with this g choice the bowing in AlGaSb becomes rather similar to the case of AlGaAs covered above. D. it is recommended that the procedure outlined in the AlGaAs section be followed. values that have been used by many subsequent workers.47 eV at low temperatures and room temperature.544 Although they pro- Downloaded 05 Dec 2002 to 140.804–0. AlGaSb AlGaSb is an important material employed in high-speed electronic525 and infrared optoelectronic526 devices.530–535 It was noted in the first study536 of epitaxial GaAs0.236 for the spin-orbit splitting. theoretical studies101.48 eV were proposed for the -valley and X-valley gaps.251. and bowing parameters of 0.813 eV was measured by Merkel et al.09Sb0.22x.org/japo/japcr. and Ram-Mohan TABLE XXI.91 lattice matched to InAs.jsp .48 and 0. Since different growth temperatures were employed in recent studies of GaAs1 x Sbx with a rather small range of compositions near x 0.542 and quite recently a bowing parameter of 1.540 and Hu et al.807 eV was smaller than that implied by previously determined bowing parameters.2.527 However.35 .44 ¯ ¯ 0.2 eV have been determined by a number of workers from absorption measurements. Although there was an early indication of appreciable X-valley bowing. respectively.5.236 in the middle of the composition range with the inflection point at x 0.251 A much more comprehensive investigation was carried out by Alibert et al.61 ¯ VBO 3.09 eV have been published by Adachi.754 ¯ Parameters eV Eg EX g EL g so 5843 Recommended values 0. In spite of the fact that only x 0.528 The – L crossover composition is quite sensitive to the exact choice of the bowing parameters. 1 June 2001 TABLE XX. although it should also be noted that at x 0.542 suggested a bowing parameter of 0. The band structure in AlGaSb was originally studied by piezomodulation.75 eV are encountered in the literature. For electron effective masses in the AlGaSb alloy. Those results were confirmed by thermoreflectance spectroscopy performed by Bellani et al. 89.254 obtained a better fit to the absorption spectra by assuming a linear band gap variation at low Al mole fractions. Parameters eV Eg EX g EL g so Appl.2 1. The composition dependence of the GaAsSb effective mass was determined by Delvin et al.23 were determined on the basis of photoluminescence measurements529 and from wavelength-modulated absorption spectra.251 and Alibert et al.69 0–0.2 respectively. Nonzero bowing parameters for GaAsSb.44 eV.. a cubic band gap variation was proposed for the direct gap of Alx Ga1 x Sb:C 0.105.41 eV was obtained by Ferrini et al. Rough estimates of the bowing parameters for the X-valley and L-valley gaps both 1.5 alloys were investigated in that article.251 later reports have established that it is quite small or nonexistent.537 A lowtemperature bowing parameter of 1. which we recommend. Vol.3 eV was deduced by Alibert et al. We recommend a bowing parameter of 1.236.255.J.3 eV was determined for GaAs0. the GaSb/ AlGaSb heterostructure is a lower-gap analog of the GaAs/ AlGaAs material system. respectively.3 Recommended values 1. Mani et al. in order to assure consistency with both the experimental crossover points and the larger adopted direct-gap bowing parameter.5Sb0.91 is lattice matched to InAs. Redistribution subject to AIP license or copyright. Appl.27 and x 0.31. If those crossover points are to be consistent with our choice for the direct gap’s dependence on composition. On the other hand.. Phys. Phys. A bowing parameter of 0.69 and 0.044 1.1–1. although it was suggested that ordering effects may have reduced the band gap.2 eV are consistent with the reported measurements. No.42–1.11 On the basis of rather limited data. although this value should be revised downward if additional investigations substantiating the partial ordering in GaAsSb with compositions close to a lattice match with InP become available. Those results implied a bowing parameter of 1. Direct-gap bowing parameters in the range 1. Rev. recently Bignazzi et al. Therefore. a low-temperature E g of 0.: Vurgaftman. That is.528 Consequently. it must be considered to be the most reliable study to date.5 on InP in 1984 that the apparent band gap of 0.527.18–0.5 composition that matches the lattice constant of InP.1–0.21 to 0. Arsenides antimonides 1.1 eV for the spin-orbit splitting in GaAsSb.044 1.21–0.aip. L-gap and X-gap bowing parameters of 1. GaAsSb GaAs1 x Sbx is most often encountered with the x 0.541 and its temperature dependence was obtained. any nonlinearity in the composition dependence of the effective mass stems entirely from the bowing of the energy gap.6 eV.. Crossover compositions of x 0.06 Range 1.0–1. owing to the proximity of the two valleys in both GaSb and AlSb.236 who incorporated the results of many other reports. Range 1. The recommended nonzero bowing parameters for AlGaSb are collected in Table XX.8. Meyer.166 have derived a considerably larger value of 0. we must choose a very weak L-valley bowing. 25 eV 560 or a large 0. 2.201 The little experimental information that is available on AlAsSb alloys lattice matched to GaSb560 and InP561 can be interpreted to support either a small 0. 557 On the basis of all these investigations.171 The best fit to the data collected in that article favored a mass of 0. see http://ojps.8 0.105.145Sb0. Rev.160.0252m 0 .72–0.855. The recommended nonzero bowing parameters for GaAsSb are collected in Table XXI.446 While magneto-optical measurements by Kuchar et al.201. including lasers545 and photodetectors.6 eV.69 eV. it is an important material for a variety of mid-infrared optoelectronic devices.09).28 eV in accordance with photoluminescence and electroreflectance measurements. Bowing parameters for the two indirect gaps are both chosen to be 0. which is near the bottom of the reported range and roughly consistent with the results of assuming the mass bowing to be caused entirely by band gap bowing.548 This estimate was revised to C 0. We recommend the latter. Theoretical considerations led to a higher projected bowing parameter of 0. Smaller than expected band gaps were obtained for compositions close to the lattice-matching condition on GaSb (x 0.. we recommend a composite bowing parameter of 0.1 eV at room temperature.516 Experimental and theoretical data for the composition dependence of the spin-orbit splitting in InAsSb were collected by Berolo et al. Appl. InAs.562 The alloy becomes indirect for x 0.03–0.7 eV. E.58–0.261.0103m 0 for the alloy with the smallest direct gap (InAs0. A safer procedure is to take the mass nonlinearity to arise from the band gap bowing as outlined above. Meyer..552 from measurements on a sequence of InAs-rich samples. 89.: Vurgaftman.516 computed an even smaller value.15 1. Phys.6 0. No. Whereas many workers assume a linear variation of the direct energy gap in AlAsSb.2 eV.101 The recommended nonzero bowing parameters for AlAsSb are collected in Table XXIII.410 which is recommended by Rogalski and Jozwikowski. Parameters E g eV E X eV g E L eV g so eV * me ( ) Recommended values 0. which corresponds to a larger mass bowing.555 Marciniak et al.31.84 ¯ ¯ ¯ ¯ VBO Downloaded 05 Dec 2002 to 140. The recommended nonzero bowing parameters for InAsSb are collected in Table XXII.09 lattice matched to GaSb implies a similar bowing parameter of 1. Nonzero bowing parameters for AlAsSb. Redistribution subject to AIP license or copyright. the roomtemperature GaSb mass obtained in that study was significantly higher than our recommendation based on a consensus of other data. or GaSb substrates.559 theoretical projections indicate a bowing parameter in the 0. 164.84 eV range. Vol.28 0.58–0.8.560 The bowing parameter for the spin-orbit splitting 0.28 0. More recent photoluminescence studies on MBE-grown InAsSb obtained C 0.09.549 while Bouarissa et al.6 eV. Plasma reflectance and other measurements of the electron effective mass in InAsSb were summarized by Thomas and Woolley. C 0.553 obtained Varshni parameters for InAs0.166.446 who suggest a bowing parameter of 1. and gaps were extrapolated to lower temperatures in a linear fashion. That result agreed well with the theory developed by Berolo et al.547 Those studies were performed at temperatures above or near 100 K. and also disagrees with the model of Rogalski and Jozwikowski. Currently.26 eV. indicated an extrapolated band edge electron mass of 0.g.org/japo/japcr. Their measurements appear to support a smaller mass bowing as well as negative bowing for the interband matrix element.6). It is now understood that this resulted in an overestimate of the low-temperature energy gap and an underestimate of the bowing parameter.426. that finding is inconsistent with a linear interpolation of the interband matrix elements and F parameters between InAs and InSb.67– 0.91Sb0.548 A recent report of the electron effective mass in InAsSb is from a cyclotron resonance measurement by Stradling et al.325 eV in InAs0.55–0.035 Range 0. Parameters eV Eg EX g EL g so Recommended values 0.551. The possible importance of ordering has been discussed in several recent works Wei and Zunger.7 ¯ 0.8 ¯ 0.67 eV. the bowing parameters for both the X-valley and L-valley gaps are both thought to be 0. Our recommended bowing parameter for the electron effective mass is 0.035m 0 . although a great deal of uncertainty is inherent in assigning a value based on two data points. 11.556 . 1 June 2001 Appl. Arsenides phosphides 1.aip.1–1.. Nonzero bowing parameters for InAsSb.. Phys.184 for two alloy compositions.8 eV 561 value. and suggested a temperature dependence of the bowing parameter based on those results.161.15 eV is taken from the theoretical estimate of Krijn.45 at 0 K 482 when the X valley minimum crosses below TABLE XXIII. but also note that the uncertainty may not greatly affect most quantum heterostructures calculations in view of the large absolute value of the gap.5844 J.6 1.91Sb0.055 posed a bowing parameter of 0. InAsSb The InAsSb alloy has the lowest band gap among all III–V semiconductors.4Sb0.67 0. with values as small as 0. 3.550 Similar results e.2 0. The estimated558 spin-orbit splitting of 0.0088m 0 for InAs0.101.546 Initial reports put the direct-gap bowing parameter in InAsSb at 0. GaAsP GaAs1 x Px is a wide-band gap alloy that is often employed in red LEDs.554 Kurtz et al.jsp . and Ram-Mohan TABLE XXII.64 eV) were obtained by Gong et al. For that reason.71 Range 0–0. AlAsSb AlAsSb is a versatile large-gap barrier material that can be lattice matched to InP. Elies et al. the results of which have been summarized by Ait Kaci et al.65 eV by a more accurate pseudopotential calculation. We recommend a value of C 0. Rev. it has been noted that the bowing parameter more than doubles if CuPt-like ordering sets in. 1 June 2001 TABLE XXIV. Although the hydrostatic deformation potentials were found to be somewhat smaller than either of the binary values.20–0.566 While a recent ellipsometry study of disordered GaAsP alloys produced a direct-gap bowing parameter of 0.572 A recent fitting of the absorption spectra of InAsP/InP strained quantum wells also yielded a weak temperature dependence. from tunneling magnetospectroscopy576 and for three different compositions by Sotomayor Torres and Stradling using far-IR magneto-optics.174–0.22 0. Phys.482.54 eV.10 eV at 300 K.426.173 This work and also the subsequent magnetophonon experiments of Nicholas et al.16 eV was determined for the spinorbit splitting. and Ram-Mohan TABLE XXV. The effective mass for InAs-rich alloys was determined by Kruzhaev et al.577 Again.21 0. With these corrections..191 However. In fact.21 eV.27 0.31.575 found a nearly linear dependence of the mass on composition.16 Range 0.446 The electron effective mass in InAsP alloys was first investigated by Kesamanly et al.467.571 Whereas the first group reported a bowing parameter of 0.87–3 m . the most recent experimental results are in very good agreement with the assumption that both the interband matrix element and the F parameter vary linearly with composition.09–0. This is somewhat higher than the value suggested by Aspnes.175–0. Although the authors conjectured a reduction in the interband matrix element in the alloy. and absorption measurements.10 0. 93. No. their quantitative conclusions are in doubt since they overestimated the directgap bowing parameter as well as the interband matrix element for InAs. 11. Both experimental and theoretical results for the L-valley bowing parameter imply C 0. and has a high electron mobility.32–0. The deformation potentials in GaAsP were studied by Gonzalez et al.93.426 and Antypas and Yep.28 0.190 A k"P calculation with explicit inclusion of the higher conduction bands and slightly different band parameters predicts a small bowing parameter of 0.482. Nonzero bowing parameters for AlAsP.567 that outlying result lacks other verification and relied on only two data points with intermediate x. 191 We recommend following the general procedure tying the mass bowing to the direct-gap bowing as outlined above.105. later reported the opposite trend for the temperature dependence of C.19 eV for the direct gap at all temperatures.25 Appl.24 0. Redistribution subject to AIP license or copyright. Since a meaningful temperature dependence cannot be extracted from the existing data. Parameters eV Eg EX g EL g so 5845 Recommended values 0.27 0. Nonzero bowing parameters for InAsP. retains a direct gap throughout.16 Range 0.201 Using their projections.570 The shear deformation potential b found in that work lies between the recommended values for GaAs 2.16–0.572. suggested similar bowing parameters of 0. we recommend C 0. InAsP spans an interesting IR wavelength range 0. The recommended nonzero bowing parameters for GaAsP are collected in Table XXIV.12 eV. it is unclear whether a nonlinear term needs to be introduced for E P .: Vurgaftman. it has found far less practical use than its quaternary cousin GalnAsP because except at the endpoints the InAsx P1 x lattice constant does not match any of the binary III–V substrate materials.22 Range ¯ ¯ ¯ Downloaded 05 Dec 2002 to 140. However. the second group obtained a similar C at T 77 K but a much smaller value 0. 0.10 and 0.27 eV at 300 K.J.0 eV and GaP 1. there is not much controversy since the crossover composition is rather well established.562.8. 89. Our recommended value (C 0.22 0. Phys.0086m 0 .38 ¯ ¯ ¯ the valley minimum. x-ray diffraction.org/japo/japcr. Meyer. due to the experimental uncertainty it is difficult to determine whether the standard procedure needs to be supplemented.562–565 A small bowing parameter is also expected on theoretical grounds. we recommend C 0. Appl.482 The spin-orbit splitting was found to vary linearly with composition. Vol.28 eV. Parameters eV Eg EX g EL g Recommended values 0. 2. for both the direct and indirect gaps. The X-valley gap bowing parameter was studied by a number of workers. that may have been an artifact of the measurements rather than an alloy-specific property.568.36 eV throughout the entire temperature range. see http://ojps. which is consistent with the latest experimental works and is slightly lower than the theoretical estimate of 0. Nonzero bowing parameters for GaAsP.aip. TABLE XXVI.20–0. We therefore assume that either it was anomalous or some ordering did occur. InAsP The dependence of the energy gap on composition was originally studied by Vishnubhatla et al.23 eV.410 The bowing parameters for the indirect gaps were estimated by Adachi166 and Glisson et al. but with values between 0.573 Similar results were reported by Wada et al.16 eV. Bodnar et al.27 eV for both X and L valleys. A bowing parameter of 0.24 eV) lies approximately in the middle of the reported range of 0.569 Again.7 eV . Most experimental results for the direct-gap bowing parameter lie within a relatively narrow range..574 who used a combination of PL. which yields reasonable agreement with that theory and experiment.10 eV.93 partly because we employ a larger band gap for GaP at 77 K. Parameters eV Eg EX g EL g Recommended values 0.jsp .563 A linear variation of the electron effective mass with x in GaAsP was reported by Wetzel et al.158 and Nicholas et al.93.19 0. 75 eV see Table XXVIII . A recent experiment587 obtained an energy gap of 0.69Sb0.580 it cannot be ruled out that ordering substantially reduced the energy gaps in these and perhaps most other investigated GaPSb alloys.579 of alloys with a range of compositions apTABLE XXVIII.40Sb0. Parameters eV Eg EX g EL g Recommended values 2. surmised that the direct-gap bowing parameter in AlAsP would be quite small 0.19 eV and InAsP 0.7 2. A partial phase decomposition of the GaInN quantum wells employed in blue and green LEDs is believed to occur.2 eV for the direct-gap bowing parameter. The bowing parameter for the spin-orbit splitting has been calculated to be 0.0 3.1x 120. it is not unreasonable to assume the same values for their bowing.: Vurgaftman.578. which led the authors to conclude that the energy gap is direct. 3. The roomtemperature PL measurements of Shimomura et al. which is lattice matched to GaAs. Unfortunately. Phys. For other information available for these compounds.101. Nitrides 1. Nonzero bowing parameters for GaPSb. since no studies have been reported see Table XXVII . AlAsP If the exotic AlAsP alloy has ever been grown. which is our recommended value. our recommended direct-gap bowing parameter is C 1.580. considering the trends in the common group-III alloys. there is still considerable disagreement over such fundamental parameters as the bowing of the energy gap. and Ram-Mohan TABLE XXIX.35. Phosphides antimonides pears to be the most useful.2–2. Since these greatly exceed the available theoretical estimates.1x 16 – 9. Vol.579.201. AlPSb 1. one would not expect the bowing parameter to exceed those in GaAsP 0. 11.201. Since the indirect gaps in InPSb have not been studied. Parameters eV Eg EX g EL g so Recommended values 1. which act as efficient radiative recombination centers.9 1.68Sb0.8 ¯ ¯ Parameters eV Eg EX g EL g Recommended values 2.aip.2–2. F.9 1. Although further work will be needed to establish complete confidence.8.32 alloy. see Table XXXI and the text. Rev.8 and 2. which is lattice matched to an InP substrate. Since it is not yet clear whether this phase segregation has been comTABLE XXX.7 2. GaPSb The growth of GaPSb was first reported by Jou et al.7 Range 1. Subsequently.105.60 lattice matched to InP has been reported. We therefore recommend C 2.7 2. Meyer.9 0. Glisson et al. Strong PL was observed.2–2. is direct or indirect.7–3.75 Range 1.579 The primary object was to determine whether the energy gap in the GaP0.org/japo/japcr. Range 2. GaInN GaInN quantum wells represent a key constituent in the active regions of blue diode lasers and LEDs. However.7 eV lower bound were derived for the -valley and X-valley gaps.7 2. it may be argued that the analysis of their data should yield a more reliable value for the direct-gap bowing parameter (C 2. No.31 lattice matched to an InAs substrate.101 3.0 1. Nonzero bowing parameters for InPSb. Appl. Redistribution subject to AIP license or copyright.583–586 The study by Jou et al. it is likely that the gaps corresponding to the three major valleys have bowing parameters that are not too different from those in GaPSb.0 ¯ ¯ ¯ Downloaded 05 Dec 2002 to 140.293 This technological significance justifies the quest for a thorough understanding of the bulk properties of wurtzite GaInN alloys. InPSb The successful growth of AlP0. Loualiche et al.22 The energy gap in InPSb remains direct at all compositions. which implies an even larger value of the bowing parameter.582 produced approximately the same result.201 was C 1.7 eV see Table XXIX .22 eV . Bowing parameters in the 1. 89. Large bowing parameters of 3.9 15 4.jsp .65P0.166. Phys. The same C is also recommended for the X and L-valley gaps. 2.582 An early projection of Glisson et al.9 eV.7 eV).7 ¯ ¯ TABLE XXVII.22 eV see Table XXVI . 1 June 2001 Appl.5846 J.588 Nearly pure InN quantum dots are formed..0 0 16 – 9. G. see http://ojps.31. respectively. Materials Wurtzite GaInN Zinc blende GaInN Wurtzite AlGaN Zinc blende AlGaN Wurtzite AlInN Zinc blende AlInN Zinc blende GaAsN Zinc blende GaPN Zinc blende InPN Zinc blende InAsN Recommended values 3. Energy-gap bowing parameters for nitride ternaries.48 eV for InP0. it was apparently not reported. Nonzero bowing parameters for AlPSb.0 eV range have been reported for the direct gap.581 studied GaSb0. however.7 The recommended nonzero bowing parameters for InAsP are collected in Table XXV.4 – 100x 3. Since at this composition the direct nature of the energy gap is not in question.201 Using the criterion relating to the bond-length difference in the endpoint binaries. Early studies suggested an energy-gap bowing parameter C of between 0 and 1.: Vurgaftman. we suggest a bowing parameter of 3 eV for both the wurtzite and zinc-blende phases.aip. at least for small In fractions. and Ram-Mohan 5847 Materials Zinc blende GaInN Zinc blende AlGaN Zinc blende AlGaN Zinc blende GaAsN Recommended values 0.org/japo/japcr. which could lead to overestimates of the bowing parameter. Bowing parameters for quantities other than the energy gap of nitride ternaries.. for Ga1 x Inx N epilayers with x 0. Similarly large bowing parameters in the range 2.6 eV if our values for the energy gaps of GaN and InN are employed was found by Li et al.604 upward.603 Some of those works tentatively attributed the previous reports of small bowing to erroneous estimates of the alloy composition. a small bowing parameter of C 0.80 eV bowing parameters are taken from the empirical pseudopotential method calculations of Fan et al. 615 We recommend continued use of the accepted bowing parameter of 1. Several studies597. and that the parameters recommended in this review are provi- sional quantities that will almost surely be revised in the course of future work. Tight-binding calculations321 provide some support for our recommended standard procedure of using the band-gap bowing parameter to derive the compositional variation of the electron effective mass and interpolating the rest of the quantities linearly.611 Other workers quite recently calculated612 and measured613 smaller bowing parameters 0.5 eV. There is also a strong possibility that the alloys studied in recent works are not truly random. There is very little information on the other band parameters for GaInN. and established that a large reduction in the band gap should be expected for that scenario.jsp . is that the parameter set most relevant to a given theoretical comparison with data may not be that representing the ideal materials. 89. but rather the nonideal properties resulting from specific growth conditions of interest.61 eV and L-valley 0.616 We therefore recommend a zero bowing parameter for this case.610 found negligible bowing. Rev.599 suggested that the more recent PL emission may have resulted from local fluctuations in the In fraction.6 eV depending on the measurement method and assumed binary end points .589. see http://ojps.597–602 A bowing parameter of 2. Brunner et al.590 Wright and Nelson more recently derived C 1 eV for zinc blende GaInN.318 reported C 1. The experimental band gap results of McCluskey et al.4–4.38 0.596 Furthermore.594 Bellaiche and Zunger595 investigated the effects of short-range atomic ordering in GaInN.5 eV.369 3. although we emphasize that at present there exists no verification that this C applies equally well to higher In compositions.0 eV.8. Theory projects that the -valley bowing parameter in zinc blende AlGaN is small. AlInN Alx In1 x N is drawing attention because at x 0. Since the most important practical applications of GaInN alloys require only a small In fraction.593 A similar bowing parameter of 1. Phys. Subsequent early PL607 and absorption608 measurements found a bowing parameter of 1.78 eV reported for highly strained layers grown on SiC.369. Shan et al.0 eV until a broader consensus is reached on the effects of strain and other issues. A further comment which applies to all of the nitride alloys as well as other systems affected by unknown degrees and types of segregation. which continues to be widely used in band structure calculations even though a number of more recent investigations question the conclusions of the early work.591 2. Vol.80 0 pletely avoided in thicker layers of GaInN.J. Recommended values for the X-valley 0.592 A slightly larger bowing parameter 1.38 eV was estimated from first principles.591 This is consistent with the experimental report of a linear variation of PL energies in thin films of cubic AlGaN.12 were found to be consistent with bowing parameters as large as 3. the strain in which cannot be considered fully relaxed.83 it can be lattice matched to GaN.31. Although all of these studies are consistent with a bowing parameter of 1 eV for the random GaInN alloy.105.591 which is relevant because of the common expectation that the zinc blende and wurtzite alloys should have approximately the same bowing parameters. Cathodoluminescence measurements for AlGaN epitaxially grown on Si 111 suggest C 1. AlGaN AlGaN is often used as the barrier material for nitride electronic and optoelectronic devices. however.25–0. interpretation of the reported bowing parameters requires great care see Tables XXX and XXXI . The first experimental study observed such a strong bowing that the band gap for the lattice- Downloaded 05 Dec 2002 to 140. and it has been suggested that the other values resulted from an incomplete relaxation of strain in the AlGaN thin films.605 and negligible606 bowing.609 This statement is supported to some extent by a large bowing parameter of 1. Redistribution subject to AIP license or copyright. Meyer. Phys.0 eV. On the other hand. on the basis of PL from GaInN/GaN superlattices.5 eV were obtained in a large number of subsequent studies by different groups. Initial studies of the compositional dependence of the energy gap reported downward.3 eV and the data of Huang and Harris614 imply an even larger bowing parameter for AlGaN epilayers grown by pulsed laser deposition.402.4 eV was reported for zinc blende GaInN. several more recent investigations of GaInN layers with small In fractions arrived at significantly larger values. For the X-valley gap in zinc blende GaInN.. Parameters eV EX g EX g EL g so Appl. No. the results were given for relatively thin GaInN layers. Appl. Nakamura found that this bowing parameter produced a good fit to the results of PL measurements for low In compositions. although in both cases residual strain due to the differing lattice and thermal expansion coefficients of AlGaN and sapphire could have affected the results.7 eV can also be inferred from a recent investigation of zinc blende GaInN.61 0. It should be emphasized that the physical understanding of these materials is far from complete. 1 June 2001 TABLE XXXI. 11. first-principles calculations performed by those authors showed that the bowing parameter itself may be a strong function of composition.609. No upper limit on the composition.629 Other studies of dilute GaAsN indicated bowing parameters as large as 22 eV.875N0. In the absence of further information. 11.621 On the theoretical side.968x 6.623.617 Furthermore. As a general rule. Rev. The interband matrix element of GaAsN and other alloys such as GaPN is predicted647 to be strongly reduced relative to the virtual crystal approximation.566. Guo et al. The deformation Downloaded 05 Dec 2002 to 140. a first-principles calculation for zinc blende AlInN yielded a bowing parameter of 2.624 The somewhat unexpected discovery of a giant bowing parameter in this and other AB1 x Nx alloys in principle opens prospects for growing direct-gap III–V semiconductors with band gaps in the near-IR onto Si substrates.651 using electroreflectance measurements to determine the splitting between the heavy-hole and light-hole bands. GaAsN Although it has been known for a long time that small quantities of nitrogen form deep-level impurities in GaAs and GaP. the substantial differences between the properties of the light-atom constituent e.627 The same result was inferred from studies of the GaAsN near the two binary limits. which is important primarily at large N compositions.g. and then use the Peng et al. respectively.. with the decrease in the energy gap being linear for N fractions as high as 3%.620 gave a cubic expression for the energy gap.2% and 2% N has been reported. the most trustworthy quantitative report appears to be that of Peng et al. The energy gap is sublinear with composition for N fractions as small as a few percent.628 A quadratic form with C 11 eV fit the results of an ellipsometry study for x 3.15. No.630–632 A series of first-principles calculations examined various aspects of the band structure for GaAsN.105. which are of interest for most device applications. with values ranging from 20 eV for dilute alloys to 5 eV for concentrated alloys. 89. This description may in fact be a rather crude approximation of the band-gap dependence over the entire range of compositions.639 a compromise cubic form for the band-gap dependence on composition at all temperatures can be derived with the following nonlinear terms: 20. On the basis of the most complete available data set. quadratic and cubic terms at all temperatures.5%. This expression avoids the early semimetallic transition predicted by using C 20 eV that was not observed in the single relevant experimental study. for which this description is valid.2%. Uesugi et al. An alternative description of the energy gap in GaAsrich GaAsN in terms of the level repulsion model has been developed recently. Redistribution subject to AIP license or copyright.jsp . Nonetheless.1x 3 eV. has yet to be verified experimentally.31. based on results over the entire range of compositions. A potentially more accurate four-level repulsion model was recently introduced by Gil. The temperature dependence of the energy gap in a few GaAsN alloys was found to be much weaker 60% than that in GaAs for N fractions as small as 1%. An early theoretical study predicted a bowing parameter of 25 eV for the direct energy gap of GaAsN. The projected bowing parameters were large and composition-dependent varying in the range from 7 to 16 eV between GaAs0. However. beyond which no experimental data are available. including ordering effects.5 and GaAs0.g.641 found a more gradual reduction of the bowing parameter with composition. E g (300 K) 1.644 for two GaAsN alloys were found to lie between those of GaAs and zinc-blende GaN.566. This theoretical result.: Vurgaftman.618 and Kim et al. Peng et al. the suggested expression. GaN and the heavyatom constituent e.635 Recent experimental work on GaAsN with N fractions as large as 15% confirmed the strong composition dependence of the bowing.622 Of these.9x 2 9. Meyer.53 eV.626 C 18 eV was obtained from PL measurements of GaAsN with N fractions of no more than 1. Appl.8.org/japo/japcr.650 The valence-band shear deformation potential b in dilute GaAsN epilayers was studied by Zhang et al. which was assumed to be equal to that in the wurtzite alloy. and that a large miscibility gap will make it difficult to prepare alloys with large N fractions. with the conduction-band wave function strongly localized on the As sublattice and the valence-band wave function on the N sublattice. see http://ojps. an abrupt increase in the effective mass in GaAsN/ GaAs quantum wells with 1. we recommend that the temperature dependence be incorporated by using the recommended end points to fix the constant and linear terms at each T. The same approach is recommended for zinc blende AlInN. which indicated somewhat weaker bowing. it may be advisable to use that description rather than the nonlinear bowing approximation for low N compositions.639 A note of caution is that this expression is expected to be valid only in the region x 0.619 subsequently presented results for InN-rich and AlN-rich AlInN.4x 2 – 100x 3 eV.649 The effective mass is larger than that predicted on the basis of theoretical calculations. Vol.648.625 Furthermore. growth of the GaAsN alloy with appreciable close to 1% N fractions has been reported only recently. It is therefore expected that GaAsN and the other analogous alloys will crystallize in a zinc blende lattice. 4.645 The spin-orbit splitting obtained from electroreflectance measurements646 was found to vary approximately linearly in GaAsN. Phys.639. GaAs call for a close scrutiny of the usual quadratic relations for the alloy band parameters.. A similarly large bowing was observed by Yamaguchi et al.125 whenever the dilute alloy displayed a localized deep impurity level in the gap.642 The transformation from N acting as an isoelectronic impurity to band formation was found to occur at x 0.aip.3% fairly well. has been corrected to reflect our recommendations for the binary end points.643 The Varshni parameters measured by Malikova et al. Phase separation has indeed been observed in GaN-rich alloys. the non-nitride constituents do not easily take the wurtzite form. Furthermore.640 On the other hand.638. in view of the strong evidence for its correctness. is available at this moment and the results have been verified only for x 3%.633–638 Those studies found that the band-edge wave functions in GaAsN tend to be localized impurity-like states.97 1. 1 June 2001 Appl. and attributed the discrepancy to different strain conditions in the different studies.5848 J. Phys. since one expects the alloy concentration dependence to be highly nonlinear. and Ram-Mohan matched composition was found to be smaller than that of GaN. the standard quadratic expression did not fit the compositional variation of the band gap very well.5N0.. which is promising for 1.639 Their results are consistent with the predictions of another model. 657 These results are quite consistent with the picture developed by Shan et al.661 and one recent experimental study of the growth of this interesting ternary has been made. the interpolation procedure introduced by Glisson et al. Redistribution subject to AIP license or copyright. 89. however.201 usually provides a reasonable approximation. Meyer.8. Another recent tight-binding study663 showed that the band gap variation for small N fractions depends on the degree of ordering present in the material and that the maximally N-clustered alloy has a lower energy gap than the Asclustered alloy. since in thermal equilibrium the components often tend to segregate into inhomogeneous mixtures of binaries and ternaries. Appl.659 Provided the accuracy and validity limits of the ‘‘band anticrossing’’ picture are conclusively established. we refrain from exploring the consequences of the band anticrossing model in more detail. InAsN Most of the band properties of GaPN are expected to be analogous to those of GaAsN.660 In spite of the low solubility of N in InP. and Ram-Mohan 5849 potential did not follow a simple linear interpolation between GaAs and GaN.658 which challenges the once accepted wisdom that GaPN retains an indirect gap for very small N concentrations 1% . the momentum matrix element in GaPN is very small for almost any concentrated GaPN alloy. Using the notation from Eq. Phys. It remains to be determined which configuration can be realized experimentally.43% and demonstrated a red LED based on GaP0.: Vurgaftman.662 The primary importance of InAsN is that it serves as one of the end points of the GaInAsN quaternary. Pseudopotential calculations indicate that even though both GaP and GaN have substantial matrix elements. QUATERNARY ALLOYS The capabilities of III–V quantum well devices can frequently be expanded by introducing quaternary layers to the design. These results are quite close to the recent tight-binding calculations of Miyoshi et al.jsp . although it must be noted that the quadratic fit in Ref. In this review. No.55 m semiconductor lasers on GaAs substrates.. extensive miscibility gaps limit the range of stable compositions. It is applicable to the most commonly encountered quaternaries of the A x B 1 x C y D 1 y type.31. found where G AC and G BC are the values at the binary end points and C ABC is the appropriate bowing.101. 5. V. the theoretical approach summarized in Ref. This is our recommended value. they.J.166.626 Recently. 661 was rather poor. 11.652–654 Sakai et al.aip.201 While no single approach guarantees good results in all cases. According to the so-called ‘‘band anticrossing’’ picture. a given band parameter for the ternary A 1 x B x C is given by G ABC x 1 x G AC xG BC x 1 x C ABC .9m 0 ) electron mass in GaP0. and further studies over a wider composition range are required to pin down the possibly complicated N fraction dependence. GaPN a significant band gap reduction that corresponded to a bowing parameter in the range 13–17 eV.18 eV by a term linear in x for small x and varying as x for larger x. This increased flexibility does.1 InPN with less than 1% N has been studied by Bi and Tu. InPN A theoretical calculation of the band structure of InAsN has been reported. respectively. 6.652 and subsequent experimental data agreed with those projections.22 eV. Similar considerations apply to other low-N-fraction-containing alloys see Sec.org/japo/japcr. Phys. We recommend an average value of C 15 eV.1 .656 recently observed intense PL from GaPN alloys with a N fraction larger than 0.647 On the other hand. and refer the reader to Sec. which yields bowing parameters of 10 and 3. A tight-binding calculation661 deduced a bowing parameter of 4. which was obtained assuming a particular value 3. Furthermore.105. incorporation of even small amounts of N into GaP changes the nature of the fundamental optical transition from indirect to direct. Xin et al. 5.975N0. IV G 4 .655 and appear to be the best available values for interpolating between GaP and zinc blende GaN using the conventional model. since N incorporation is expected to affect primarily the conduction band of GaAsN. see http://ojps.989N0. General methods for deriving quaternary alloy band parameters from those of the underlying binary and ternary materials have been summarized by a number of authors.. used the same theoretical description and obtained similar results.025 /GaP quantum wells. The optical transition energy is smaller than the nitrogen level in GaP 2. The main complication is that GaP is an indirect-gap semiconductor. The recommended bowing parameters for all the nitride ternary alloys are collected in Tables XXX and XXXI. Both the -valley and X-valley gaps in GaPN were predicted to have bowing parameters of 14 eV. that are made up of two group-III and two group-V elements. These authors formulated a model based on the interaction between highly localized nitrogen states and extended states at the conduction-band minimum. Another piece of the evidence supporting strong – X mixing is the recent measurement of a heavy (0. Vol. 1 June 2001 Appl.011. The corresponding band parameter in the quaternary A x B 1 x C y D 1 y is then expressed as a weighted sum of the related ternary values: Downloaded 05 Dec 2002 to 140. 658 should be employed to determine the optical transition energies in GaPN. 7.9 eV for the X-valley and -valley gaps. IV G 4 for the necessary caveats. come at the expense of a more difficult growth coupled with the need for multiple tedious calibration runs to accurately fix the composition. Bi and Tu were able to observe the energy-gap variation for alloys incorporating up to 16% N.79 eV for the valence-band discontinuity between InAs and InN. inaccessible composition gaps remain for some of the III–V quaternary systems. based on the simple observation that the N impurity behaves in a similar manner in both GaAs and GaP. The cause is not quite clear. Rev. 4. While the nonequilibrium MBE growth process can extend the miscibility boundaries considerably. 3 tends to give better agreement with experiment than an alternative treatment of Moon et al. 6.51In0.g. PL excitation PLE .: Vurgaftman.51In0. Using C 0. or GaSb . Using linear interpolation for the X-valley energy gap in AlGaInP supported by the PL data of Najda et al. 5. In practice.507 . 5. 5..org/japo/japcr. at T 300 K.473.31.691z 0. types664 5.51In0.49P z .y(x) that are approximately lattice matched to one of the common binary substrate materials GaAs. Phys.3 for the energy gaps and spin-orbit splittings of several III–V quaternaries. which is expected on theoretical grounds because the two constituents have identical lattice constants. 2.49P) z /(GaAs) 1 z quaternary alloys.2 This approach can be extended to treat quaternary alloys of the AB x C y D 1 G ABCD x.500 and ellipsometry508 measurements indicated that a small additional bowing parameter between 0.5P.aip.51In0. The quaternary may then be represented as a combination of two lattice-matched constituents. 6. Appl.15Ga0. linear interpolation of the end point ternary masses should also give adequate results.4 AlInP. which is considerably easier to grow. one of which must be a ternary while the other may be either a binary or a ternary. however. 11. except that electron masses in the lattice-matched ternaries should be used as the end points in place of binaries. In this particular example. Redistribution subject to AIP license or copyright. There has been little motivation to pursue this quaternary.49P and Al0.51In0.. lattice matched to GaAs.49P) 1 z and (Ga0. 5. InAs. in which the -valley gap is given by a solid curve and the X-valley gap by a dashed curve. we will assume two lattice matched e.502 There appears to be only one cyclotron resonance study of the electron mass in Al0. more accurately. most experiments have focused on the onedimensional subsets. 5. The treatment is considerably simplified by the usual absence of any strong bowing of the band parameters for such an alloy. as expected.201. For example.2 and 5.67 . Phys. and Ram-Mohan G ABCD x.665 which is known to overestimate the quaternary bowing. No.55. y 1 x y x 5.498 Early studies of lattice-matched AlGaInP.3 or simple linear interpolation.48P) z / Ga0.666 Krijn101 gives polynomial expansions of Q(x.51In0.2 and 5.49P is indeed nearly linear.g. 5.51In0. Meyer. 89. Downloaded 05 Dec 2002 to 140. Lowest energy gaps as a function of composition for (Al0.494.502 thermoreflectance. since its direct band gap spans roughly the same range as direct-gap AlGaAs.y . which is a quaternary of the second type with one group-V element . Generally speaking. The region of AlGaInP for which the X-valley gap is lowest is indicated with a dashed line. Rev. v (2 x 2y)/2.51In0.48P) z /(Ga0.18 eV is needed to fully account for the data.49P or. For lattice-matched quaternaries.505. which are combined with arbitrary composition z to form the lattice-matched quaternary alloy 1 z z . A. In the following.4 can be used to find the lattice-matched AlGaInP gaps for all z and T.8. and w (2 2x y)/2.5850 J.11 and 0. 495 in which ordering and L-valley interactions could have distorted the reported electron mass of 0. there has been some work668.507 The composition-dependent variation of the 300 K energy gap in the lattice-matched quaternary (Alz Ga1 z ) 0. see http://ojps.18 eV in conjunction with the recommended expressions for the temperature-dependent direct gaps of GaInP and FIG.4 with the available experimental evidence to determine C for each property should lead to a better representation than either the procedure of Eqs.35In0.. It is therefore suggested that the standard procedure be followed. AC 1 y D y . binary or ternary end points. We then employ the expression G z 1 z G zG z 1 z C .3 where u (1 x y)/2.49P is plotted by Fig.007(1 z) 2. a given quaternary comprises a vast two-dimensional space of compositions.105.669 on latticematched and strained alloys in the vicinity of z 0.507 electroreflectance. InP.y) derived from Eqs. for 1. GaInAsP where G and G are the values at the end points and C is the additional bowing associated with combining the two end point materials to form a quaternary. Lattice matched to GaAs Not very much is known about the band structure of GaInAsP lattice matched to GaAs or (GaAs) 1 z Ga0.jsp . (Al0.14m 0 .18z(1 z) eV.52In0. found that the band gap variation between Ga0. Vol. we find that the direct-to-indirect crossover at 0 K should occur at z 0. subsequent PL.y x 1 x 1 y G ABD x yG ABC x x 1 x y 1 y 1 y xG ACD y y x y 1 x G BCD y and B x C y D 1 yA .y xyG ABD u y 1 x xy y 1 x x y G BCD v 1 x y xG ACD w . AlGaInP (Alz Ga1 z ) 0. 1 June 2001 Appl. x. A 1 x B x C and e. The approach of Eqs.49P 1 z lattice matched to GaAs is often employed as the barrier and cladding material in GaInP/AlGaInP red diode lasers. Linear interpolation between the latticematched alloys is also suggested for the L-valley gap and the spin-orbit splitting.494. which is in good agreement with experiment.2 and 5. Eq. at T 0 we obtain E g 2.52In0. However. x.667 However. using Eq.. GaInAsP Band gaps for strained AlGaInAs on GaAs with low Al and In fractions have been reported by Jensen et al. Vol. The compositionC X 0.670 on the basis of the experimental result of Jones et al.4 This procedure yields E g 1.25 eV underestimated the gaps somewhat in analyzing their electroreflectance data. the alloy may be thought of as (GaAs) 1 z InAs0. An alternative approach proposed by Chow et al. Lattice matched to InP 1.427. For the most part. The results of absorption672 and photomodulation spectroscopy673 are in accord with the PL measurement of Jones et al. lattice matched to InP.62 eV.677 and at least one book. Energy gaps as a function of composition for (InP) z (Ga0.47z.6. at T 300 K.jsp . 1 June 2001 Appl.53As z . a small spread in the experimental data was found.149 eV.73 for the direct-to-indirect crossover point. 5. 4. a straightforward evaluation of the bowing parameters for the lattice-matched quaternary (GaAs) 1 z Ga0.677 and deduced a bowing parameter of 0. Since the authors greatly overestimated the X valley gap in InAs. their corresponding bowing parameter cannot be considered reliable. and Ram-Mohan 5851 which the quaternary constituents may be rewritten (GaP) x InAs 1 x with x z for the case of lattice matching to GaAs .J. 3.13 at all temperatures. The recommended parameters imply a direct band gap at all compositions z.53As) 1 z quaternary alloys.51In0. GaInAsP lattice matched to InP (InP) 1 z Ga0. No.816z 0. where is the difference between the in-plane strains computed for the Incontaining ternary and quaternary we have revised the coefficient in order to fit our band-gap scheme . GaInAsN The GaInAsN quaternary has drawn considerable attention recently. Absorption measurements669 yielded x c 0.55 m and electronic especially high-electron-mobility transistor devices.8.62N0. An early tightbinding calculation also yielded a bowing parameter of 0.53As) 1 z . and such experiments may run into difficulty in the future owing to the expected miscibility gap. which is Gax In1 x Asz P1 z with x 0. and it was pointed out that Perea et al.31.53 eV and C dependent variation of the 300 K energy gap in GaInAsP lattice matched to GaAs is plotted in Fig. Phys. Unfortunately.3 and 1. not z with GaAs and Ga0. Instead we adopt their direct-gap bowing parameter of 0.671 Pseudopotential calculations674 are in good agreement with this approach for low N fractions. It should be noted that results for the GaP-rich quaternary do not necessarily support upward bowing. This alloy has been the subject of numerous review articles5. IV G 4.681. In terms of the band structure properties. which is consistent with the relations currently employed to estimate device characteristics.682 .38) z and represents a quaternary analog of the nitrogen-containing zinc blende ternaries discussed in the previous section.682 Although the band gaps obtained in the two studies were similar.47In0.429.aip.671 is to derive the energy gap from the GaInAs alloy with the same In fraction and then reduce it by 53 eV.038 eV.674.737z 0.51In0. and (GaAs0.13z 2 eV at 0 K and E g 1. Two studies have reported Varshni parameters for GaInAsP. Deducing the temperature variation of the quaternary band gap from the bulk Varshni parameters given above is therefore probably a safer procedure and gives reasonable agreement with the results of Satzke et al.53As) 1 z . 7. AlGaInAs FIG.4 Numerous measurements of the direct energy gap in GaInAsP have been reported. 6. Meyer.49P as end points .40 eV and estimate C X 0.4236(1 z) 0.28 eV from the crossover composition note that these bowings are in terms of x with GaP and InAs as end points. B. the resulting Varshni parameters were very different.13z 2 eV at 300 K.19 eV. (Al0.105..org/japo/japcr.48In0. Appl.353(1 z) 0.443. Rev.52As) z (Ga0.4 with a bowing parameter of C 0.666. Phys. whereas a linear variation does produce a reasonably good fit.441 on the basis of PL measurements. since the addition of a small N fraction compensates the compressive strain that limits the critical thickness of GaInAs layers grown on GaAs substrates. 7. Calculations and measurements for GaInAsN lattice matched to InP have also been reported.47In0. is an extremely important quaternary alloy.678–680 Pearsall summarized the experimental results available by 1982 in his review. A linear variation is usually assumed for the indirect band gaps Downloaded 05 Dec 2002 to 140.47In0.47In0.443 (C 0.49P z gives 0.676 This result appears to invalidate any simple interpolation scheme and favor the authors’ proposed model of the interaction between localized N states and the extended states of the semiconductor matrix as discussed in Sec.5) z (Ga0. We recommend using Eq. 89.: Vurgaftman. Further electroreflectance experiments of Lahtinen and Tuomi680 indicated a substantially smaller bowing parameter of 0. Redistribution subject to AIP license or copyright. It is currently employed in commercial optoelectronic especially semiconductor lasers emitting at 1.675 Recently. the properties of InAsN have not been measured.47In0.428 with error bounds sufficient to include almost all of the experimental data sets.53As z is plotted in Fig. a large increase in the electron mass in GaInAsN with a small N fraction was observed via reflectivity measurements. 11. see http://ojps.5Sb0. Using the results for (GaP) x InAs 1 x discussed above. The composition-dependent variation of the 300 K energy gap in the lattice-matched quaternary (InP) 1 z Ga0.. 47In0. Fan and Chen obtained a 1. The approximate location of the miscibility gap according to recent calculations689 is indicated with the dotted line.79 eV . we obtain a composite direct-gap bowing parameter of 0.5) 1 z has been reported over the entire composition range. 447 and 458. Using our adopted band gap variation and interpolating the interband matrix element and the F parameter linearly. Based on this data point we recommend a composition dependence of E g (T 0) 0. 449.36As0.31. the split-off mass can be determined using Eqs. even though the cutoff wavelengths are close to the important 1..6 eV or Ga0.677 However.683 We derive our recommended value of 0.aip.52As) z Ga0. and 684.47In0.448.53As and 0. and requires a rather large bowing parameter of C 6. 3.016m 0 .48In0.453.48In0.688 as compared to 0. Rev. for which there is strong evidence for a slight upward bowing.679 This upward bowing was explained by considering the interband and intraband contributions to disorder-induced mixing of conduction-band and valence-band states. the usefulness of this quaternary is limited because both end points have nearly the same energy gap.52As in that scheme. we recommend using a slightly modified version of the Adachi expression.105. see Fig. with C 5. Adachi suggested a bowing parameter of 0.456 who found a direct-gap bowing parameter of 0.225 eV between those two extremes. By measuring the pressure dependence of the stimulated emission in a buried heterostructure near-IR diode laser.48In0.55 m low-loss window for optical fiber communications.459 On the basis of those data.: Vurgaftman. The only other AlGaInAs band structure parameter with a validated nonlinear compositional variation is the electron effective mass. Appl.63 in Al0.22z(1 z) eV. 5.6.33z 0.g.685 This represents a smaller absolute value than in either InP 6. which combines two lattice-matched ternary alloys. 448.687. Meyer.691 The growth of slightly strained GaInAsSb layers has also been reported by Shin et al.469 This can be explained by disorderinduced band mixing.64In0.808(1 z) 0. we find the totality of the data to be consistent with that procedure. 1 June 2001 Appl.47In0.47In0. Lattice matched to InAs Another important quaternary lattice matched to InP is AlGaInAs or (Al0. and Ram-Mohan between the two end point materials.4 and 2.47In0. The light-hole effective mass in GaInAsP lattice matched to InP was measured by Hermann and Pearsall.7 in Ref. 453.0302z 2 ) eV. 7. m * (0.688 However.53As( 7.68 eV adjusted to provide the correct result for AlGaInAs with x 0. which is close to the values of Olego et al.108(1 z) C( so) so 0.099z lh 0.816z 0. the growth of metastable GaInAsSb lattice matched to InP or (Ga0.470 Averaging the various experimental results.465 and Cury et al.06 eV.5Sb0. in order to assure consistency with the end point values in Ga0. here we suggest an effective-mass bowing parameter of 0.684 while others obtained appreciable downward bowing.84Sb0.22 eV.5.684 Some studies found roughly zero bowing. GaInAsSb Despite the presence of a miscibility gap. 11. Whereas the evidence for a similar mechanism in GaInAsP was inconclusive.5) 1 z is plotted in Fig. The recommended composition-dependent variation of the 300 K energy gap in the lattice-matched quaternary (Ga0.680 or negative.68 eV.89 in Ga0. 89.686 suggested a large bowing parameter of 0.18 . Phys. it was claimed that the lack of effective mass bowing was due to the band gap bowing being compensated by a disorder-induced bowing of the interband matrix element. No.52As) z Ga0. GaInAsSb GAInAsSb lattice matched to InAs or (InAs) 1 z GaAs0. 2. 6. but not nearly as small as in Ref.443.7 eV was determined for Gax In1 x Asz P1 z with y 0. Electroreflectance studies have concluded that the bowing parameter for the spin-orbit splitting is either close to zero678.165.4 .453 In the former case.16 at 8 K implied a gap of 0. The electron mass in GaInAsP has been measured by a variety of approaches such as cyclotron resonance. magnetophonon resonance. Shubnikov–de Haas oscillations.448–451.6 eV suggested by Downloaded 05 Dec 2002 to 140. a hydrostatic deformation potential of a 5.92) z has been studied by a number of authors. This is consistent with the other parameters if E P is assumed to have a quadratic dependence.20 eV when cast into the form of Eq.1208 0. Vol.451.458 while Shen and Fan calculated a rather small bowing using the tight-binding method with the virtual-crystal approximation.47In0. The F parameter is then interpolated linearly between 2.8. see http://ojps.81 eV at the two end points.53As 1 z .53As) z GaAs0. The resulting masses are slightly lower than those in Refs.53As 1 z is plotted in Fig.458 whose effect on the interband matrix element is described by expressions in Refs.7654 eV.06z 2 eV. by averaging all reported spin-orbit bowing parameters.jsp .08Sb0. Subsequent PL measurements of Kopf et al.690.456 and Fan and Chen.687 whereas more recent PL measurements on bulk Ga0. While we recommend this value in the absence of other information.457. 4 However. AlGaInAs value of 0. from a consideration of all available experimental data there is no obvious reason to deviate from our standard mass-bowing procedure e. Further study is clearly desirable. The first reported growth and characterization study of this quaternary obtained little bowing.450.5852 J.org/japo/japcr.47In0. which implies 0.7 eV. 5. Phys. additional experiments are necessary to confirm this strong bowing. C.449.03m 0 .5Sb0. whereas the lowtemperature PL results of Bohrer et al.. 4 .457 implied a linear variation of the energy gap. Redistribution subject to AIP license or copyright. Using linear interpolation for the heavy-hole mass and the valence-band anisotropy. The precise extent of the miscibility gap depends on the growth procedure and temperature.4 although that dependence has apparently not been verified experimentally. and shallow donor photoconductivity. Initial characterization of this quaternary was performed by Olego et al. the available results are consistent with the relatively large bowing parameter of 0..458 The composition-dependent variation of the 300 K energy gap in the lattice-matched quaternary (Al0.53As) z GaAs0.53As and InP. 7. and the growth of metastable materials inside the gap is not ruled out.692 Although data for the composition dependence of the direct band gap are somewhat sparse.447. J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Appl. Phys. Rev.: Vurgaftman, Meyer, and Ram-Mohan 5853 FIG. 8. Energy gaps as a function of composition for (InAs) 1 z (InSb0.31P0.69) z and (InAs) 1 z (GaAs0.08Sb0.92) z quaternary alloys, lattice matched to InAs, at T 300 K. The approximate locations of miscibility gaps are indicated by dotted lines. Levinshtein et al.11 see also Fig. 3 of Ref. 691 . This is our recommended value, which implies E g (T 0) 0.412z 0.876(1 z) 0.6z(1 z) eV. In the following section it will be seen that this value is similar to the recommended bowing parameter for GaInAsSb on GaSb, which is not surprising in view of the near equality of the InAs and GaSb lattice constants. The empirical relation suggested in Ref. 691 also appears to produce good agreement with the data, although it cannot be recast in the form of Eq. 5.4 with a constant bowing parameter. While in one study Varshni parameters have been deduced for GaInAsSb on InAs,165 it is recommended that our usual procedure be followed to derive the temperature dependence of the energy gap in this quaternary. The composition-dependent variation of the 300 K energy gap in GaInAsSb lattice matched to InAs is plotted in Fig. 8. The approximate location of the miscibility gap is indicated by the dotted line. Bouarissa693 obtains X-valley and L-valley bowing parameters of 0.15 and 0.60 eV from pseudopotential calculations accommodating the effects of alloy disorder. 2. AlGaAsSb fully grown on InAs substrates (InAs) 1 z InSb0.31P0.69 z , where z x y by several groups.583,695–697 Because of the large uncertainty in the InSb0.31P0.69 energy gap, the first study tried to use the quaternary data, assuming a linear variation between the InAs and InP0.69Sb0.31 end points, to deduce the bowing parameter for the ternary.583 Subsequent studies similarly derived a vanishing bowing parameter for the quaternary.695–697 Since with that assumption the most recent data696,697 are consistent with our adopted band gap for InP0.69Sb0.31, we recommend C 0. However, Adachi166 suggested the possibility of upward bowing based on the general quaternary relations of Glisson et al.,201 and the data of Voronina et al.695 can possibly be explained in that manner. The recommended composition-dependent variation of the 300 K energy gap in InAsSbP lattice matched to InAs is plotted in Fig. 8. The approximate location of the miscibility gap is indicated with a dotted line. The spin-orbit splitting in InAsSbP has been found to be larger than in either InAs or InP0.69Sb0.31, 696 although only theoretical estimates are available for the latter. The measurements imply the form: so 0.39(1 z) 0.166z 0.75z(1 z), where the upward bowing parameter is larger than in Ref. 696 owing to a different value assumed for InPSb. While an electron effective mass of 0.027m 0 determined698 for InAs0.62Sb0.12P0.26 is lower than the value of 0.0288m 0 derived from a linear interpolation of the interband matrix element and the F parameter, the latter is nonetheless quite close to the band edge mass found from the band structure fits to the carrier density dependence performed in the same reference. We therefore recommend employing the usual procedure. D. Lattice matched to GaSb 1. GaInAsSb The direct and indirect energy gaps in AlGaAsSb lattice matched to InAs or (GaAs0.08Sb0.92) 1 z (AlAs0.16Sb0.84) z were studied theoretically by Adachi,166 and Anwar and Webster.559 They respectively employed expressions suggested by Glisson et al.201 and Moon et al.665 who combined the direct and indirect-gap composition dependences . Abid et al.694 also treated AlGaAsSb, using the empirical pseudopotential method with the virtual crystal approximation. That little bowing was found for any of the energy gaps may be an artifact of neglecting the disorder potential. We therefore recommend using the bowing parameters specified below for AlGaAsSb on GaSb. 3. InAsSbP InAs1 x y Sbx Py is the only quaternary with three group-V elements that has been studied in the literature. In spite of some miscibility-gap problems, it has been success- GaInAsSb lattice matched to GaSb or (GaSb) 1 z (InAs0.91Sb0.09) z is particularly well studied,699 in part because it is an important active-region constituent of diode lasers emitting at 2 m. 700 Early work687,690,701 on the direct band gap in GaSb-rich GaInAsSb was summarized by Karouta et al.,558 who suggested a bowing parameter of 0.6 eV. At the other extreme, data for InAs0.91Sb0.09-rich alloys were found to be consistent with a slightly higher bowing parameter of 0.65–0.73 eV.695,702 Photoreflectance studies by Herrera-Perez et al.703 and spectral ellipsometry results of Munoz et al.704 support an even higher value for C. Similarly, recent reports of GaInAsSb grown by liquid-phase epitaxy tend toward higher bowing parameters.705,706 Our recommended value of C 0.75 eV is a composite obtained by averaging all of the available results. The dependence on composition is then: E g 0.812(1 z) 0.346z 0.75z(1 z) eV at 0 K and E g 0.727(1 z) 0.283z 0.75z(1 z) eV at 300 K. The data of Karouta et al.558 suggest C 0.26 eV for the spin-orbit splitting, which implies: 0 0.76(1 z) 0.33z 0.26z(1 z) eV. However, this expression is at variance with the recent ellipsometric data of Munoz et al., which suggests downward bowing of the spinorbit splitting with C 0.25 eV. 704 The latter result was obtained only for compositions of z 0.14– 0.15. Both the Downloaded 05 Dec 2002 to 140.105.8.31. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 5854 J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Appl. Phys. Rev.: Vurgaftman, Meyer, and Ram-Mohan E. Other substrates 1. AlGaAsP AlGaAsP has been grown on commercially available GaAs0.61P0.39 substrates.711–713 It can be considered as a combination of GaAsP and AlAsP alloys with phosphorus fractions similar to the substrate. A careful investigation of the pump intensity dependence of the PL peaks revealed both impurity and band-to-band transitions.711 Those results imply a surprisingly large direct-gap bowing parameter of 1.3 eV for the quaternary. However, that value would be reduced considerably if it turns out that the theoretical projection of 0.22 eV for the bowing parameter in AlAsP see above is too small. FIG. 9. Energy gaps as a function of composition for (GaSb) 1 z (AlAs0.08Sb0.92) z and (InAs0.91Sb0.09) 1 z (GaSb) z quaternary alloys, lattice matched to GaSb, at T 300 K. The approximate location of a miscibility gap for InGaAsSb is indicated by a dotted line. F. Nitride quaternaries downward bowing of the energy gap and the upward bowing of the spin-orbit splitting are well described699 quantitatively by the expression of Moon et al.,665 although it should be remarked that in performing such calculations some authors used different bowing parameters for the related ternary alloys.695 Energy gaps for certain strained GaInAsSb compositions have also been reported.707–709 The compositiondependent variation of the 300 K energy gap in GaInAsSb lattice matched to GaSb is plotted in Fig. 9. The approximate location of the miscibility gap is indicated by the dotted line. Pseudopotential results of Bouarissa710 predict bowing parameters of 0.85 and 0.43 eV for the L-valley and X-valley gaps, respectively. The direct-gap bowing parameter quoted in that reference is in reasonably good agreement with the experimental results. The growth of AlGaInN has been reported,602,621 although little is known about its band structure properties. Recent results indicate a nearly linear band gap reduction for small In compositions 2% .714 The cutoff wavelengths of AlGaInN lattice matched to GaN ultraviolet photodetectors were also generally consistent with a linear interpolation.715 Improved crystal quality in comparison with AlGaN has also been noted.716 Until more precise data become available, we suggest employing the usual quaternary expressions in order to estimate the parameters of this poorly explored material. VI. HETEROSTRUCTURE BAND OFFSETS 2. AlGaAsSb AlGaAsSb lattice matched to GaSb or (GaSb) 1 z (AlAs0.08Sb0.92) z is a natural barrier and cladding material for mid-infrared semiconductor lasers. Relations for the direct and indirect energy gaps were calculated by Adachi,166 and the experimental results have been summarized by Ait Kaci et al.560 The quoted direct-gap bowing parameter of 0.47 eV agreed well with the pseudopotential calculation of Abid et al.694 and the photoreflectance measurements of Herrera-Perez et al.703 Based on all of these data points, we recommend a composite result of C 0.48 eV. The band gap at 300 K is then: E g 0.727(1 This compositionz) 2.297z 0.48z(1 z) eV. dependent variation of the direct energy gap in AlGaAsSb lattice matched to GaSb is plotted in Fig. 9. Although general considerations imply that the bowing of the L-valley gap should be similar while the X-valley gap pseudopotential should display little bowing,166 694 calculations have suggested bowing parameters of 0.807 and 1.454 eV, respectively. A consequence of the large X-valley bowing would be a decrease of the predicted directto-indirect crossover composition to z 0.14. The preceding sections have discussed the bulk properties of III–V semiconductors and their alloys in isolation. In this section, we turn to a consideration of the conduction and valence band alignments that result when the materials are joined to form heterojunctions in various combinations. Fortunately, it is usually a good approximation to view the valence band position as a bulk parameter for each individual material, which can then be subtracted to determine the relative band alignment at a given heterojunction. The interface dipole contribution, that is particular to each material combination tends to be small, since it is largely screened even when the interface bonding configurations are vastly different. However, it will be seen below that at least for the case of an InAs/GaSb interface, which has no common anion or cation, there is reliable experimental evidence for a small dependence of the offset on the interface bond type. Our discussion will build upon the previous summary of Yu et al.717 who comprehensively reviewed the understanding of band offsets as of 1991. That work, which may be considered an update of earlier reviews by Kroemer,718,719 also provided an excellent overview of the methods commonly used in experimental band offset determinations. Some of the existing theories, such as the model solid theory of Van de Walle,129 assert that very little bowing of the valence band offset should be expected although some bowing may arise if there is a strong nonlinearity in the spin-orbit splitting . However, if we are to maintain consistency with the most reliable experimental results for a variety of heterojunctions e.g., GaAs/AlAs and lattice-matched Ga0.47In0.53As/Al0.48In0.52As , a bowing parameter must be assigned to some of the ternary alloys. Since there are almost Downloaded 05 Dec 2002 to 140.105.8.31. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp J. Appl. Phys., Vol. 89, No. 11, 1 June 2001 Appl. Phys. Rev.: Vurgaftman, Meyer, and Ram-Mohan 5855 FIG. 10. Conduction filled and valence open band offsets for the 12 binaries. The -valley energy gap for a given binary corresponds to the difference between the conduction and valence band positions, i.e., the length of the vertical line connecting the filled and open points. Similarly, the conduction valence band offset between two distinct binaries corresponds to the energy difference between their respective conduction or valence band positions on the absolute energy scale of the figure. FIG. 12. Conduction band offsets corresponding to the VBOs in Fig. 11. The various points and curves have the same meaning as in that figure. no reports of temperature variations that exceed the experimental uncertainties, in all cases we will take the valence band offsets to be independent of T. Recommended valence band offsets VBOs open points and conduction band offsets CBOs filled points for all 12 of the binaries are summarized in Fig. 10. The extent of the energy gap for each material is indicated by the vertical line. Relative positions of the CBOs and VBOs in this figure may be compared to determine the offset for any given heterojunction combination. The recommended VBOs for materials lattice matched to the common substrate materials of GaAs, InP, InAs, and GaSb are shown in Fig. 11. The points indicate offsets for binary and ternary compounds, while the vertical lines signify VBO ranges that are available using lattice-matched quaternaries. Since a linear variation with composition is assumed for all quaternaries, simple interpolation between the end point offsets yields the VBO for any desired quaternary alloy. The dashed lines illustrate VBO variations in a number of important lattice-mismatched ternary alloys. Corresponding conduction-band offsets are given in Fig. 12. Although strain effects are neglected in these plots, they are relatively strong and must be included to determine the correct CBO. Note also that since the band gap variation with composition is in general nonlinear and sometimes double valued , a given point on one of the vertical lines in Fig. 12 does not necessarily map to a single, distinct quaternary alloy composition. A. GaAsÕAlAs FIG. 11. Valence band offset as a function of lattice constant. The offsets for binaries and lattice-matched ternaries are indicated by points, offset variations with composition for lattice-mismatched ternaries not including strain effects are given by dashed curves, and the VBO ranges for quaternary alloys lattice matched to a particular substrate material GaAs, InP, InAs, or GaSb are given by the vertical solid lines. The GaAs/AlAs heterojunction, which is unique among the III–V semiconductors in terms of growth quality and lattice match, is also the one that has received the most intensive investigation over the years. Although the early work by Dingle et al.720,721 suggested that nearly all of the discontinuity was in the conduction band, later measurements established the well-known 65:35 split between the conduction and valence bands, respectively.717 Batey and Wright examined the full range of AlGaAs compositions and found that a linear variation of the band offset with Al fraction fitted the results quite well.722 Although other reports have implied a slight deviation from linearity,723 we will take the small bowing to occur entirely in the CBO. With this assumption, we average the results obtained for GaAs/AlGaAs by various measurement methods717,724–743 to obtain the relative VBO between GaAs and AlAs. The result is E v 0.53 eV 0.34 E g , which is the best known value for all of the III–V semiconductors and is well within the uncertainty limits of most experiments. Ref. 717 presented a compilation of early theoretical results for the GaAs/AlAs band offset. While our composite experimental value agrees quite well with the predictions of first-principles calculations by Christensen,744 Lambrecht et al.,745 and Wei and Zunger,746 the model-solid theory of Van de Walle129 obtained a slightly larger offset of E v 0.59 eV and the transition-metal impurity theory of Langer et al. yielded a smaller value of 0.453 eV.747 Similarly small values were also predicted by the dielectric midgap energy models of Cardona and Christensen748 and Lambrecht and Downloaded 05 Dec 2002 to 140.105.8.31. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp 759.769–774 One group reported noncommutativity with a 53 meV band-offset difference for that heterojunction.608–0.5856 J.768 The average VBO of 0.755. Making use of the already determined GaAs/AlAs VBO. we can also derive the difference between the offset bowing parameters for the two alloys.53As/InP band offset. irrespective of the growth sequence.770 A first-principles pseudopotential calculation by Hybertsen763 found the GaInAs/InP offset to be transitive to within 10 meV.23 eV once again agreed reasonably well with the experiments that did not find transitivity violations.754 0. from photoreflectance data on single quantum wells. CBO determinations include 0. direct measurement of its band offset is considerably complicated by the high degree of strain that was not present in the more straightforward GaAs/AlAs and Downloaded 05 Dec 2002 to 140. Phys. A much larger CBO of 0.21 eV .752 0.717 and subsequent data have consistently favored a CBO in the 0.47In0. 1 June 2001 Appl. Rev. This is higher than the value of 0. Redistribution subject to AIP license or copyright.47In0. yielded a VBO of 0. depending on whether the growth sequence employed InAs-like or GaInP-like interface bonds.52As results. observed nontransitivity for the GaInAs/AlInAs CBO using a combination of internal photoemission.048 eV suggested by the averagebond-theory results of Zheng et al.53 eV range. and PLE spectroscopy values of 0.750 The interface dipole theory of Ohler et al. Landesman et al.22 eV for the VBO.org/japo/japcr.505 eV by Satzke et al. In light of the well-established GaAs/AlAs result.52As/InP.53As/Al0.48In0.764.14–0.26 eV. No.47In0. measured the same result using photocurrent spectroscopy. we can further determine how this bowing is distributed between the two alloys.52 eV by Welch et al.36 to 0.758 By carefully modeling the results of PL measurements.22 and 0. With the assumption of transitivity. The issue of noncommutativity at heterojunctions with no common anion across the interface is controversial from the theoretical point of view as well. used ultraviolet transmission spectroscopy to study the junction and found a considerable 180 meV difference between the offsets resulting from the two possible growth sequences with different interface bond types . Strained InAsÕGaAsÕInP and related ternaries In Ga As/GaAs is another important heterojunction that is used in a wide variety of electronic and optoelectronic devices. our recommended offset values can still be used as long as they are considered to be an average for the two bond-type combinations.748 A CBO of 0.52 eV by Baltagi et al.761 Theoretical work by Van de Walle129 and Hybertsen763 indicated CBOs in the 0.54 eV were obtained by Wang et al.767 respectively.51–0. Meyer.. which corresponds to a CBO of 0. E v 0. we can also extract reliable band offsets for the Ga0. Waldrop et al. from electroabsorption data. Vol. This assignment is in excellent agreement with the later work of Bohrer et al.11–0. obtained 0.748. Phys.765 It will be seen below that by correlating with the data for other heterojunctions.53As/Al0.47In0.64 eV were obtained for the two possible growth sequences764 . current–voltage (I – V) measurements. from photocurrent spectroscopy.: Vurgaftman.763 which was in good agreement with earlier theoretical determinations 0.732 and the XPS measurements of Waldrop et al. from Schottky diode transport. However.5 eV by Lugand et al. Based on this broad and remarkably consistent variety of experimental and theoretical determinations.38 eV. we do not specify an interfacebond-type dependence of the band offset in this review. whereas the selfconsistent tight-binding model of Foulon and Priester769 yielded a 60 meV difference.753 0.aip. A smaller noncommutativity of 86 meV was also reported by Seidel et al.263 eV. Yu et al.775 C. see http://ojps. 11.52As/InP interface.53 eV by Morris et al.52 eV 0.465 eV .756 0.48In0.105. we recommend a composite result of 0.2 eV were obtained by Lee and Forrest766 and Guillot et al. For example.53As/InP heterojunction is 0. we also recommend a VBO of 0. which is found to be 0.760 From an XPS study of the Ga0. Bohrer et al. On the basis of experimental reports up to 1991. However.48In0.764 whose average CBO of 0. further investigations of that effect are called for.516 eV was determined from tight-binding calculations of Shen and Fan. Using the Ga0. yielded the lowest of the recently reported values.8.470 While Seidel et al.53As/InP constituted approximately 40% of the total band gap discontinuity of 0.52As/InP heterojunctions. This value is near the lower end of the 0.17 eV from first-principles calculations.686.48In0.749 Offsets ranging from 0.25 eV with E c 0.129. GaInAsÕAlInAsÕInP The other well-studied group of heterojunctions is Ga0.5 and 0. This system is especially interesting in that it provides a direct test of the degree of offset bowing. the expected VBO in the absence of any bowing would be E v 0.759 Slightly smaller CBOs of 0.616 eV.52As junction.757 and 0.762 Hybertsen derived a VBO of 0.2–0. 751 Considering the uncertainties involved in reliably calculating band offsets.19 eV for the CBO VBO at the Ga0.472.47In0.763.466. If future work confirms noncommutativity for a particular heterojunction..761 while Tanaka et al.41 eV was reported from the results of absorption spectroscopy by Koteles.52As heterojunction.jsp .763.155 eV for the staggered Al0.46– 0. Since the evidence for appreciable noncommutativity is inconclusive at this point.35 eV obtained in that study is in good agreement with the results given in other reports. both the early evidence summarized by Yu et al. since the lattice-matched GaInAs and AlInAs alloys have nearly identical InAs fractions.50–0. from low-temperature PL studies.31.47In0.53As/Al0.504 eV. from the alignment of the average bonding–antibonding energy on the two sides of the heterojunction.47In0.345 eV. Our recommended composite VBO for the Ga0..48In0.31 eV range of values reported in the literature.27 eV . and Ram-Mohan Segall.53As/Al0.717 suggested that the CBO for Ga0.53As/InP and Al0.769. suggested E c 0. 759 and a similar result was reported by Huang and Chang on the basis of capacitance–voltage (C – V) and current–voltage–temperature data. using C – V techniques.47In0.34 eV corresponding to E c 0. B. Appl. 89.48In0.49 eV by Huang and Chang from an admittance spectroscopy technique.26 eV range. it must be concluded that the bulk of the theoretical work agrees reasonably well with the experiments. A number of works have reported nontransitivity of the Ga0. another DLTS study of InAs/GaAs self-organized quantum dots found a CBO of 0.779 implied a consistent offset value of 0. An early Shubnikov–de Haas experiment yielded a CBO of 0. Variation of the offset with growth direction was also reported.12 eV.aip. whereas Ohler et al. and find 0.39 eV was determined from PL measurements by Disseix et al. the discussion above implies that the VBO for the unstrained GaAs/InP heterojunction should be 0.05 and 0. Early results for strained InGaAs/GaAs were summarized by Yu et al. and Ohler et al. 89. Phys. respectively..34 eV for the VBO.35 eV range.69 eV for the strained CBO.341 eV.19 eV .52As/InP heterojunction and then make some assumption regarding the GaAs/InP band alignment.1–0.19 eV using the conduction–voltage profiling technique.783 Numerous reports of band offsets in InGaAs/GaAs quantum wells have been published.827 and Feng et al.777 Correlating the results of Hirakawa et al. 11.57–0.826 Lee et al. Menendez et al. Hrivnak pointed out the consistency of several experiments with an unstrained conduction valence band offset of 0.27 eV. and imply a large VBO bowing parameter of 1.47In0. GaInPÕAlInPÕGaAs The band gap for the lattice-matched alloy Ga0.105. and Ram-Mohan 5857 Ga0.809 Considering the wide spread in the experimental offsets for In Ga As/GaAs.48In0. These data are reasonably well converged for the case of GaAsSb lattice matched to InP.732. Meyer.804 and a theoretical fit of PL data indicated an even smaller value of 0. unstrained InAs/GaAs junction. although it is somewhat questionable whether strain was completely relieved by dislocations in all of those studies. A similar study by Ohler et al.777 predicted VBOs of 0. an intermediate VBO value of 0.776 and Kowalczyk et al. we obtain an average VBO of 0.813–816 although a considerably larger VBO was found in one study.751 and Tersoft810 calculated smaller values of 0.807 A study of InAs/AlAs superlattices produced an unstrained VBO of 0.808 I – V measurements on relaxed InAs/GaAs interfaces yielded 0.39 eV.561 On the basis of this result. Relative CBOs with respect to the gap difference tended to be in the 0.537.803 The recent results of Brubach et al. Assuming transitivity.778.751 The common-anion rule.365 eV.49 eV for the InAs/GaAs junction.53As/Al0.48In0. but the VBO was determined incorrectly.820–822 In Ref. although strain effects must again be subtracted from the offsets that were actually measured for heavy and light holes.38 and 0.779 With these results in hand. we tentatively assign a large bowing parameter of 1.64 eV.49 eV higher than that of GaAs in the temperature range up to 300 K.812 Similar offsets were deduced from InAsP/InP quantum well measurements. Accurate measurements of the VBO at heterojunctions combining GaAsSb with GaInAs and AlInAs have also been performed.782 More recently.28 eV.53As/Al0.49P is 0.780 for strained InAs/GaAs heterojunctions with our assumed deformation potentials.717 as reformulated by Wei and Zunger for the Ga/In cation pair.13 eV.28 eV.746 Weighing the large number of experimental and theoretical findings together. respectively.: Vurgaftman. extrapolating to InAs/GaAs is of doubtful validity. the accurate result being 0. 747 Using midgap energy levels as a point of reference.8. Redistribution subject to AIP license or copyright. the CBO appears reliable.581 A VBO of 0.717 Although an explicit value for the band offset was not derived in most works.51In0.5 eV.541. obtained a slightly larger result of 0.33 eV.53As/InP or Al0.805 A combination of C – V and deep level transient spectroscopy DLTS measurements yielded 0. The model-solid theory of Van de Walle129 predicted E v 0.573.781 claimed good agreement with the model-solid theory of Van de Walle. which is roughly consistent with the result of x-ray photoemission spectroscopy 0. 823.802 InAs/GaAs band offsets have also been determined from optical measurements on very thin InAs layers imbedded in GaAs.825 which is in good agreement with similar studies by Rao et al. Rev.52As/InP cases. Menendez811 predicted a VBO of 0.69 0.. Appl.817 An unstrained VBO of 0.806 On the other hand.47In0. No. we conclude that the VBO for the unstrained InAs/GaAs heterojunction is most likely in the 0. Similar measurements by Waldrop et al.828 and Downloaded 05 Dec 2002 to 140..44 eV. for the bulk.org/japo/japcr. One approach is to measure the offset for the lattice-matched Ga0.17 0.. In order to be consistent with the majority of investigations.26–0.90 range.779 A somewhat smaller offset of 0. predicts a much smaller VBO of 0. we can calculate VBO bowing parameters for the GaInAs and AlInAs alloys.41 eV was obtained from fits to the PL data for very thin InAs/InP quantum wells.71 eV to the AlAsSb alloy. 1 June 2001 Appl.jsp .11 0. are consistent with an unstrained VBO of approximately 0.27 eV was reported on the basis of optical data.06 eV.48In0.38 eV. extrapolated E v 0. Measurements of the offsets for heterojunctions with varying degrees of strain should be useful.31 eV for the VBO at the InAs/InP heterojunction. Note that the negative sign for the VBO bowing parameter is consistent with the reduction of the energy gap below the virtual-crystal approximation in alloys. yielded E v 0.06 eV.21 eV. see http://ojps.14 eV.48 eV. GaPSb lattice matched to InP has also been studied and tentatively found to exhibit a VBO of 0. insofar as InAs is present in both alloys in almost equal amounts.5 eV implying a nearly null VBO for InAs/GaAs . it is useful to compare with theoretical findings.22 eV. Vol.J. D. The Schottky-barrier arguments of Tersoff led to an offset of 0.47In0.784–801 Since many of those values were found not to be a constant fraction of the band gap. as long as a consistent set of deformation potentials is used to eliminate the strain contributions. The x-ray photoemission spectroscopy measurements of Hwang et al.2 eV. We recommend a composite value of 0. although the error bounds were rather large for that result.33 eV. Phys.52As offset is not helpful.35 eV is recommended for the unstrained InAs/InP heterojunction.28 eV has been reported for the InAlAs/AlAsSb heterojunction lattice matched to InP with a type-II staggered alignment .07 eV.824 Watanabe and Ohba measured a smaller CBO of 0.129 yielding an offset of 0.. Note that determination of the Ga0. X-ray photoemission spectroscopy has yielded 0.810 while the transition-metal impurity theory of Langer et al.08 eV. which is roughly consistent with a linear variation of the VBO in this alloy no bowing .818 and 0.819 The modelsolid theory of Van de Walle129 predicted a VBO of 0.31. 746.27 eV.55 eV. Phys. although the disagreement with the smaller recommended result is nearly within the stated error bounds. respectively.5858 J. while the X-valley conduction minima line up in the two unstrained materials. and is consistent with the latest studies. Subsequent PL and PLE studies489.855 Experimental and theoretical studies of the GaAs/GaP band alignment are also available. Two studies498. respectively. No. 89. It is unclear why these latter studies appear to disagree with the converging PL data on which we base our recommended value of E v 0.27 eV from a comparison of resonant Raman scattering experiments with tight-binding theory.34–0.875 deduced E v 0. Gualtieri et al.851 gave only 25% 0.105.: Vurgaftman.857 while Gourley and Biefeld obtained 0. The earliest PL study843 assigned 57% of the total GaInP/AlInP band-gap discontinuity of 0.47 eV.35 eV from Downloaded 05 Dec 2002 to 140. This value is near the median of the reported range.869 although extrapolation to GaP may be problematic in that case. 830–837 One study obtained a small CBO for the GaInP/AlGaAs heterojunction in the low-Al-fraction limit. which is also in the middle of the theoretical range and equal to recent firstprinciples calculations.51In0.852. Using x-ray photoemission spectroscopy.852 x-ray photoemission spectroscopy.63 eV range.838 while other recent reports have found values intermediate between the two limits.6 eV from PL/PLE measurements.32 eV. and GaAs/GaInP offsets derived above.874 In view of the GaAs/InAs.8. Redistribution subject to AIP license or copyright.31–0.49P.844 found the offset to be 35% and 25%.6 eV. optical experiments on GaAs/GaAsP quantum wells found a much smaller VBO of 0. Averaging the reported experimental values we obtain a recommended GaAs/GaP VBO of 0. 35% . On the other hand. Linear extrapolation yields an offset of 0. which is similar to the value calculated by Di Ventra et al.24 eV 35% of E g .858 The assumption by Pistol et al. We recommend that the unconfirmed VBO bowing for the AlGaInP quaternary be disregarded. Meyer.41. Further inference is that the VBO bowing parameters for GaInP and AlInP are nominally equal the simplest assumption is that they both vanish . 32% . A linear variation of the VBO may be taken for the AlGaP alloy. PLE. the GaInP/AlInP junction was also investigated and found to exhibit506. Rev.878 Menendez et al.305 eV and no substantial deviation from linearity.19–0.746 This value is also fully consistent with an independent report of 0.867 Experimental and calculated band offsets for the GaAsP/AlGaAs heterojunction with small P and Al fractions have also been reported.746. Various theories129.. Appl. These values can be compared directly with the GaInP/AlInP VBO. InAs/ InP. 1 June 2001 Appl.17 eV . 11.24 eV in good agreement with the other reports. Early results suggesting a small VBO were reviewed by Yu et al.47 eV for the GaP/ AlP interface. Phys.863 Large CBOs were derived by many of the same authors for GaAsP/GaP quantum wells.22 eV in the AlInP limit.846 Whereas all of those authors considered a quaternary on one side of the heterojunction. and Ram-Mohan with the DLTS measurements of Biswas et al.748–750.org/japo/japcr. F.876 reported E v 0. A wide variety of theoretical calculations129.853 and PL854 indicated E v 0.40 eV with relatively large 38% error bounds.842 The important GaInP/Al Ga InP heterojunction for which both constituent materials are lattice matched to GaAs has also been investigated extensively. photoemission measurements at a considerably larger number of compositions yielded E v 0.870–873 found values in the 0.717 However. Two available studies of the GaAs/AlInP heterojunction put the VBO at 0. see http://ojps.860 that nearly all of the low-temperature band gap discontinuity of 0. which has a type-I band alignment.41 eV. On the other hand. Tejedor et al. Another recent optical study861 obtained E v 0.63 eV.45 eV using a light-scattering method.877 who suggested a revision to 0.862. and photoreflectance PR investigations of Ishitani et al.879 Cebulla et al. Foulon et al. Katnani and Margaritondo used photoemission to determine an unstrained VBO of 0. it is apparent that the VBO bowing for GaInP and by implication AlInP can be assumed to vanish.jsp . the former authors responded by insisting on the accuracy of their result. obtained E v 0. the combined PL.868.859.36 eV 850 was 53% of the total band gap discontinuity.848 considered the full composition range of the quaternary and found an offset of 0.855. 0.849 The VBO obtained from DLTS 0. was corroborated by PL measurements. GaSbÕInAsÕAlSb E.493 as well as Kowalski et al.39 eV.54 eV is in the valence band.501 and Zhang et al.839–841 Considering the persisting disagreement. Some extrapolated from the GaAsP alloy with the assumption that there is no offset bowing.38–0. we recommend this value.63 eV. with evidence for a VBO bowing parameter of 0. Vol.46 eV). the small strain correction. We first focus on the GaSb/AlSb heterojunction.32– 0. on the basis of pressure-optical measurements.865 Pseudopotential calculations in conjunction with PL measurements performed by Neff et al.28 eV was also proposed by Shan et al.157 eV.6 eV for the VBO at the GaP/InP heterojunction.43.866 imply a VBO of 0. found 0.69 eV range.847 E v 0. While that finding was later disputed by Ley. The smaller values were confirmed by the widely cited report of Dawson and Duggan who found a VBO of 33%. predicted noncommutativity for the band offset at the GaInP/GaAs interface. we have averaged all of the available data points to obtain a composite recommended VBO of 0. On the other hand. In view of the experimental uncertainty and Since the InAs/GaAs band offset was already established above. since the InP fraction in the latter does not change across the interface. GaP and AlP Both experimental and theoretical VBOs have been reported for the nearly lattice-matched GaP/AlP heterojunction.825. 31% . we can use the alignment for the nearly latticematched InAs/GaSb and InAs/AlSb heterojunctions to forge a link between the antimonides and the GaAs-based and InPbased systems.856 produced results falling mostly in the 0.829 Other experiments found that the VBO consitutes an even larger fraction of the band gap discontinuity ( E v 0.864 A small extrapolated VBO of 0.aip.31. and 0.62–0.839 Transitivity implies a GaInP/AlInP VBO of 0.31 eV for Ga0.770. C – V profiling.845 Interholzinger et al.68 eV to the VBO. 912.893–895 Based on a magnetotransport study the Naval Research Laboratory NRL concluded that the valence band offset is 14 meV larger for InSb-like bonds.901 measured E v 0.48 eV from a comparison of band structure calculations with tunneling measurements on InAs/AlSb/GaSb singlebarrier interband diodes.902 obtained 0. 910. InAs/GaSb valence-band offsets derived from fits to energy gaps measured for various type-II quantum well and superlattice structures. 927. 925. Since most of the experimental and theoretical studies have found a small but real dependence on bond type.870. 916.95Sb0. deduced a VBO of 0.. 921 multiplication signs .075 eV from fits to the PL spectra for GaSb/AlGaSb quantum wells.899 It is possible that the offset may depend on details of the interface structure produced by particular growth conditions. depending on the interface bond type. and energies on the order of kT have been subtracted from the PL emission peaks.900 Whereas Srivastava et al. 13.749. and 2 fits to the measured optical transitions in semiconducting superlattices and quantum wells i.896 The Oxford University group obtained 40 meV897 and 30 meV898 differences in two studies.jsp . Experimental band offset determinations for this material system fall into two main classes: 1 direct determinations. measured 0.1 eV using x-ray photoemission FIG. spectroscopy.888.8. Phys. obtained a VBO of 0. 13.39 eV using x-ray photoelectron spectroscopy. and Ram-Mohan 5859 absorption and excitation spectroscopy.J. The range of fitted VBO values is surprisingly large.770. 932 open squares . found a 90 meV variation of the VBO based on growth sequence InAs on GaSb versus GaSb on InAs . X-ray photoelectron spectroscopy yielded 0. spanning more than 200 meV. 911.52 eV. 1 June 2001 Appl.62 eV.54 eV..43–0. which is our recommendation as well. the Oxford group measured band overlap energies of 100–140 meV.885.744–746. we discuss a previously unpublished application of the second approach. in this case an eight-band finite-element method k"P algorithm. Results for the fitted VBO.769 Dandrea et al.. 926 crosses . obtained 0. Yu et al. Ab initio molecular dynamics calculations of Hemstreet et al..904–934 have been fit to theory.770.897 That those values increased by 30 meV at room temperature implies an average VBO of 0.30–0.882 Chen et al.750.2–300 K range. Meyer. plotted as a function of energy gap for the given structure. Especially noticeable are the substantial systematic differences between the offsets derived using data from different groups or sometimes within Downloaded 05 Dec 2002 to 140. VII. with the bottom of the conduction band in InAs being lower than the top of the valence band in GaSb.889 the most reliable tending to yield results in the 0.23 eV from PR measurements on GaSb/AlSb quantum wells.717. Another study by the same group produced an average offset of 0. Vol.89Sb0.810.11 interface using essentially the same technique.903 For an InAs/GaSb long-period superlattice at 4 K. are presented in Fig. while for GaAs-like bonds 15 meV should be subtracted. For example. There have been many theoretical calculations of the valence band offset at the InAs/GaSb interface.891 later refinements in the calculation reduced this difference to 40 meV.881 and Shen et al.51 0. with the only fitting parameter being the InAs/ Ga In Sb interface VBO that is taken to be consistent with the recommended GaSb/InSb VBO discussed below. 917 open inverted triangle . 914. Mebarki et al. An 8-band k"p finite-element algorithm was used to calculate the offset corresponding to each energy gap when all other band structure parameters assumed their recommended values. which are identified in the caption. Several models predicted that the VBO should be larger for the InSblike interface bond type than for GaAs-like interfaces. 923. Phys. 906 solid upright triangles . energy gaps were measured to be 25–90 meV lower in InAs/GaSb superlattices with InSb-like interface bonds than in structures with nominally identical layer thicknesses and GaAs-like bonds. in which there is enough quantum confinement to induce an energy gap .748–750. noted previously717 that most of the later experimental studies converge on an average value of 0.59 eV range.e.05 heterojunction.105.745. 907. No. see http://ojps. yielded a difference as large as 150 meV due to varying interface charge distributions.org/japo/japcr.aip. More recent theoretical studies have also produced results in the 0. Most of the data are from PL and mid-IR laser experiments at temperatures in the 4.31.899 Next. whereas Wang et al. with little temperature variation 8 meV .129. For InSblike bonds 15 meV should be added to that result.3 0.880 Yu et al. Among the former class of results. 904 solid squares .898 Wang et al. 929 open circles . 909 diamond . 930 open upright triangles . 922. 924.883 Leroux and Massies884 derived an unstrained offset of 0. 908. 89.886 Theory predicts a linear variation of the offset in the AlGaSb ternary.67 eV from C – V profiling of a GaSb/InAs0. 11.888 reported an average difference of 35 meV.49 eV range. and XVIII are employed. The data are taken from Refs. 915.129. 913. and 919 star . Gualtieri et al.890 and Montanari et al. Experimental optical transition energies for a variety of semiconducting type-II superlattices and quantum wells893.746. 920. 933 solid inverted triangles . 905 solid circles . Rev. Appl. This unusual band alignment has stimulated numerous investigations of type-II superlattices and quantum wells. 931.769. Foulon et al. we recommend that the ‘‘average’’ InAs/GaSb VBO specified below should be applied only to cases where no particular bond type was forced in the growth. did not observe any variation of the VBO with bond type. The various types of points correspond to data for structures grown by different groups.38 eV. Redistribution subject to AIP license or copyright.887 The InAs/GaSb junction has a type-II broken-gap lineup.36 eV for a GaSb/InAs0. the junction exhibits semimetallic properties as long as quantum confinement and field-induced energy shifts are not too strong.57 The important strain effects are included and the recommended band structure parameters in Tables III. 918.: Vurgaftman.892 Experimentally. Other calculations129. and Ram-Mohan the same group for different types of structures or for structures grown during different time intervals .745.936 Averaging all of the band offsets displayed in Fig. We also recommend neglecting any dependence of the InAs/AlSb VBO on interface bond type. a recent study of exciton transitions in InSb/AlInSb strained quantum wells produced heavy-hole offsets that were 38% of the total band gap discontinuity for Al fractions below 12%. which yields a type-I or type-II staggered alignment depending on details of the strain and ordering conditions. Since the fluctuations in reported values are so large for this system at its current level of understanding. Again.16 eV129.908. subsequent TEM measurements showed that threading dislocations are present in the samples grown above the optimal growth temperature. Phys. and cross-sectional STM indicated greater interface roughness. Waldrop et al.549 Other experiments950–952 are in much better agreement with the usual theoretical finding of an essentially null CBO.62 eV. the recommended 0.920.916. a firstprinciples calculation by Dandrea and Duke941 found no dependence of the VBO on bond type. Nakagawa et al. although in one study957 the PL peak energies could not be fit using a reasonable dependence. found that the band alignment between InAs1 x Sbx /AlSb quantum wells becomes type I when x 0.36– 0. electroluminescence. this corresponds to a VBO of 0. Using our recommended band gap parameters. A few groups954–956 have used PL. More recently.937 employed C – V profiling to obtain a CBO of 1.56 eV range that is usually employed in modeling antimonide materials. If all the offsets are referenced to the InSb valence band maximum.8. 11. The combined experimental and theoretical evidence appear to offer no compelling reason to reject the transitivity rule when applied to the antimonide heterojunctions. Finally. see http://ojps.943 where we take the sign to be positive if the valence band maximum is higher in InSb .929 yield 0.949 Wei and Zunger pointed out that a negative VBO for InAs/InSb directly contradicts other theoretical and experimental evidence. G.09 eV.749.889. Downloaded 05 Dec 2002 to 140.935 Although the primary mechanism has not been isolated. InAsSb was realized as a digital superlattice. and suggested that Waldrop et al. For example.27 eV. that work was extended to AlAsSb barriers. This value is somewhat larger than the earlier suggestion of 0.945 In the As-rich limit small x and y 0 .53 eV and structures grown at the University of Houston924.925. Redistribution subject to AIP license or copyright.769 we can examine whether that value is consistent with the direct experimental and theoretical evidence for this interface. GaSbÕInSb and InAsÕInSb The corrected common-anion rule predicts a negligible band offset for the unstrained GaSb/InSb heterojunction.958 Unfortunately.947 That result implied a substantial CBO and negative VBO for small x. and photoconductivity to measure VBOs for GaInSb/GaSb quantum wells. Bearing in mind that the transitivity assumption may be of questionable validity when applied to systems with more than one anion.717 and is at the high end of the 0.939 In that study.942.56 eV represents an ‘‘average’’ value that should be corrected for the interface bond type.18–0. Such differences are well outside the usual bounds of experimental uncertainties in the spectral data and layer thicknesses.940 However.872. obtained an average VBO of 0.746. implies an ‘‘average’’ VBO of 0.810.. concluded from fits to magneto-optical spectra that the top of the InAsSb valence band appeared lower than that in InAs ( 0.54 eV all with fluctuations of at least 100 meV .910. 946. this offset must be derived from measurements on heterojunctions such as GaSb/Ga1 x Inx Sb and InAs1 y Sby /InAs1 x Sbx due to the large lattice mismatch between the two binaries. Vol. with the most reliable values clustered around 0.51–0. we recommend a GaSb/InSb VBO of 0.35 eV between the -valley minimum in InAs and the X-valley minimum in AlSb.41)(1 x) eV.717.54 eV.912. Li et al. Phys.aip..940 misinterpreted their data by discarding the smaller offset obtained for an AlAs-like bond in one experiment. In some cases the differences are as large as 100 meV for structures that are nominally quite similar. Possible implications include: 1 the growth conditions actually influence the offset.105.03 eV. 13.948.05–0.810.18 eV for the staggered InAs/AlSb heterojunction.08 to 0. has a larger-than-expected effect on the energy gap. Appl.5860 J. related to interface roughness or anion cross contamination. 2 the growth-dependent nonideality of the structure.927. or 3 the layer-thickness calibrations have large uncertainties. Meyer.918. A PL study by Yang et al. the band gaps corresponding to NRL growths911.: Vurgaftman. extrapolation to the InSb/AlSb VBO from the results of this work may not be justified.jsp .953 one cannot place high confidence in that result owing to the difficulty of precisely accounting for the very large strain effects.15.873. this implies that the AlSb VBO is no more than 85% of the InAs VBO.19 eV and derived a difference of 60 meV between the two bond types. 89.g.org/japo/japcr.746 Other theories have produced values in the range 0.914. e. Those studies assumed a linear variation of the Ga1 x Inx Sb VBO with alloy composition.31.84x eV).750. All of the above works found that the unstrained VBO in InAs1 x Sbx depends almost linearly on composition x. we obtain a composite InAs/GaSb VBO of 0.922 yield an average VBO of 0.938 The findings are in reasonable agreement with the previously assumed large VBO 2 eV in AlAsSb. applied in conjunction with the recommended InAs/GaSb and GaSb/AlSb band offsets. on the other hand.889 have found E v spanning the wide range between 0 and 0. Rev. While an unstrained VBO of 1.873.913. 1 June 2001 Appl.871.933 imply a much larger average VBO of 0. A relatively strong dependence of the energy gap on growth temperature for nominally identical structures has also been reported. 944. while the energy gaps corresponding to growths at the Fraunhofer Institute915. Using x-ray photoemission spectroscopy to study interfaces with InSb-like and AlAs-like bonds. initial optical measurements supported an unstrained VBO of (0.56 eV.921 and HRL Laboratories907.1 eV was derived for ultrathin InSb embedded in InP. In experimental practice. No. along with the direct determinations summarized above. it is advisable to account for the source and type of the structure in deciding which offset to use. Accounting for the effects of strain and averaging the various results. The transitivity rule. For an InAs1 y Sby /InAs1 x Sbx junction in the Sb-rich limit large x and y 1 .51 eV.770. The investigations of the VBO in the GaAsN/GaN heterojunctions yielded a range of different results. spontaneous polarization.959 See Sec.980 and Huang et al. both of which exhibit appreciable VBO bowing. Band offset measurements have also been reported for the strained GaInAsSb/AlGaAsSb system. which is barely larger than the estimated experimental uncertainty. Appl. Furthermore.29P0.31. In particular. Meyer. Sugawara has theoretically predicted a slight bowing in the position of the valence-band maximum for GaInAsP on InP. Polyakov et al. Vol.686. which is slightly larger than the assumed value of 1. Phys. The implication of a staggered alignment with E c 0. The small direct-gap bowing parameter and the results discussed above also imply that any bowing in the VBO for the AlGaInP alloy should be small.105. Forrest et al. This is primarily because the reported results have rarely included the full effects of residual strain.960 Since the direct GaInAsP band gap appears to be nearly independent of composition. which.965 The band offsets for AlGaInAs on InP have also been studied both experimentally and theoretically. we interpret it as reflecting the uncertainty in the bowing parameter for AlAsSb.5 eV and a large positive CBO by Martin et al. predicted some bowing in the VBO.559 In particular. Those VBOs are much smaller than the error bounds for current experimental determinations of the nitride offsets.J.702 for which the discrepancies are opposite in sign. Mikhailova and Titkov have reviewed band offset results for the GaInAsSb quaternary on InAs and GaSb up to 1994 . implies a negligible VBO bowing.aip. The most significant future advancements in the understanding of nitride offsets will probably be connected with that issue. should be assigned to the CBO or the VBO.971 Rather than using this value to derive the bowing parameter for AlGaAsSb.977 Except for the case of GaInAsSb.688. a series of three articles reported determinations of the offsets for GaInAsSb and AlInAsSb. Rev. considered the GaInP/GaInAsP interface lattice matched to GaAs. Cho et al. Phys.969. While the effects of macroscopic polarization were not included.8.970 All of the results agree with linear interpolations of our recommended values with appropriate VBO bowing parameters to within the cited experimental uncertainty. V A 1 for a discussion of the AlGaInP/GaAs heterojunction. we see no compelling reason to introduce bowing. and Ram-Mohan 5861 H.972 are in good agreement with a linear interpolation of our recommended offsets for InAsSb and GaSb.13In0.15 eV for AlGaAsSb on GaSb. 1 June 2001 Appl.976. in combination with the small band gap bowing.966–968 There is no clear agreement as to whether most of the band gap bowing.973 The linear interpolation approach differed appreciably only with the findings of Baranov et al.71 /InP.978 which projected VBOs for the two phases that differed by only 34 meV in GaN and 56 meV in AlN no results were quoted for InN .org/japo/japcr. Considering all of the reported experimental results.470.4 eV. Recently. We recommend the VBOs for AlGaAsSb obtained by linear interpolation between the ternary relations. The VBOs have also been reported for the GaInAsSb/AlGaAsSb heterojunctions lattice matched to GaSb. lattice matched to InP.1 eV. No. and the N frac- Downloaded 05 Dec 2002 to 140.963 Although error bounds were not cited.974 and Afrailov et al.08 eV was measured for Ga0. Quaternaries Band offsets involving lattice-matched quaternaries have also been studied both experimentally and theoretically. these results provisionally allow us to align the wurtzite and zinc blende materials on an absolute energy scale. a VBO of 0.10 eV from linear interpolation. The issue was addressed by Murayama and Nakayama using a first-principles pseudopotential calculation.09 eV. Since the nitride materials typically crystallize in the wurtzite form. and suggested a linear variation of the CBO with quaternary composition. However.jsp . Calculations of the band offsets for AlGaAsSb quaternaries lattice matched to various substrates have been reported.981 from electrical measurements.975 The results for both In-rich and In-poor junctions indicated reasonably good agreement with a linear interpolation. provided a linear variation is assumed for each constituent. note that the value employed for the absolute gap was somewhat different from our recommendation. We recommend a linear interpolation between the dependence for GaInAs and AlInAs.962 Experimentally. and AlN We emphasize at the outset that the band offsets recommended below for the nitride system should be understood to have large uncertainties.2 eV for GaN/InN and AlN/InN heterojunctions. study of the GaAs/GaN zinc blende heterojunction has provided a tentative connection with the other III–V materials. InN.03 eV strongly disagrees with the finding of E v 0. I. an obvious question is how the valence band edge of that phase lines up with the zinc blende phase of the same compounds. are also consistent with that procedure. which is rather small in any event. 89. and also a difference on the order of 0. from fits to low-temperature PL measurements. The discrepancy may be related to strain and other uncertainties in the electrical studies. found a small bowing parameter of 0.87As0. a tight-binding calculation959 supports our conclusion that the bowing in these quaternaries is negligible. Soucail et al. 979 which is the only available direct measurement and our recommended value..964 found evidence that the CBO bowing is at most small. The study on the quaternary implies a bowing parameter of 2. X-ray photoemission spectroscopy yielded a VBO of 1. 11.959 Results of the direct experimental study of GaInAsSb/GaSb by Mebarki et al.. GaN. and piezoelectric fields in a completely satisfying manner. Wei and Zunger326 calculated a similar difference of 30 meV between the wurtzite and zinc blende forms of the GaN/AlN interface. as compared to 0. Redistribution subject to AIP license or copyright.7 eV. The same authors also investigated the band offset transitivity in AlGaAs/ GaInP/GaInAsP heterostructures lattice matched to GaAs. C – V measurements of Polyakov et al. see http://ojps.961 The results are in good agreement with our suggested offsets.84 0. this implies a linear variation of the VBO as well.: Vurgaftman. obtained a VBO of 0. the presence of macroscopic polarization can render the notion of reference bulk energy levels somewhat ambiguous. this discrepancy is probably within the experimental uncertainty.699 A theoretical work by Nakao et al. we caution again that the effects of spontaneous polarization and piezoelectric fields must be very carefully accounted for when applying this recommendation to the modeling of real GaN/AlN interfaces.70 eV in a later article by the same authors.05 eV for wurtzite GaN/InN. While the most fundamental parameters such as the energy gaps and effective masses are by now fairly well established for most of the III–V materials. calculations were performed by Albanesi et al.36 eV. However.85 eV..986 Those authors also predicted a strong dependence on the interface properties. No.org/japo/japcr. and is also closest to the larg- est number of experimental and theoretical results.985 Their result of 2.: Vurgaftman.4 eV range was reported by Rizzi et al.995 for the zinc blende AlN/ GaN interface.aip. Bernardini and Fiorentini1001 studied macroscopic bulk polarization effects on the interface-charge contribution to the offset at the wurtzite heterojunction. In view of the rapid ongoing progress on a broad front. which has been used as a reference in GaN. Theoretically.06 eV.326 The valence band in the technologically important GaInN alloy may be obtained from a linear interpolation. defects. The large disagreement with the intuitive expectation of a small offset for this common-anion heterojunction remains to be resolved. we derive 1. the GaAs/GaN VBO was first estimated by Harrison and Tersoff.992 They surmised that the differences arose from strain. 89. Rev.86 eV for the free-standing i. 1 June 2001 Appl.365 who obtained 1. as free of internal contradictions and significant omissions as is practically possible in a work of this scope. significantly complicate any experimental determination of the GaN/InN and AlN/InN band offsets. found a VBO of 0.48 eV for the wurtzite phase.982–984 The observed VBO was found to be quite small.991 Using x-ray and ultraviolet photoelectron spectroscopy. our goal has been to provide a comprehensive and even-handed reference source.5 eV by measuring the difference between the acceptor levels of iron in each material. We recommend using an unstrained band offset of 0. Theoretical values for the unstrained GaN/InN VBO are 0. we recommend using the results of Wei and Zunger326 slightly modified to ensure transitivity : 0.37 eV were calculated.18–2.85 eV for the VBO of the wurtzite AlN/InN junction. and even quinternary alloys continue to be introduced and improved with an eye toward achieving greater flexibility in the design of quantum heterostructure devices. In comparison with GaN/AlN.746 A first-principles linear-muffin-tinorbital calculation by Agrawal et al. strain-free GaAs/GaN superlattice.5862 J. Waldrop and Grant found a considerably different value of 1.44–0. we adopt a VBO of 1.993 who pointed out that the Ga 3d core level.988 which was revised to 0. did not address all parameters of interest. the GaN/InN and AlN/ InN junctions have strongly mismatched lattice constants.28 eV recently suggested by Bellaiche et al. most of the reported difference was from band-edge shifts in the bulk band structure.73 eV for the strained zinc blende interface depending on the substrate lattice constant and 0.8 eV.94 eV for the relaxed zinc blende interface. On the other hand. Redistribution subject to AIP license or copyright. quaternary. yielded 1.21 eV is quite similar to the value of 2.8 eV at the wurtzite GaN/AlN junction.105..57 eV for the strained wurtzite interface. Meyer.. Provisionally.6 eV was calculated by Monch. VBOs of 0. novel ternary. Furthermore. with the question of type-I versus type-II alignment remaining somewhat controversial.5 to 0. and film stoichiometry effects. All of these works obtained VBOs in a rather narrow range from 0. Baur et al. A slightly lower value of 0. Earlier reviews were either restricted to particular material systems. this review should Downloaded 05 Dec 2002 to 140.989 The VBO results of 1. found that the GaN/ AlN VBO ranged from 0. The valence-band discontinuity at the zinc blende GaN/AlN interface was first probed experimentally by Sitar et al. is in fact hybridized with other valence bands.jsp . Phys.59 eV..26 eV and 1. Subsequently. Only one experimental study of these two interfaces has been reported to date.85 eV corresponding to the underlying GaN and AlN lattice constants. They found VBO values of 0. On the theoretical front. For the zinc blende GaN/InN and AlN/InN interfaces.31.999 while the latter obtained 0. VII. Using transitivity.e.996 Ke et al. for the wurtzite GaN/InN and AlN/InN junctions strained to AlN. We have also illustrated how the proposed parameters fit into the band structure computations.1000 Strain-induced piezoelectric fields. A VBO in the 0.20 and 0. King et al. Appl. respectively.8 eV for both wurtzite and zinc blende interfaces.81 eV were roughly corrected for piezoelectric fields due to residual strains. Whereas numerous reports of such parameters may be found in the literature. Phys. we anticipate many new advances. and Ram-Mohan tion was too low to extrapolate the GaAs/GaN VBO with any confidence.. which can depend on the growth sequence..990 Those authors also reported a nearly linear VBO variation in the AlGaN alloy.15–0. with only 0.4 eV from fits to optical measurements on GaN/AlN superlattices.8. no complete and fully consistent set has been published previously. the agreement between experiment and theory should be considered quite good apart from the electrical studies . and by Satta et al.18 eV due to the interface-charge contribution. In view of the present uncertainties.994 and Chen et al. Vol. and it was concluded that transitivity for the GaN/AlN/InN system is obeyed to within experimental precision.1000 Recently.997 and Wei and Zunger746 for the corresponding wurtzite junction. and Nardelli et al. respectively.7 to 0. particularly concerning band offsets and other parameters for the less mature systems such as the nitrides and antimonides. 11. The semiconductor band parameter knowledge base continues to expand as new reports are published daily. or were biased to the results of a specific group of investigators. The last two articles found almost no difference between offsets for the cubic and hexagonal versions of the junction. depending on the growth temperature.989 Using the same approach. This represents the median of the reported values.3 eV381 and 0.70 and 1.26 eV326 for the zinc blende phase and 0.987 X-ray photoemission spectroscopy yielded a VBO of 0. However. see http://ojps.636. SUMMARY We have reviewed the available information about band structure parameters for 12 technologically important III–V semiconductors and their ternary and quaternary alloys at the close of the 20th century.998 The importance of strain was studied by Binggeli et al. with a positive bowing parameter of 0.05 and 1. The former found E v 0. Cohen. L. J. New York. The Theory of Brillouin Zones and Electronic States in Crystals North-Holland. Status Solidi B 68. 708 1991 . 1991 . L. Phys. and Ram-Mohan 29 30 5863 be regarded as a snapshot of the status at a given moment in time rather than the final word on III–V semiconductor band parameters. Phys. 1994 . Meyer. Piezoelectricity McGraw-Hill. Heterostructure Lasers.-H. 1396 1951 . Y. 4.aip. 71 D. Phys. Rev. G. Quantum Electron. Phys. Bassani. Appl. Bowen. Solid State Commun. C. Pfeffer. p.8. Shur World Scientific. 67 Y. Phys. New York. Semiconductors-Basic Data. 1991 . 2. 66 J. P. 1975 . 9081 1998 . O. K. 51. Smith and C. F. S. Smorchkova et al. Bassani and G. 1. 74. Loehr and J. Phys. 5404 1999 . No. R. New York. Mater. 29 1989 . Ram-Mohan. 5053 1993 . 1978 . DC. K. 3 S. Nitride Semiconductors and Devices Springer. J.. 45 J. Sci. 975 1999 . B. Phys. and M. Kim. reprinted in O. Yu and M. Christensen. C. Pfeffer and W. 49. Rev. Englewood Cliffs. see http://ojps. EMIS datareviews series. Rev. Rev. 1561 1990 . Materials Aspects of GaAs and InP Based Structures Prentice Hall. Tom Reinecke and Dr. 18 E. Macrander. The goal has been to provide a one-stop summary of the present understanding. Sci. Blakeslee. B 14. M. Klimeck. Chaps. 64 H. 63 N. Bassani. 2. H. Yoo. 68. Swaminathan and A. K. No. 36 S. Vol. Phys. R. 53. Weiss. and L. 1. Lazzouni. Kiselev. 28 L. Dayton. 86. UK. Electron. Vol. Chem. Rumyantsev. Rev. Cryst. L. 1204 1992 . 61 M. Rodriguez. Ram-Mohan. 1 and 2. Phys. Chem. A. Phys. M. 1 June 2001 Appl. K. Appl. 1670 1992 . Lett. 7 Properties of Lattice-Matched and Strained Indium Gallium Arsenide. Rev. Stevenage. Mailhiot.jsp . R. B 45. La Rocca. in Handbook on Semiconductors. A. 192. 1117 1999 . Superlattices Microstruct. edited by O. Stroscio. and R. and L.31. New York. Rev. B 41. Chang. edited by A. Symmetry and Strain-Induced Effects in Semiconductors Wiley. Madelung. editor. J. Gil Clarendon. Pikus. D. Phys. Rev. B 60. People and S. 62 W. Singapore. Lett. 1992 .R. and Dr. edited by S. New York. 25. Phys. 44 W. 54 K. Appl. H. New York. Luttinger and W. B. 943 1984 . Rev. New York. Mathews and A. 46 I. INSPEC. 2695 1988 . 27. Fasol. 115. New York. 1. 5 V. Zawadzki. Technol. Rev. Chem. and F. Dutta. 520 2000 . France. 405 1975 . Sun. 1657 1996 . 11469 1993 . Ohio. edited by P. 13498 1993 . 74. Rev. Chen. B 38. Phys. 23 E. B 57. and references therein. 2035 1991 . R. Electronic States and Optical Transitions in Solids Pergamon. edited by T. and K. Strikwerda. Zunger. 1979 1984 . C. Vols. Bir and G. T. Rossler. P. Logothetidis. 1960 . L. p. Berlin. 72 P. Rev. 53 L. 265 1976 . Phys. Physics and Applications. 193. Kane. Phys. Pearsall. Katz Artech House. F. Ram-Mohan. 9 Properties of Gallium Arsenide. 48 H. John Loehr and Dr. Phys. S. 31 P. Mod. Chap. C. 51 J. Beer Academic. 1987 . L. 27. Nuovo Cimento 12. L. Levinshtein. Rev. J. Phys. 1989 . 6. A. Phys. Y. Phys. S. 56 F. M. Willardson and A. McCaldin. Rev. B 39. and Devices. M. 889 1989 . 7. I. 97. Rev. S. 21 J. W. 55 B. 19 M.J. Phys. 191 1995 . 1. O. One of the authors L. L. 1999 . N. Downloaded 05 Dec 2002 to 140. J. Rev. Vol. 1974 . R. Ehrenreich and D. Chadi and M. Stroscio. Redistribution subject to AIP license or copyright. edited by W. 4777 1993 . B 47. A. Koster. 73 G. A. 1985 . J. Chuang and C. and augmented by future experimental and theoretical investigations. Physica Amsterdam 34. J. 1990 . 16 G. G. McGill. J. 1995 . Phys. L. 3222 1999 . Burt. 58 K. and J. Sirenko. Tom Nelson at the Air Force Research Laboratory. 38 G. Adachi INSPEC. 32 ¨ U. Finite-Difference Schemes and Partial Differential Equations Wadsworth and Brooks. Burt. 32. 27 Y. edited by R. No. van Haeringen. Chuang. A 7. NJ. Meyer. H. E. Fundamentals of Semiconductors Springer. 1995 . Hayata. Physics of Optoelectronic Devices Wiley. J. New York. R. J. 50 E. 2. Nakamura. Turnbull Academic. Vol. 288 1994 . Oxford. 1997 1996 . Haddad. Hjalmarson. E. 1996 . InAs. Phys. Cuypers and W. in Indium Phosphide and Related Materials: Processing. 1 1989 . E.. and A. 18th International Conference on Physics of Semiconductors World Scientific. Vogl. Chuang. Erdogan. Physics of Optoelectronic Devices Wiley. Pikus. 13 F. Rev. Zawadzki. Sigg. Phys. 57 L. Blood. Fu. New York. Ambacher et al. M. and A. Phys. Solid State Physics. New York. Comput. Lett. 47 O. EMIS datareviews series. 2.org/japo/japcr. 2 H. Phys. and M. Madelung. Beer Academic. Aggarwal. 1998 . Yoo. J. 14 G. Kane. 1988 . Phys. 69 J. IEEE J. and D. Pfeffer and W. K. B 41. 72. 20 M. Liu. 24 E. Status Solidi B 216. 74. Phys. Kim. 2491 1996 . 1996 . Adachi. Superlattices Microstruct. Cardona. Phys. p. Passler. p. 11 Handbook Series on Semiconductor Parameters. 4 S. M. edited by M. Casey. L. Willardson. Kohn. 15 P. Dow. Amsterdam. J. 19. UK. and H. Boykin. 22 P. Cardona. and G. and M. Singh. 52 J. 8 Properties of Aluminum Gallium Arsenide. Jr. Vol. Kuhn. R. Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology. J.R. Berlin. 149 1967 . Chap. 6651 1992 . L. and M.: Vurgaftman. 9819 1988 . 94. Paul NorthHolland. C. 415 1989 . 34 S. Rev. Boston. C. New series. Vol. G. Appl. O. Vol. R. O. Technology. Ben Shanabrook at the Naval Research Laboratory. Singapore. and P. Springer. Li and K. 173 1990 . U. 1946 . L. C. and InGaAsP Wiley. 1996 . H. Herts.: Condens. 777 1985 . Aggarwal. Jackson. edited by H. Vac. Appl. 4 and 5. 11. C. 1993 . 1990 . R. C. Yu. Phys. 701 E 1987 . Ivchenko. 42 S. 60 G. wishes to thank Dr. M. R. Amsterdam. Yang. Pacific Grove. B 37. Ren. Matter 4. K. A. GaP. Wave Mechanics Applied to Semiconductor Heterostructures Editions de Physique. P. 17 1982 . P. T. B. Riv. Szmulowicz. Part 2: Electron. 12 H. 89. T. O. B 54. Varshni. and F. 6151 1988 . M. p. Appl. 28. R. 10 Properties of Indium Phosphide INSPEC. 59 T. Cohen. 119. Kane. Schultz. for their hospitality during his sabbatical visits there. 39 J. GaAs and Related Materials: Bulk Semiconducting and Superlattice Properties World Scientific. Swaminathan. Shimizu. C. Wei and A. Lowdin. New York. 1995 . 1133. Structurally Induced States from Strain and Confinement. Phys. 1993 . 1498 1954 . K. Singapore. Yoo. 62.. 365 1983 . Part A: Fundamental Principles Academic. Cady. 41 T. S. and T. and T. 17 D. Nonlinear Opt. 27. and G. Berlin. Zawadzki. Phys. 2nd ed. Cardona. edited by B. Chang. 70 J. 46. Kim. 1966 . Liu. 9913 E 1992 . 4520 1990 . Slater and G. B. Littlejohn. Koshiba. Technol. Physical Properties of Crystals Oxford University Press. L. Solid State Commun. 85. 11992 1990 . B. Adachi. Oxford. Ram-Mohan. Willander. Cwik. 35 S. and M. 2nd ed. B 30.105. InGaAs. Vina. Appl. K. Nelson. in Semiconductors and Semimetals. Phys. Chelikowsky and M. W. W. Bhattacharya INSPEC. Chuang and C. M. B 53. Ivchenko and P. IEEE J. Les Ulis. CA. F. 68 M. 1019 1987 . 43 S. Appl. 236 1958 . Physical Properties of III–V Semiconductor Compounds: InP. 1982 . 6 V. in Semiconductors and Semimetals. refined. 37 Yu. J. 65 H. Phys. 35 1990 . P. 49 Group III Nitride Semiconductor Compounds. Ram-Mohan and J. Solids 44. 2. which will be revised. London. Jones. Jeon.. 33 P. F. Jpn. 26 J. P. J. Nye. Rodriguez. 460 1987 . ACKNOWLEDGMENTS The authors wish to thank Quantum Semiconductor Algorithms for the use of their finite element band structure software that was employed to test many of the input numbers. A. 1992 . 1992 . Washington. Morkoc. Superlattices and Other Heterostructures: Symmetry and Optical Phenomena Springer. New York. 46. La Rocca. B 38. GaAs. P. 40 R. L. Phys. Bahder. J. B 48. S. Semicond. 1 ¨ R. Rev. Quantum Electron. Solids 6. Phys.. P. Panish. Commun. and H. Mains. Growth 32. Liu. E. 25 E. Bastard. Pastori Parravicini. 869 1955 . 12808 1989 . 556 1976 . C. R. Phillips and L. and G. C. Physica B 210. C. Weisbuch. 40. Gray. Loesch. J. Mitchell. 275 1998 . Yokoi. 4310 1990 . Phys. 142 J. T. Garriga. Hermann and C. Aubel. Suemune. I. Sci. Meisel Elsevier Science. C. G. 106 P. J. Wrobel. R. Phys. Rev. B 5. Davis. 501 1987 . Cohen and V. Leotin. and L. B 13. 5. 77 J. E. N. and O. H. 145 D. Hess.-R. edited by D. 257. J. Cardona. Phys. H. 102 N. and S. Sugimasa. Technol. and P. 156 F. J. Rev. Porro. K. Topol. and K. Walukiewicz. Auluck. J. and E. Phys. D. C 3. Schmid. N. 963 1991 . R. Schlapp. Turnbull. Walukiewicz. Appl. Anastassakis and J. Vol. Zunger. L. Veje. Bimberg. Gilbert. J. 1282 1986 . Krijn. W. 1. and S. Appl. Skolnick. Phys. 1. Jpn. B 53. W. New York. Brown. O. New York. 112 B. Z. New York. P. P. Pavesi. edited by H. 59. 1994 . Watkins. Rev. Lagomarsino. Enquist. 2056 1985 . G. and W. M. Sci. E. S. Heine. Bouarissa and H.aip. 5753 1984 . Van de Walle. Yan. 100 A. 98 H. Rev. Zunger. L. Stern. 111 L. Lagowski. S. Dawson. 187 1973 . I. Wang and A. Keller. 1997 . M. Physics of Strained Quantum Well Lasers Kluwer Academic. Adams. Phys. Fischer. Zawadzki. 95 R. U. 777 1981 . and W. Dunlap. and D. G. and J. J. F. T. Phys. Loehr. B 43. Rev. Appl. 11950 1991 . Pavesi. Semicond. L. Pavesi and M. Kuehn. Fonstad. Phys. in Solid State Physics. Ekardt. 1988 . and R. Imachi. J. 287 1959 . 343 1999 . 1970 . Rev. Tran. R. Stradling. J. Emlin. 143 J. SpringThorpe. F. C. Bauser. S. Williamson. Springer Series in Solid-State Sciences. D. L. 472 1958 . Pettit. W. The Pseudopotential Concept. T. Imachi. Rev. Phys. 115 D. 146 R. J. and D. 122. 129 C. Meyer. B 33. W. and C. Comas. A. Lipari. Seitz. B 7. Rev. Shanabrook.: Optoelectron. S.31. Phys. Roberts. Christensen. P. Aubel. 157 1987 . Rev. Monemar. B 15. Choi. edited by S. P. Zamboni. and A. O’Reilly. B 39. Saxena. Rev. 22. D. Phys. E. J. 86 L. V. J. T. Sci. M. Broekaert and C. J. Phys. D. A. Etienne. 83 M. E. p. and Z. Jain. Solid State Commun. 58. Hazama. Cohen and J. 59. Rev. Festkoerperprobleme XVII. 133 B. Subramaniam. Zawadzki. K. 5429 1994 . Phys. Rev. M. J. S. E. E. Woolley. 125 I. Neumann. P. 82 V. IEEE Electron Device Lett. S. Appl. Phys. 27 1991 . C. in Semiconductor Nanoclusters. 145. Phys. B 20. K. L. Rev. R. Karasyuk. Phys. Aspnes and A. 1. A. 96 L. 97 H. Berlin. Bernstein. Technol. Redistribution subject to AIP license or copyright. J. Appl. Suski. W. Neumann. Ehrenreich. Vol. Unger. K. 1080 1988 . Walukiewicz. Sacks. O. Guzzi. Gorczyca. Status Solidi B 49. Logothetidis. Semicond. 1638 1992 . 149 B. B 43. N. Szmyd. 6. 61. Physica B 139–140. Rev. H. Soc. Status Solidi B 157. 659 1980 . P. and H. J. L. Pidgeon. 4429 1984 . 5711 1973 . 90 H. 116. 495 1985 . Wei. K. Phys. Chang. Shantharama. Atomic Energy Commission. Stradling and R. IEE Proc. V. 55. 76 Y. A. Rev. Infrared Phys. 5590 1999 . Oggioni. Zollner. C. Rev. G. 141 A. 14734 1991 . Zunger. Phys. 737 1967 . edited by E. 11. B 50. and B. H. L. Status Solidi B 210. 135 A. in 10th International Conference on Semiconductor Physics. B 37. Molenkamp. Technol. L. Phys. Staehli. S. Hang. Tapfer. W. Semicond. 150 N. 120 S. 151 W. M. Phys. Moore. I. J. B 33. Phys. 154. P. Tidemand-Petersson. 4314 1988 . Turnbull. Studies in Surface Science and Catalysis. Technol. B. New York. 5331 1976 . H. Phys. Hamaguchi. and R. Logothetidis. 147 M. 132 V. B 38. Yu. H. E. J. Baldereschi. Bassett. E. C. and K. Seitz. Goiran. L. Vurgaftman. 155 J. 4571 1984 . edited by M. Rev. Appl. 24 Academic. S. 99 P. Ravindra. Phys. E. D. 26. Askenazy. Appl. DC. P. 1970 . Phys. and F. A. R. Rev. Litwin-Staszewska. L. 213 1990 . 3460 1971 . Nicholas. H. 123 N. R. Rev. Mattila. 8215 1988 . Schulze. 7. Meyer. Schulman and Y. Appl. Phys. C. Leotin.-H. 92 M. 118 I. Broido. 131 S. and G. C. 140 H. P. p. Phys. B 60. Cardona. M. 51. J. Loehr. Phys. Lei. Stern U. 7949 1996 . Landheer. J. 127 D. J. B 8. E. 1821 1961 . and Ram-Mohan R. Noethe. Ousset. and A. N. B 4. Sarkar. Chang. J. 113 M. p. Hensen. 195 1977 . Reddy. K. Phys. A. T. Rev. K. 126 W. Hamaguchi.-W. Rev. J. Guzzi. Chelikowsky. in Proceedings of 22nd International Conference On Physics of Semiconductors. P. Nakwaski. 1871 1989 . L. J. Haller. Presting. 110 Ch. Ehrenreich. P. I. B 37. Sci. L. 94 D. Sundaram. Adams. and K. 1990 . Heine. Phys.. Phys. Phys. Superlattices Microstruct. L.S. Klipstein. B 48. p.-M. Ahmed et al. and R. Rev. S. R. 89. Sci. J. 91 E. 80 M. and D. Studna. 75. and M. 89 P. W. 823 1977 . J..-W. 68. 401 1986 . 111. 4605 1973 . III. B 45. see http://ojps. N. Phys. Thurmond. Binggeli and A. Status Solidi B 55. D. Martin. Rev. Lautenschlager. A. Sharma. and W. SpringThorpe. El Allali. B 53.8. Singapore. A. Phys. Phys.jsp . B. Meyer et al. and C. 9174 1987 . J. U. Phys. Juravel. 11. Rev. B 46. M. Lawaetz. M. 128 1986 . 269 1988 . R. 3577 1986 . A. 1970 . Woodall. P. 24 Academic. Ploog. 87 J. 117 A. 107 M. Burnham. S. Grilli. 116 C. 84 L. 108 D. Askenazy. Tekh. in Proceedings of 20th International Conference On Physics of Semiconductors. Onton. J. N. Status Solidi B 120. Zverev. 8564 1986 . J. Y. 101 M. B 14. Grilli. Nolte. C. Blakemore. edited by P. Vol. L94 1970 . Phys. 122. Sugimasa. Phys. Phys. 114 N. 68. Dumke. L. Weimann. 130 E. Foxon.: Vurgaftman. Phys. 148 E. Eppenga.-C. Phys. A. B 39. 2367 1990 . C 9. Cardona. R. Cohen and V. Y. 4398 1993 . Solid State Commun. I. B 30. 137 W. C. Planel. B 21. 53. Poluprovodn. S.105. E.. Sorensen. Leng.-H. Dmowski. 53. M. Wasilewski. Aers. Pfeffer. 134 L. 93 D. and C. 429 1995 . in Solid State Physics. Said and M. Chadi. Pollak. 1039 1991 . Joannopoulos World Scientific. Rev. Cardona. Coldren. Phys. M. A. M. P. 157 C. and C. Majerfeld. Phys. and L.5864 74 75 J. Phys. p. Lautenschlager. and E. 2978 1972 . 12813 1996 and references therein. Technol. Soc. Phys. Rev. S. Phys. Neumann. Chem. H. R. J. 81 M. B 35. Vol. Cardona. Logothetidis. No. R. J. Phys. 465 1992 . Downloaded 05 Dec 2002 to 140. Garriga. 54. 3411 1989 . Vol. Schulman and Y. Lockwood World Scientific. Jpn. Phys. Vac. Bosio. T. Vol. N. R123 1983 and references therein. 128 S. Miura. Comas. 2594 1986 . Garriga. J. 85 D. Sov. Rev. Wood and A. Status Solidi B 126. J. 38. 138 S. Wei. and L. J. S. Shantharama. Lee. J. B 31. 105 D. 1735. C. W. Rev. S. C. 161. R. p. and M. 55 1992 . M. Gatos. Wang. Bimberg. 144 T. Soc. B 58. Guzzi. H. A. 1 1995 and references therein. A. and R. 353 1998 .-Peterburg 22. Koch. and P. Beard. Gorczyca. Sundaram. Phys. 4466 1976 . Krupski. 1133 1975 . 3488 1985 . A. Thewalt. Appl. and W. J. 103 N. G. T. Srivastava. Chow. 79. and J. G. V. Vol. Zunger. Washington. Ley. Tribe. 104 W. Status Solidi B 105. 69 1996 . P. K. 4779 1994 . Rheinlaender. Rev. 152 M. Grein. Nicholas. R1710 1998 . Pan. B 45. Ruda. Rev. C. ’t Hooft. edited by H. Singapore. Ahmad. 103. Corzine. Christensen. 11 1984 and references therein. 122 A. H. Phys. Zawadzki. R. J. K167 1972 . and G. and S. 715 1983 . F. Phys. Smith. 154 D. 78 J. Phys. 1464 1987 . and V. 922 1988 . J. M. Technol. J. 311 1990 . H. Rev. 179 1984 and references therein. 3303 1979 . A. F. L.-C. Rev. Phys. C. Lett. Pfeffer. Pfeffer and W. Kono. L. H. 139 M. Solid State Commun. Blacha. 3. 4328 1992 . Phys. C. Phys. C 17. Lorenz. Wood.org/japo/japcr. Phys. A. Rut. H. Rev. IEEE J. R. 124 W. J. 6. 1 June 2001 119 Appl. 107. Hazama. and I. and M. G. and N. 88 C. L. 153 S. 357 1992 .-H. Matossi and F. The Fitting of Pseudopotentials to Experimental Data and their Subsequent Application. D. Rev. P. T. M. 79 J. Rev. Semicond. Lett. Cardona. 121 P. 75. 163 1988 Fiz. Sasaki. Quantum Electron. 1996 . Chang. 17. Kanehisa. Phys. Clark. Rev. M. and S. Kamat and D. Cardona Springer. P. 109 W. Aspnes. Gorczyca. Semicond. Shen. Phys. Electrochem. 136 M. and G. Wang. R. Aourag. Phys. and J. 2809 1976 . 66. Glembocki. J. Solids 56. Heine. Electronic Structure and Optical Properties of Semiconductors. B 30. Phys. Kleinman. 10951 1992 . Zachau. Rev. Physica B 177. H. Phys. Ares. 2108 1989 . and references therein. org/japo/japcr. Lipari. Rapaport. 2081 1978 . Otsuka. H. 2838 1983 . Jpn. Phys. Smirnova. Phys. Pichakhchi. 52. 85 1975 . 4946 1983 . Lacroix. Schlachetzki. Phys. Electron. Kolodziejczak and S. Askenazy. 50. 1048 1995 . Phys. Garbuzov. 876 1968 . 52. J. Aoyama. C 10. M.31. Efros. S. M. in Proceedings of 23rd International Conference On Physics of Semiconductors. Schneider. p. A. Phys. I. and A. Phys. Solid State Commun. K. B. 69 1983 . Lassnig. H. 184 R. A. F. Sov. Thomas and J. 231 P. Sov. 237 C. E. and M. Sybert. 4394 1978 . Poluprovodn. Malik. Rev. B 47. Phys. 6. 11. Phys. 677 1967 . Suekane. and P. T. 59. New York. P. P. U. I. 24. Solid State Commun. B 52. p. J. Appl. B 27. Rev. Sov. 171. 1996 . Phys.Peterburg 9. R. 4491 1996 . Kobayashi. Gornik. 187 ¨ R. G. M. 1710 1971 . Wicks.aip. Z. Magnanini. and Ram-Mohan 199 200 5865 I. 67. A. Appl. Rev. H. V. 12. J. 12. Zein Eddin. and V. Shen. A 127. Cardona. H. A. F. H. 15 1990 . K87 1967 . Kan. M.J. M. 23. 281 1994 . Kokhanovskii.. Phys. Euthymiou. 3. 693 1974 . Phys. B 12. Emlin. Phys. H. 197 C. Street and W. Vol. and Yu. Can. L. B. B. Tekh. M. J.-U. D. Gaur. Hamaguchi. Appl. P. Phys. 230 ¨ G. Hansen. Phys. 202 Zh. P. Scheffler and R. 175 A. 208 P. I. Tekh.-C. 212 Z. Tekh. Tarricone. Sapega. 73. Omling. W. E. 54 1975 Fiz. Taylor. 170 N. J. A. P. Nomura. K. Sander. and L. 177 P. and H. Appl. H.3. S. M. Solid State Commun. Jpn. J. and B. P. D.. E. Phys. G. 186 M. G. B. 81 1997 . Ohyama. 1 1978 . 211 P. A. Lautenschlager. A. Komeno. 72. G. DiForte-Poisson. Wu and C. D. 569 1988 . Huang and W. Helm. A. Mishurnyi. Meyer. B 44. Phys. Mishra and A. J. Dutta. Zawadzki. 112 1970 . and C. Ukhanov. 203 D. 1568 1973 Fiz. Mathieu. 928 1981 .-Z. 2052 1971 . 159 L. 80. and T. Singapore. Status Solidi 24. 977 1985 . B 12. Semicond. 33 1996 . Morgenstern. G. Matter 100. and H. Al. Wang. G. Sov.: Condens. 189 T. Lett. R. Phys. Solids 46. 198 J. 162 Y. S. Yu. 160 J. Takayama. and F. and M. V. B 19. Woolley. S. 869 1999 . Tekh. 171 M. 185 S. J. Suppl. Phys. R. 2175 1973 . T. 210 L. A. L. Senske. Phys. B: Condens. M. A. Tekh. Kobori. Le. 89. S. A. I. and V. 81. Ching. Sov. Rev. Kazakova. and G. Taylor. T. B. Reine. Solid State Commun. Irmer. R. Shiraki. D. Stradling. 269. Suzuki. Appl. Hopkins. 174 D. C. Thewalt. and D. 11. Stradling. 7. Merle. Rev. N. J. Can. Jaw. E. Downloaded 05 Dec 2002 to 140. and Y.-Peterburg 22. Kumagawa. and S. Jpn. Nakashima. Stradling. S. Phys. Pichakhchi. Warner. Carter. R. Piazza. 779 1972 . Rev. 61. L. 4275 1992 . P.. Girault. Viturro. 1740 1994 . 223 D. 53. I. 2nd ed. Part 1 33. Glisson. 173 F. Skolnick. J. Lorenz. Zverev. Phys. 1844 1981 . N. Camassel. 9052 1991 . Phys. 845 1998 . Sakata. V. M. Magnanini. Phys. Physica B 48. Ma. Phys. Soc. 425 1979 . 4813 1987 . 50. E. Schaff. Tekh. Leotin. Appl. Cardona. Yu. E. 221 M. Humphreys. R. R. B 19. Rowell. and R. 209 Z. Ilegems. and Yu. Phys. L. W. Holmes. Kanskaya. Adachi.-C. S. 161 W. Phys. A. edited by M. B. Ohta. Jr. Soc. Coderre and J. Washburn. Kop’ev. Jpn. 1057 1983 . Rev. Mal’tsev. 9. Bradley.. F. I. Bosacchi. Ya.. S. 172 Yu. Poluprovodn. A. Weinstein. Phys. 166 S. A. Phys. Joullie. H. 188 D. J. 1292 1976 . Semicond. 3033 1972 . P. Pollak. W. R. Poluprovodn. Arimoto. 216 K. R. R. Semicond. 7. C. J. I. Seidenbuch. M. Miller. J. Schoenfelder. Fukui. S. G. Bodnar. J. Status Solidi B 210. Ohyama. Tran. Ukhanov. J. C. Phys. Jpn. Rinfret. Physics of Semiconductor Devices. Samorukov. Cohen. 196 C. Pfeffer. 235 A. Rev. F. and L. Mal’tsev. N. Phys. No. Aggarwal. Phys. N. Maeda. 204 S. 1207 1968 . Mathieu.-Peterburg 17. Wang. Cardona. Li. Lax. and P. Komeno. P. 625 1998 . 15588 1993 . Schwerdtfeger. Tekh. Min’kov. Takizawa. C. M. 139 1977 . 228 M. Rochon and E. 4869 1987 . Vol. Yuen. Schneider. 15. Bimberg. A. R. Ya. Phys. Hauser. Jpn. J. V. 215 T. Poluprovodn. M. 449 1983 Fiz. F. C. I. 37. Tekh. Bimberg. Lukomskii. Appl. Karymshakov. Hamaguchi. 226 D. J. Phys. Woolley.-Peterburg 4. A. V. L. Eksp. 169 1980 . New York. K. Altarelli. Stradling. P. Weber and W. Bellani. 1265 1981 . Mater. I. and C. Karlik. Technol. and R. A. 4. M. Camassel. Jpn.-Q.-Peterburg 7. K. S. 4369 1996 . S. 725 1985 . K. J. 183 C. A. Merle. Redistribution subject to AIP license or copyright. Status Solidi 16. 73. E. Rev. L742 1983 . G. Rev. 67. 104. Woolley and J. Meyer. Fischbach. Appl. C. 207 P. 182 M. 1879 1964 . I. J. S. 767 1992 . K173 1976 . R. Barbaste. JETP Lett. Phys. B 36. Phys. Kazakova. 54. 22. M. 5821 1997 . K55 1966 . 234 V. B 18. Merle. Semicond. 192 L. Rotelli. Shealy. Bour. 7034 1990 . Physica B 89. T. Rev. Fukui. A. Solid State Commun. L.: Vurgaftman. Infrared Phys. 4872 1979 . 222 D. and O. Garriga. Phys. 5. 1184 1971 Fiz. Triboulet. Appl. S. Kostsova. Status Solidi A 37. 311 1983 . H. E. Poiblaud. Phys. W. J. Yagup’ev. A. 214 J. B: Condens. Phys. J. S. Chem. J. 1998 . T. Wiley. 46. J. Fiz. and H. Part 1 20. Karlik. Littlejohn. Simmonds. Stockton. Part 2 22. D. Pettit. B 22. Appl. M. 205 F. 206 T. N. 220 M. 178 D. 4813 1987 . Semicond. and J. R. Solid State Commun. 547 1985 . Rev. Wilson. I. H. Shen. L. A. 5803 1975 . Teor. Poluprovodn. and R. 5111 1977 . J. Phys. L. Sapega. DiLernia. Sze. Jpn. Phys. Phys. Zimmerman World Scientific. D. Ya. K. and R. E. C. Matter 8. Merkulov. Poluprovodn. Wiesendanger. C. Y. 213 G. Phys. Phys. Status Solidi B 92. Appl. J. and K. J. Pavesi. and J. C. R. M. 181 L. Kido. R. Solid State Commun. Alibert. Carlin. Appl. M. A. Sites. U. P. Skolnick. B 18. Zverev. J. W. J. 2209 1979 . and V. Soc. 15 1990 . Ukhanov. Yamada. Knap. Z. S. O. G. O. 80. L. Soc. and G. Ruerup. 1243 1978 Fiz. Auvergne. M. Proceedings of 1998 International Conference on Microwave and Millimeter Wave Technology Publishing House of Electronics Industry. J. Yamada. S. S. Sov. 164 Z. 169 U. S. Semicond. P. Kruzhaev. Skolnick. Matter 95. Solid State Commun. Mathieu. J. and W.. A. and M. Nakashima. Nashel’skii. Rossler. Gong. 1178 1968 . 165 X. Adachi. Rut. H. Tiwari. S. and V. 163 E. Phys. S. Lett. 6416 1996 . M. Ukhanov. Geddo. Y. Mirlin. Skripkin. 1816 1973 . P. and M. 195 A. G. Phys. Walton. and A. Can.-Peterburg 12. J. de Oliveira. 17. 31. and V. Mirlin. C. Sci. J. Phys. Schlachetzki. 219 T. X. Phys. 373 1988 . and Y. Pollak. J. P. Compound Semiconductor Device Physics Academic. D. A. V. Chap. Joullie. Phys. 225 I. 194 D. G. 193 N. Semicond. I. S. Seiler. Status Solidi B 211. Phys. A. A. Yukish.8. D. J. and M. S. Soc. 5590 1978 . Miura. Bayo. and F. P. 7. Shi. and D. and R.-G. Rev. Z. E. 1071 1984 and references therein. Schneider. 3553 1984 . 53.-Peterburg 5. Grubert. Chen. Rev. M. Guizzetti. Alekseev. Ritter. E. 5. 229 M. 2231 1979 . Rev.jsp . Gauthier. Hamaguchi. Fan. and M. Shen and X. Burdukov. Fortin. and M. J. Groves. Semicond.105. Phys. Issiki. Plumridge. Joullie. Archilla. Dean. S. Wieder. 236 C. L. A. Ozeki. S. S. Xin. and M. A. 1981 . Hess. P. T. 31. Chen. S. V. 1992 . C 6. Khalilov. Papioannou. B 36. Sov. 1586 1973 and references therein. C. 218 Y. Zukotynski. see http://ojps. R. K. Solid State Commun. Phys. 1495 1972 Fiz. and M. B 5. Bekris. V. 42. P. 49. 2020 1980 . China. J. Stradling. Chikazumi. Verma. and P. Kesamanly. 1449 1974 Fiz. Lau and W. Portal. and C. Seisyan. 154 1980 Pis’ma Zh. L. Dombrowski. C. V. Y. Williams. H. Nicholas. Ruerup. Alekseev. Lee and J. Rev. Phys. Semicond. Lett. C. Feinleib. Ance. Miura. A. Franchi. Phys. 232 M. 227 R. Technol. Bour. A. and G. B 12. 615 1987 . Ghezzi. 176 J. 23. Can. Phys. 239 M. J. 49. 179 M. H. and N. 568 1987 . Liu. Ameziane. R. M. Chung. Fang. C. Tsui. M. 5739 1975 . Imanaka. 2223. 201 T. M. D. Phys. Beijing. Garriga. Konnikov. Hang. 355 1988 Fiz. Appl. Lett. K. and S. Rev. Appl. 238 H. F. R. Rudra. Jpn. and A. 167 L. 233 C. Ozeki. D. Stephens. 2. Shen. Miura. Yamaguchi. Stringfellow. J. Pidgeon. T. J. W. Ruhle. Fukatsu. and R. S. J. C. I. J. Phys. 224 X. B 23. Brink. G. and N. J. H. Korovina. Alferov. Phys. 168 J. Hang. Lautenschlager. H. D. J. 180 H. T. Sov. 12. A. B. Bosacchi. Pitt. Wetzel. 217 T. V. Semicond. B. G. Rut. Phys. K. A. Physica B 256–258. 1371 1975 . Watkins. Taki. 190 C. Wittneven. Rev. Poluprovodn. Phys. A. Phys. 191 S. V. and B. Poluprovodn. 1390 1970 . J. Rev. Yu. Franchi. R. A. D. Phys. 718 1983 . N. 1463 1995 . R. Z. R. Woolley. Rev. and Kh. Sci. Tuchendler. 413 1973 . R. Plichta. and N. Phys. Kourkoutas. Ferguson. Shimomae. Parisini.-Peterburg 6. Chr. 1 June 2001 158 Appl. Phys. Yu. A. 4560 1998 . Amano. Phys. Rev. Phys. Lett. 275 P. N. H. Weili. 2266 1974 . Shushi. and R. T. and M. A. R. Lett. 1413 1987 . Phys. 80. Appl. Charfi. Brunel. B 1. Monemar. Status Solidi B 167. P. Sov. 248 M. K. A. 560 1980 . Pollak.-Peterburg 33. 289 Properties of Group-III Nitrides. 67. 286 A. Reynolds. and M. D. Magnanini. Kim. Poluprovodn. Sov. E. C. 262 O. Morkoc. S. Ya. Meisels and F. 16425 1996 . Willander. 2. E. Phys. Grzegory. R17028 1995 . Van Overstraeten. Lett. Alibert. 89. B 1. and R. H.jsp . 271 X. Status Solidi B 135. 712 1996 . and C. B 50. Aulombard. 251 H. Suski. N. Nelson. Semicond. H. C7-393 1981 . 242 A. 575 1966 . K. B 10. J. 1 June 2001 282 Appl. and G. J. 283 A. J. J. B 8. Phys. A. L. Senda. 5846 1975 . A. Rev. Kolbas. 8. E. and A. Chen. Poluprovodn. 267 N. V. and K. W. 36.-Peterburg 21. 196 1973 . 155 1998 . J. 308 K. and D. Steube. Chem. Rev. and I. Raisin. Kleiner. Akasaki. B. 24. Solids 35. 274 T. J. B 12. Fasol Springer. Tekh. Kahlert. 47. Walker. Pankove. Phys. 311 D. and E. Smith. W. 349 1991 . 3852 1973 . Pidgeon and R. 305 J. J. Solid State Commun. Stutzmann. Chenjia. J. 67. I. B 47. Petalas. Phys. Cryst. Lee. R. S. Semicond. and P. People. P. M. Bignazzi. 49. S. Shan. 87. 694 1987 . 225 1974 . Phys. L. L. Li. 1533 1974 . Jr. 133 1974 . Azuhata. Dingle. J. Phys. 4. Kaufmann. R. Brunner. Phys. Stokowski. Petalas. Monemar. M. Narayan. 311 1979 . W. J. 284 S. Song. V. p. Goldenberg. Guzzi. 281 E. Phys. Appl. M. 81. Phys. Jiang. 1468 1978 . Asif Khan. Appl. Berlin. T. Phys. Rev. Jpn. G. Meyer. Cardona. Christensen. Beaumont. H. Solids 1. 1173 1999 . A. F. K. Dimitrov. Appl. Kim. 58. Sheregii. Qijiang. 163 1975 . O. Kessler. 859 1987 Fiz. 303 C. Aktas. Casey. Phys. Seiler. 18017 1994 . 7. A. H. 11. E. 1997 . Dinqyuan. Lukomskii. X. Appl. Phys. B 58. Zollner. 288 P. C. Appl. Semicond. Steuber. T. 660 1990 Fiz. J. Logothetidis. Bohringer. Xuezhong. 287 D. Chin. 965 2000 . 292 S. W. Semicond. D. Aktas. Technol. V. M. Groves.-Peterburg 7. Phys. Pidgeon and S. 258 M. Ugrin. Phys. C. 6. Harbeke. P. Cho. I. F. 8082 1995 . J. Phys. Tsidil’kovskii and M. Zwerdling. M. H. Poluprovodn. 297 O. 1998 . J. Phys. 7. Lagerstedt and B. Alouani. 246 R. 279 R. M. Downloaded 05 Dec 2002 to 140. Chichibu. S. Poluprovodn. Merle. A. U. Phys. Auvergne. 424 1987 Fiz. Phys. 313 S. Camassel. Lett. 2784 1996 . and L. Rev. Rev. Phys. Z. Appl. Dmitriev. 3109 1991 . and O. X. B 16. S. 1060 1980 . Thin Solid Films 190. Logan. and T. Poluprovodn. Y. Phys. Phys. S. F. and H. Botchkarev. Semicond. Phys. 594 1996 . X. Rev. Yen. I. Brown. 315 J. K. Phys. Jiang. M. Tanaka. I. Hamaguchi. Miura. Shouxu. V. and L. Im. 307 C. Rocher. B 52. Teisseyre. Phys. Horino. 318 D. Phys. Protasov. Rev. e. Dingle. 79. 250 N. X. Malikova. J. Y. Rev. Lee. B 52. DenBaars. G. J. 76. 2429 1994 . M. R. N. D. Phys. M. Rustagi. 254 A. Kido. 9056 1991 . C. 16274 1993 . 42. Lett. Manasreh. E. and A. Tekh. Froelich. and S. J. 243 A. Kasai. 290 J. Salvador. Christensen and I. J. Hathcox. Y. Chiba. Sov. Phys. P. S. M. Poluprovodn. B 4. 178 1979 Fiz. Joullie. 79. Razeghi. Appl. 299 W. Moustakas. 261 M. Semicond. Nicholas. E. 302 G. MRS Internet J. C. I. 312 J. T. 255 F. 244 H. Bergman. C. 247 H. M. S. Laude. Phys. Freudenberg. S. and A. 68. Yinkang. Ohyama. J. K. L. 296 See. Wei. Ilegems. and R. and F. and A. Lin. 20. Bosacchi. and R. 217 1966 . Phys. Phys. S. Nicholas. Auvergne. 11. Kopylov. and T. M. Phys. Lett.-L. 29. Goldenberg. 298 B. Chen. Phys. Scholz. 631 1979 . Poluprovodn. Tae. H. C. 249 ¨ ¨ S. C. Moritz. D. S. Phys. Morimoto.8. Rev. Lee. Appl. 1067 1999 Fiz. Lin. D. C. Deleporte. S. 2072 1976 . Rev. 21. Look. N. J. 319 N. N. Seiler and K. Tekh. M. 300 W. Pollack. 252 G. F. M. J. L. 9251 1997 . and H. Hamaguchi. 676 1974 . Akasaki. Phys. J. Rev. Botchkarev. 277 C. Ryskin. Sota. Poluprovodn. and R. Van Camp. Tekh. Y. Stradling. Benoit a la Guillaume. S. Roth. G. S.-Peterburg 13. 146. Fasol. Phys. V. Appl. Sell. B 55. R. M. Semicond. 131 1979 . T. Edgar INSPEC. J. Growth 189Õ190. Mason. M. Rouli. Hill and C. S. H.org/japo/japcr. C.-Peterburg 21. E. Yakunin. Roth and E. 293 The Blue Laser Diode. and Ram-Mohan K. Delalande. 13. Phys. R. Sov. and M. Phys. O. O. S.31. Appl. K. Bustarret. 3322 1995 . 295 M. Jung. 11. Phys. Cardona. Chen. and S. Semicond. Phys. Shan. 285 D. 256 L. K. 301 B. Semicond. 33. Tekh. Phys. Bloom. Reimann. O. 985 1995 . 278 E. and A. Phys. Phys. Weiler. edited by S. Q. EMIS Datareviews Series No. B. Semicond. F. Fortin. Rev. R. Kesamanly. P. Sov. Schonherr. Belov. C. Phys. J. Seiler. 264 Y. 263 C. Sci. Angerer.-Peterburg 7. RCA Rev. 10. Rev. Otsuka. 1211 1971 . Colloq. Jizhou. 43. Shimomae. C. and V. Leshko and E. G. Kunzer. S.-H. Logothetidis. Xie. Lett. B.g. Filipchenko and L. M. 383 1989 . Chem. B 38. H. and F. Sota. Mishra. Yafyasov. C. Jain. and A. Mathieu. Littler and D. Gaillard. C. H. Park. Phys. 1436 1970 .: Vurgaftman. Nitride Semicond. Pikhtin. 320 S. Sov. Miura. D. 557 1983 . 52. 249 1957 . A. 2784 1996 . B 18. Appl. and J. J. 272 F. Kuramata. Faurie. Nikolaev. F. B 44. K139 1973 . Res. 2572 1997 . J. Lett. Schwerdtfeger. B 50. 647 1972 . Phys. 986 1985 . 3450 1970 . Res. Can. J. Tekh. Nitride Semicond. 652 1998 . Kuchar. W. 7001 1996 . 16274 1993 . Moustakas. Yu. and H. Phys. G. 266 C. and R. H.aip. 309 B. Monakhov. Vol. Ilegems. Fortin. Rev. Glinskii. Shikanai. Maramzina.105. 314 H. 1451 1974 Fiz. J. Nakamura. 259 A. V. Menushenkov and E. C. O. J. A. K. Cardona. 32. Wills. 279.5866 240 241 J.. Semicond. Kane. 2512 1995 . V. IEE. Magn. Talwar. 276 I. Paul. Tekh. J. Lin. Appl. I. Appl. Van Doren. 417 1997 . Chichibu. R. Kosogov. W. A. Appl. and A. N. 824 1969 . Opto-Electron. Y. P. J. Da Silva.-Peterburg 8. 186. Hwang. Leroux. Lett. J. E. 306 A. 20. 1. Appl. Porowski. B 57. O. Tekh. Hangleiter. Tekh. F. Morkoc. Poluprovodn. J. Phys. J. Monemar. Song. A. F. A. 45. Khan. Proceedings of the 8th International Conference on Narrow-Gap Semiconductors World Scientific. Caixia. S. T. Can. and J. Hoepler. Z. 260 D. Filion and E. 230 1983 . and C. S. Merz. Soc. Muth. S. Shmagin. Rev. Rev. R. London. Bocchi. Wecht. Ambacher. Sov. J. J. Appl. Phys. G. 489 1988 . and M. 1319 1979 . H. Poluprovodn. Zouaghi. E. Romanov. P. and J. I. 8650 1986 . Gil. D. Rev. Solids 35. S. A. O. A. see http://ojps. 291 F. 2822 1977 and references therein. Fortin. 316 A. Phys. De. Sov. M. and K. and T. 773 1979 Fiz. Haerle. Rev. Lett. Jun. 273 B. A. Phys. Phys. 8. MRS Internet J. Rev. N. J. 549 1983 . Redistribution subject to AIP license or copyright. 310 M. Zhang. J.-Peterburg 24. 30. 954 1986 . Varfolomeev. T. B 53. Phys. 5090 1997 . 147 1974 Fiz. 4397 1994 . Theriault. O. Semicond. Nakamura. Phys. J. Chem. G. V. 2295 1998 . Mathieu. Seisyan. and S. M. Li. Phys. Nakamura and G. 4. Semicond. D. Dmowski. A. Yang. Rev. Gibart. 257 E. Tekh. 304 M. Technol. 70. P. 265 S. 2118 1961 . C. Appl. S. P. J.-Peterburg 10. Appl. 631 1997 . M. Arimoto. Zubrilov. Phys. Maaref. S. F. and S. P. Rev. S. M. K. Smith. 13. 10 1997 . 3797 1972 . Status Solidi B 116. Salvador. Phys. K129 1986 . A. Phys. Yang. Sov. Phys. Y. P. 294 R. D. 253 ` M. 2179 1973 . M. 1234 1977 Fiz. No. 66. P. 56. Sov. Sci. Pietraszko. Appl. Radaikina. Sov. Magn. Semicond. I. Gorczyca. 1994 . Phys. Baj. London. Status Solidi B 55. W. A. 1806 1988 . 2 1996 . Briot. L. Joullie. 46. Schmidt. Tekh. D. Mater. H. Arimoto. and G. J. 268 H. M. Yakunin. W. Sun. Franchi. and J.-Peterburg 13. C. Clarke. S. Devreese. W. J. A. N. Rev. Sun. Maan. 21. A. A. H. V. Poluprovodn. 82.. Phys. Keeler. and A. Appl. J. K. Guenaud. edited by J. R. S. 317 A. Boultadakis. and J. 269 M. Phys. Liu. D. A. Chin. E. Phys. Voos. Amano. Stephens. W. J. Fujii. J. T. 603 1986 Fiz. N. Rev. 280 M. 66. D. J. 11. U. and B. Bajaj. 5667 1978 . Jacobson. Phys. Phys. 270 V. Cardona. Buyanova. Semicond. Rev. Melnik. S. 21 1990 . Perlin. M. S417 1993 . 140 1973 Fiz. Keller. and C. O. A. 69. Guozhen. 71. Phys. C.-Peterburg 20. Huant. P. Huang. Grilli. Sheregii and Yu. Sirota and A. E. and B. 245 H. Nies. H. 1047 1990 . J. Azuhata.. J. B 34. Liu and J. H. J. Technol. 3714 1999 . Wu. Sadowski. 70. Bloom. Physica B 219–220. Muensit. Nakajima. Lett. Lett. and I. Nauk SSSR. Phys. Rev. A. 363 S. Phys. R. L1178 1995 . B 55. 68. Tiwald. H. 368 G. Meyer. Perry. Phys. Iso. 2123 1997 . 21 1972 . Tekh. Brand. 76. Yoshida. Phys. M. Greene. L. Lett. K. see http://ojps. K. Vanderbilt. Phys. B. Appl. Mikoshiba. 3378 1996 . Ooya. Sov. Mast. 948 1997 . Volm. 15144 1993 . and M. 87. Phys.-W. V. J. W. 337 A. Appl. Akasaki. B 61. F. Kim. Kuroda. Li. Choyke. J. J.090. Abbar. C. Massies. Niwa. 338 S. Ito. Phys. Iizuka. S. Bai. Jpn. Amano. Phys. Appl. Rev. L. L822 1995 . Phys. Hossain. K. Stofko. and M. Shalabutov. Gibart. K. Kaplan. Wu. Appl. 339 A. Appl. Segall. Guy. Rev. Detchprohm. and E. 366 R. T. M. R. 2833 1997 . Orton. R. 1549 1995 . K. F. and P. M. 346 M. Phys. K123 1974 . K. 367 H. 1122 1997 . 46. 377 D. 64. and D. G. R. Baranowski. V. A. B 7. W. Wakahara. Phys. Sota. Appl. Appl. and T. J. 347 D. F. Phys. B 57. 7731 1996 . Appl. Ramirez-Flores. Gaskill. 2407 1999 . S. Appl. Lett. B 62. B 53. G. Rev. T. I. Uenoyama. Lett. Ilegems. 7018 1997 . Chang. 395 M. 188 1996 . 319 1978 . 342 S. Ploog. Phys. Rheinlander and H. Iafrate. Phys. Sveshkova. L. 4154 1999 . J. R. Krasiko. Hutson. 1. E. Brand. Poluprovodn. W. 79. 73. M. Burgiel. 373 J. Ohno. B 54. M. Zhuang. Harbeke. A. A. D. Yang and Z. D. Azuhata. Appl. B 56. Davis. Sitar. 362 ¨ F. A. and R. Amano. Appl. 396 N. J. 343 B. Detchprohm. M. Technol. P. Paisley. Phys. Li. 331 B. 1429 1998 . and J. T. 296 1996 . Zhao. Phys. E. Kim. A. and T. Lambrecht. 79. Chen. Grimsditch. J. Kasic. Nakamura. Akasaki. Phys. Leroux. Guy. Kosicki. Kim. Phys. Schwarz. Abram. V. McAvoy IEEE. J. H. J. Lett.. J. L. Yang. Yanase. W. 1982 . Bechstedt. Suzuki. S.. and Yu. 382 K.-H. Sci. No. 11. F. Phys. Poluprovodn. Fiorentini. 189 1993 . 7363 1997 . Park and S. 1518 1997 . A. 3025 2000 . Tsubouchi. and B. Kamiyama. 360 F. Phys. Sakai. A. Lumin. Li. and R. Part 1 33. D. 344 R. 1391 1998 . H. and J. S. Phys. Shiraishi. Stroscio. 1309 1976 Fiz. Phys. 24. Lett. G. Y. S. Thin Solid Films 192. Phys. Li. 356 S. H. Tadjer. K. 95.. F. Witowski. Shur. Chong. Rev. Sov. Strite. Sheleg and A. and H. V. 386 R. Zunger. Knap et al. Jimenez. Appl. 326 S. Ettenberg. and S. M. 379 A. H. 1257 1979 . Kim. 403 N. Jr. 374 D. Muensit and I. 2711 2000 . Z. F. edited by B. J. 1257 1977 Fiz. Narayan. U. 3432 1975 . W. Tsuchiya. W. Thin Solid Films 36. Phys. W. Guo and A. Appl. 1428 2000 . H. Meyer. Fong. M. I. K. B 54. and M. Hoffman. Solids 254. and S. D. R. 392 A. Jahn. B. Einfeldt. M. Meier. Rev. Appl. Phys. and R. 340 L.: Vurgaftman. J. 335 Y. 371 S. Rezki. 261 1992 . Aourag. 1881 1996 . Phys. 17577 1996 . Naka. Appl. Lett. Sirenko. J. R10024 1997 . Bernardini. Kaminski. 79. 387 X. Appl. 2577 1997 . 341 T. van Schilfgaarde. Lett. 14. Wei and A. Suzuki. and J.876 May 21. Li. H. and I. 67. Davis. Rev. Ahart. Lett. Lett. Rev. L.105. Jpn. Neugebauer. and I. 75. Navarro-Contreras. L. Phys. Shan et al. Ahn. J. R. A. Li. A. Phys. R. and B. M. 70. T. 33. Phys. A. T. and T. 1981 . Inushima. Goldenberg. Knee. S. C.aip. Kuroda. L. 4360 1997 . 324 Yu. 322 Z. Appl. B. Foley. Shields. Sci. Grandjean. Phys. Dalmasso. B. Phys. D. J. 391 L.. T. 357 I. Salvador.-H. D. Phys. 2491 1996 . and A. 8132 1995 . and M. Phys. Choy. B 52. K. Phys. 3343 1996 .. 101 1995 . Wang. Sci. Kamiya. R. 897 1996 . J. B. p. C. and J. Technol. 385 Q. Phys. Zanzucchi. J.jsp . 328 A. R. J. Semicond. 348 K. Phys. Appl. Greene. Suzuki and T. Chen. D. Bechstedt. 2719 1996 . and K. Part 1 34. 1071 1990 . Phys.31. Brandt. Appl. Solid State Commun. Rosamond. B 61. Semicond. and A. Vacuum 41. Appl. and R.. R. Jiang. M. Flynn. L. and M. Brett. Sci. 352 A. Rev. Phys. 79. E. J. J. Lambrecht. Rev. and J. 1924 1991 . 11. J. 1896 1998 . and V. 86. E. H. Phys. Spencer. 1501 1998 . S. M. 340. Xia. 59. K. 1132 1993 . A. Meyer. 4951 1998 . Fanciulli. Froelich. and M. 389 W. Ran. Phys. B 56. 375 M.-Peterburg 11. and J. R. Grimditch. 76. Phys. Phys. Cingolani et al. C. and R. Sugai. 4133 1999 . Tang. D. Vispute. J. 351 A. Uenoyama. 384 P. 399 S. Grzegory. H. and P. 372 J. Tyagai. Phys. and M. 390 K. Malakhov. T. B. 358 C. 76. Lambrecht. 82. and H. Top. Tsubouchi. Tekh. Phys. Am. M. J. M. H. Hogg. Yaguchi. J. Rev. 323 Y. G. Ohtoshi. P. Shagalov. Solids 60. 123 1999 . Brander. 394 T. Lett. Okumura. Bremser. Lett. Semicond. H. 1598 1979 Inorg. C. Wongchotigul. Lett. 3. Sota. 7404 1997 . C. A. Phys. K. 397 J. Lett. Phys. Quantum Electron. Mitchel. L. Rutz. J. 398 R. H. S. P. 406 K. Phys. Ohtoshi. F. 1374 1998 . Part 2 34. J. Powell. Mikoshiba. B. 2200 1976 . J. Fan. Wyder. Rev. A. Appl. S. J. 4421 1996 . and P. 72. Chem. Sakai. L. Morkoc. J. Shimada. Adams. 359 A. U. Munoz. Appl. Akad. B 60. Moustakas. Chen. 2454 1994 . Phys. 84. Reimann. M. Appl. C. Appl. M. Yim. Leroux. and A. T. and J. D. J. 72. 11. G. Phys. Norman. D. 2997 1994 . Khachaturyan. B. M. Neorg. Niwa. 369 2000 . and M. 72. Uenoyama. Certier. M. Drechsler. K. Jeon. Rev. S. Osamura.-L. D. Phys. 400 R. 369 W. Okahisa. Appl. N. Saxler et al. Phys. W. Littlejohn. 8007 1996 . Doverspike. 3241 1986 . A. 329 B. K. 71. J. Semicond. B. J. Appl. F. 83. Furthmuller. Phys. M. Meney. 69. Sugai. Q. Menoret. Phys. W. Andreeva. R. 44. 70. J. S. Mater. Part 1 35. Status Solidi B 66. M. T. Appl. Ohno. 393 K.-E.S. Chan. Suzuki. Pugh. Appl. Evstigneev. W. D. Akasaki. Nelson. 818 1996 . B 48. B. B 54. Sanchez-Rojas. 354 Y. W. Wright. A. Gil. R. B 53. 10. 2274 1998 . M. P. Lefebvre. Yang. J. Technol. A. Dugdale. J. McNeil. F. Appl. 1963 . Appl. K. L. 401 K. J. J. 378 M. Rev. Y. 404 V. Yang. 15. Lett. Appl. F. Goldys. p. Soc. Suzuki. and T. U. L. 5912 1995 . 408 T. Rev. W. Lett. N. C. J. 597 1995 . S.Peterburg 10. G. Rev. Grossner. and D. Chen. J. M. Y. D. Westra and M. Nagase. E. 1421 1970 . Tischler. Jpn. B 9. 383 W. T. Lee.. and T. J. 376 W. J. M. Smith. Steube.. 345 J. and M. Khan. 350 T. C. N. French. Phys. Mater. M. 141 1976 . B. 332 A. 2737 2000 . R. Sci. New York. Phys. 2067 1997 . 355 R. 2142 1977 . S. Bigenwald. Appl. Chuang and C. Cunningham. and N. S. Rev. L. Wickenden. Murakami. Lett. Menniger. 361 K. Rev. Yoshida. D.org/japo/japcr. 375. B. J. 73. T. C. Weber. Omnes. Choyke. Van de Walle and J. Wu. P. Phys. B. and Ram-Mohan 5867 T. 333 M. 419 1999 . M. J. 405 T. Phys. 349 W.. Non-Cryst. S. J. Phys. Phys. Ahoujja. Wright. Surya. Proceedings of the IEEE Ultrasonic Symposium IEEE. Elhamri. Segall. 68. J. 7365 2000 . W. 13460 1996 . 1981 2000 . Lei. Graber. Chuang. Ohnaka. Laugt. Lastras-Martinez. 15. and S. 23 1999 . in 1981 Ultrasonics Symposium. Phys. Phys. Chow. M. Chow. Appl. Phys.. and K. N. 336 W. Song. Dugdale. Appl. 4. Sel. A. E. Izv. W. J. 402 K. Schubert. Karch and F. Perry and R. Rev. Rev. Phys. Mater. Redwing. Appl.J. 161 1974 . Appl. Hauenstein. Patent No. Bykhovski. Perlin et al. Massies. Puychevrier and M. J. 292 1973 . J. Amono. Cai. J. 75. L. Jpn. Ortenburger. 325 S. S. Newrock. Jpn. M. Yeo. Sidorov. M. 364 S. H. Lett. Wang. S. Lett. S. K. and Y. Grandjean. Ya. Ikedo. Onable. W. Pakula. K. Phys. Appl. F. E. U. Status Solidi B 64. IEEE J. R. T. Damilano. 227 1990 . E. Fischer. 381 C. Abram. Barker. 89. Lee. Powell. Wang. Semicond. and G. B 56. and G. 69. Lett. Neumann. Li. Xu. A. D. Part 2 34. and E. Savastenko. J. 68. Appl. Appl.. A. O. Shan. S. Phys. 330 V. K. 76. K. Pankove. 547 1996 . and S. Appl. Segall. K. Wong. and B. A. Yaguchi. 11. C. B. 388 K. Gilbert. 75. Chong. E. Vol. 71. Ruan. Lett. K. B 56. C. Garrido. Hommel. S. 12933 2000 . Phys. Appl. 16310 1996 . 82. and N.8. Lett. A. Lett. and J. 334 P. A. and H. 76. B 50. Redistribution subject to AIP license or copyright. 527 1998 . 8003 2000 . 380 T. 353 A. Clarke. Yoshida. and T. Xu. Alt. Rev. Z. and I. 8433 1994 . 365 Downloaded 05 Dec 2002 to 140. Kim. Vac. C. and J. 1114 1996 . A. Appl. J. Phys. S. Lett. Lett. and S. Lueng. Takagi. Appl. 743 1973 . 407 A. O’Reilly. Tansley and C. H. Phys. J. Phys. 10. J. 1 June 2001 321 Appl. M. Polian. 5. H. 327 M. T. Phys. B 62. Ng. Appl. Pepper. Ceram. New York. 1496 1999 . Powell. J. M. D. Phys. Vol. 370 A. T. Rev. Bordure. 483 C. 456 D. J. L. 1239 1996 . 23. Vac. 590 1989 . A. S. P.105. Lett. Nakanisi. Technol.jsp . 36. Sotomayor-Torres. 441 1991 . Bradley. 5136 1982 . Ferguson. Phys. 21. 33. Solid State Commun. Qiang. 486 T. and G. 353 1972 . J. and H. Towe. A. J. Bour. M. Lin. Kelso. and J. 1256 1995 . F. Appl. Pollak. 436 E. 455 M. Phys. 978 1980 . 772 1979 . Beerens. 1194 1979 Fiz. Sugawara. Eisele. Hosoda. Alavi. 512 1985 . C 19. 3113 1990 . J. Bertness. K. Chevallier. Sci. J. 80. S. Cho. A. A. Wei. A. 430 ¨ K. Phys. 472 C. M. Rev. and R. 187. Tekh. K. J. Phys. J. Semicond. 438 E. and S. Onton. and H. Sci. Poole. J. Restorrf. A. Potemski. J. and H. A. 463 E. Appl. Appl. Matter 9. Miller. Groves. Rev. Appl. A. Hvam. 406 1988 . Yaremenko.8. Solid State Commun. H. 5447 1988 . Phys. C. E. A. Appl. Sirtori. B. Phys. Basu. Lindquist. 414 D. 2386 1992 . Phys. G. C. 630 1992 . Chevallier. and G. J. Takeda. 23. Guillot. Phys. Stringfellow. 425 F. K. Garcia-Perez. Solid State Commun. 59. E. Appl. 35. L. Lett. L. and M. Nahory. Rev. Portal. and X. Cheng.. P. Caridi. and T. Scott. M. Ansems. K. J. R. 505 1987 . and D. G. 445 J. 8672 1991 . Rev. O’Reilly. Lett. Lett. and R. Appl. 57. F. P. 469 Y. L. Mater. Hayakawa. Y. R. and M. R. H. Cho. Prins. Liedenbaum. J. Cury. F. L1553 1988 . G. Sugawara. R. Mabbitt. Y. Appl. Berolo. B. 468 1987 . B 27. S. and R. and R. J. 1993 . 13. S. D. and C. Bernier. Pearsall. H. Phys. Phys. 444 K. T. Fan and Y. Woolley. A. 470 S. 4071 1999 . A. Olsen. R. R. Cryst. Weimann. Cohen. Rev. Auvergne. Waters. 2698 1990 . Gibart. Pu. Phys. Nicholas. J. J. Fonstad. 443 E. 3151 1997 . 419 R. Lange. Shen and X. 86. E. and R. T. 1970 . S. H. H. B. 3586 1981 . D. 475 A. Zory Academic. Heider. 40. 76. Lambkin. 444. 1311 1980 . J. G. J. Okazaki. 245 1971 . 2584 1999 . L. R. 63. Bhat. S. 54. Yeh. Yamazaki. J. H. McAlister. 2587 1983 . 437 1972 . H. Part 2 27. Appl. p. 29. Zunger. T. Sarkar. P. Appl. Sacilotti. Electron. V. 442 Z. D. 418 K. and G. M. Praseuth. 452 C.-S. M. 10546 1991 . Morkoc. G. G. Phys. B 1. 53. 80. Bosio. T. Solid State Commun. Y. 5405 1976 . 490 F. M. Perley. M. 449 R. D. and T. Frank. 4543 1983 . Van Vechten. 446 O. Appl. W. Lasserre. 691 1994 Fiz. 6229 1996 . Chevallier. Yamamoto. P. 3420 1971 . A. and S. Appl. Donecker. 1804 1993 . Karachevtseva. Puetz. Loehr. Adachi. C. Davey. and H. C. W. Selders. T. 2196 1986 . 440 J. Rev. Pettit. C. C. Powazinik. G. J. Electron. E. R. Jpn. 464 B. S. Mendez. 480 D. 57. 432 S. 482 M. Pearsall. Appl. Razeghi. C. and J. Phys. Stringfellow. J. Littlejohn. Chen. 10. Portal. G. Yasuami. P. P. Y. 462 V. Z. G. C. F. Pinczuk. 441 J. Pietzonka. Appl. G. J. Phys. Massies. Lett. Appl. 461 R. 416 D. P. R. R. Phys. Zunger. L335 1986 . Vishnubhatla. 481 P. 243 1989 . Status Solidi B 73. Appl. Fujii. Kontkiewicz. Huang. S. E. Perea. Bergstresser. People. Christman. and J. Solid State Commun. 58. 341 1984 . Downloaded 05 Dec 2002 to 140. Phys. Benyattou. 421 P. 427 R. Lorenz. 38. McNeil. 73. 457 L. Appl. S.31. Appl. 53. N. T. 2046 1979 . Olego. Fan. Phys. 28.. 450 1981 . A. Mokerov. A. F. F. Quantum Electron. Phys. S. Staehli. Phys. El-Masry and S. J. Faist. Pollak. M. Meyer. Rev. Phys. T. Hermann and T. M. Lett. Appl. J. Appl. J. Lam. Rev. Letartre. Woolley. Jacobs. Jayaraman. 60. L. 41. Mariette. W. J. 423 R. E. S. Laframboise. Phatak. Phys. N. J. Appl. and Ram-Mohan E. Roksnoer. G. B. A. P. Appl. Schweizer. Nakamura. 1034 1991 . A. K. 429 S. B. C. Okazaki. Nelson. Technol. Werber. Wakefield. W. B 42. J. 1585 1995 . W.-Q. 665 1998 . Nahory. 485 R. and C. H. Aulombard. T. 8102 1993 . 11833 1993 . and P. Maeder and A. Alibert. Howard. Lett. Mendez. F. and S. K. R. D. and S. Alonso. Woolley. 8848 1993 . Phys. B 44. H. Portal. 476 1982 . G. G. and J. 423 1982 . Chen. G. 467 M. N. S. Phys. 60. Sci. Takagi. Berolo. Fan. Lett. Chevrier. P. A. 1087 1990 . Menna. H. Davies. Driad. Jr. Appl. Auvergne. and B. Appl. Hickman. Ignat’ev. 2667 1985 . 827 1991 . I. Electron. Paff. J. Laugier and J. Phys. 428 W. IEEE J. J. Can. Livescu. Reuter. 447 J. Yan. Phys. T. M. Lett. 439 P. L. J. B 15. J. and F. Lett. Sci. Johnston. No. Matyas. Pelenc. 125 1994 . D.org/japo/japcr. 1661 1969 . 47. Johnson. B 48. 1301 1972 . Ohba. J. Appl. Sov. B 48. L. Wecht. Sugawara. K. 487 L. W. and N. p. 1211 1994 . 7105 1983 and references therein. H. Wood. C. Allgaier. 85. 80. Lett. Silberg. M. 411 C. 8775 1982 . Growth 93. Sessions. Takahashi. J. Razeghi. J. 6761 1996 . Phys. P. Appl. D. G. K. and H. Laugier. K. M. Bimberg. Bhat. O. R. F. Paul. Logan. P. see http://ojps. J. P. 49. Mathieu. New York. P. 1248 1992 . Rev. Phys. J. Nicholas. Wilkinson. C. A. Solid State Commun. C. H. Houlbert. 409 S. D. 69. Mater. Strakhov. Phys. Technol. J. 2277 1980 . 477 G. Aspnes. Condens. 451 J. B 48. Xiong.. A. Phys. J. 471 I. Phys. Phys. G. Abraham. 448 R. Sasaki. and W. H. J. Semicond. V. Phys. 2124 1988 . A. Pearsall. B. 426 S. M. Henning. Dai. J. B 44. C. Merle. T. Hang. Emeny. J. Phys. Phys. 465 R. Charbonneau. Phys. J. Horner. J. 51. Beerens. J. Langbein. 89. 412 T. 468 M.-Peterburg 28. Houston. J. F. A. Sov. Kana’ah. M. 437 K. J. Semicond. C. V. and W. Semicond. B. and J. P. Barns. B 51. Jurgensen. B. M. Rev. Capasso. Lu. 492 1979 . Yamazaki. Strite and H. F. Fonstad. and J. 478 A. M. Van Vechten. and J. Lett. J. 476 C. Streubel. Kurtz. Schmidt. G. Kopf. R. Phys. Bedair. T. Lett. P. Olson. Goetz. 415. 52. Phys. Valster. B 52. Stormer. Sci. A. Kotera. M.5868 J. 413 G. E. 3794 1973 . Sass. C. Phys. 34. Lett. E. Cavenett. edited by P. Rev. B 38. G. U. H.-G. J. J. 754 1986 . P. Nicholas. H. 59. Phys. Tekh. Perrier. Appl. J. 488 T. 85. 52. T. Cho. Jensen. Lett. 231 1997 . 459 C. Eyglunent. Logan. and T. and W. P. and T. Pollak. and H. Yan. Appl. K. B 6. 434 M. 10462 1995 . Reddy. S. A. Mater. L. Phys. and S. Rowe. T.-H. T. Lee. T. N. Bimberg. 44. 460 K. 489 C. C. Kerr. 424 Y. 422 H. Poluprovodn. G. Fan and Y. 659 1978 . H. Rev. M. 9. Y. J. Rev. Phys. M. B. V. Y. Appl. Phys. p. 3561 1999 . J. 2032 1977 . B 21. Vol. S.aip. Appl. S. 1237 1992 . G. Schwabe. 3481 1985 . 47. 466 P. and A. H. and J. H. C 18. Rev. 1400 1972 . Poluprovodn. Aggarwal. Technol. Appl. 473 D. Phys. F. 51. A. Kuphal. Kuech. D. Nozaki. J. J. A. Perea. P. Technol. and A. J. Brendecke. Phys. S. 178 1980 . Y. 433 D. 459 1980 . 28. 458 J. Rev. Mascarenhas. 437 1977 . Appl. Friedrich. Z. J. J. Pollack. Phys. Phys. 410 J. 633 1976 . Cambridge. Hijikata. 474 A. McKinnon. M. J. Guzzi. J. 420 J. Phys. and R. 63. Mathieu. Proceedings of 7th International Conference on InP and Related Materials. and J. and E. Magri and A. Phys. Appl.: Vurgaftman. A. A. M. Singh. 4. Phys. L. Roy. Phys. Phys. 102. Zielinski. Lett.-Peterburg 13. Kelleher. Zemon. and J. Lett. G. Burri. Quantum Electron. J. 484 N. Phys. Bugajski. E. 42. Burmeister. 1. Onton. in Quantum Well Lasers. Dunstan. Appl. Semicond. 454 M. Wright. Miner. G. Tiwari and D. Steverens. Nemtsev. 1995. Kim. 60. J. Lorenz and A. Phys. J. A. S. Lett. E. Phys. Phys. Phys. D. S. 417 R. Chang. Omnes and M. Porod and D. J. B 28. and A. D. Phys. Appl. 1 June 2001 450 Appl. 2. Andrews. Redistribution subject to AIP license or copyright. N. Rev. Portal. Morkoc. Y. Ji. 907 1984 . Woodall. Forrest. Van Vechten and T. ’t Hooft. Lesser. Solomonov. S. R. Appl. C. Sivco. 415 A small negative bowing parameter was determined by N. Phys. Fujii. and T. 453 H. K. Beales. Chen. 67. Phys. 11. Christen. A. and D. 69. Ferry. D. H. E. 9. Semicond. Rev. A. G. Tombrello. Rev. and R. and G. Oelgart. 37. 10. S. Halliwell. Phys. and J. S909 1991 . Lett. Phys. Can. H. Appl. and P. P. Cheng. Opt. 3263 1988 . M. Wolford. Lange. and C. 4. J. J. B 10. 431 S. Phys. Proceedings of the 10th International Conference on Physics of Semiconductors Cambridge University Press. Merle. D. A. Phys. and S. Appl. S. E. Imamura. and R. Phys. J. Razeghi. 435 Y. El Jani. A. Phys. B 8. Appl. Farrell. Su. R. 14682 1995 . 479 H. 3351 1970 . Glinskii. Tanaka. Yu and E. and J. A. G. Selber. Sly. B. 542 H. Goldammer. Biefeld. Ferrini. S. 36. Phys. J. 34 2000 . 557 A. and K. 601 1966 . 86. Porowski. M. J. P. Lett. Nakatsasa. 927 1987 . B 52. A. Can. A. Turner. Heravi. A. Res. Redistribution subject to AIP license or copyright. F. G. W. M. Kowalski. Bright. J. V. 755 1995 . M.. Curzon. Y. Rowell. Appl. Phys. Lett. and L. K. Downloaded 05 Dec 2002 to 140. Phys. Sel. Phys. Y. and C. 11. A. 546 W. 495 P. Yoshimatsu. Kavanagh. Rinfret. 507 S. A. Stillman. Rev. E. 738 1997 . Matyas.. V. G. Magnanini. Jaroshevich. T. 65. M. J. Sirota and E. J. 545 P. McGroddy. J. Joullie. R. Meyer. 520 D. Xie and W. 34. Bethea. J. Phys. 1 June 2001 491 Appl. Jpn. 563 A. Krutogolova. M. Kaplan. Dunstan. S. Phys. Phys. K. 540 K. Bouarissa. 24. G. Phys. B. Sato. Poluprovodn. Poluprovodn. IEEE J. J. S. J. 776 1993 . J. and A. Skolnick. and K. J. Wang. Kawamura. Riviere. 555 S. W. Matsushima. O. Phillips. DeWinter. Kaspi. L. S. and M. 403 1997 . Cho. Kuo. M. Meney. 498 A. 2442 1994 . Fuchs. Kryukov. Barjon. B 46. Lett. 66. Geddo. Status Solidi A 163. D. Part 1 17. Scheibler. W. M. 50. F. 35. Technol. and A. 1459 1987 . Xu. A. Prat. Lett. Singer. S. R. P. Sly. M. M. G. Oueslatti. Appl. Watkins. Revenko. L. Technol. Matine. Aourag. C. J. Kimata. R. I. A. L. Phys. 24. Thewalt. Sci. Lett. and R. A. Paris 42. Vodop’yanov. 550 M. Growth 160. Wei and A. Sci. Tekh. 2799 1998 . Krutogolov. 516 N. J. E. Biryulin. Furukawa and M. M. P. H. and J. M. Appl. Craford. 3178 1989 . Duggan. 536 W. J. J. and D. K. Bouarissa and H. Mizuta. P. E. Kamada. 539 P. Kowalski. J. C. Yu. Bolkhovityanov. 84. Phys. Phys. G. 544 P. 15. 64. S. H. Pietzonka. Appl. O. Stroessner. 887 1989 . L. Mangyou. David. Adachi. H. 548 A. Rev. L. Valster. C. D. Yamaguchi. Amrane. W. J. and C. Status Solidi A 128. Lett. and M. A. N. M. B. Phys. F. C. N. H. 510 L. Kean. Polyanskaya. R. Isomura. Yu. Armelles. Kurisu. IBM J. Appl. 41. and H. Kan. Diordiev. Phys. E. Appl. Ram-Mohan. 533 A. 564 R. 1151 1981 . Hirlimann. A. 63. P. Zunger. I. R. 4075 1972 . Appl. Guizzetti. Jozwikowski. Lett. Najda. Phys. A. M. Elies. Terekhov. C. Dawson and G. K. 3169 1992 . Klem. E. 5415 1976 . Appl. R. Li. 501 K. Antypas and L. Infrared Phys. and P. A. Joullie. H. I. Thiagarajan. Vul’. B 50. Agaev and N. Cryst. Phys. 527 J. A. 5. Phys. Fortin. Huang. K141 1970 . M. 506 M. Phys. Pollack. F. K. Doezema. Appl. 1272. Phys. Rev. Luyten. H. Singapore. A. 494 A. J. Status Solidi A 4. Duggan. 547 G. Weimer. Appl. C. Phys. J. B 39. Joullie. Y. J. 1523 1971 . Spain. Phys. Y. Appl. T. S. Bekmedova. Webster. G. Capano. Lett. Appl. G. A. and J. Berger. Coderre. C. Magnanini. 480 1998 . D 26. M. Holonyak. D. Bocchi. J. 1364 1987 . S. 509 H. Phillips. M. Groves. 553 S. 743 1974 . and B. B 13. N. Dai. F. H. Naumori. A. 504 Yu. 213 1994 . S. Leroux. and J. 76. Salvador. 515 F. and J. Y. Vennegues. W. 2369 1993 . Marciniak. N. 2849 1994 . Tang. K. Lett. Quantum Electron. A. Meyer. Nahory. Phys. Heremans. Electron. Status Solidi A 2. J. Top. Mater. Appl. Martinez. 48. Phys. T. Yano. Phys. Wang. Fouquet. Schubert. 86. S. T. M. 2101 1987 . J. J. Y. 554 S. G. Phys. Phys. Chu. E. K89 1991 . C. 101 1997 . 71. Rev. Hu. and A. Pletschen. Franchi. M. A. Rodriguez and G. Solid-State Electron. Sov. Electron. R. Infrared Phys. P. 1. J. T. Y. Vol. Y. Semicond. P. 504 1994 . J. 52. Phys.. 537 1996 . T. Cryst. H. K. 159 1993 . M. 525 A. Phys. 913 1977 Fiz. 583 1969 . Phys. No. Hoffman. J. Chiu. 500 S. Sov. Wagner. 565 M. 1555 1977 . 562 M. J. 514 L. S. and W. 531 M. and J. and L. van Landuyt. Kan. 497 T. L. L757 1997 . J. Ait Kaci. Kirchner. 69. Appl. Rowell. and H. Part 1 36. and G. J. Phys. H. Meney. Emanuelsson. Ozaki. Armelles. 23. Appl. W. Rev. M. Interholzinger.-Peterburg 34. Cardona. 50. Phys. Patrini. Poluprovodn. T. 558 F. 146. 697 1995 . G. Wei and A. Tekh. Ishii. R. and A. Yeo. B. F. Yen. K. Rev. J. and K. 496 A. 556 M. Rev. T. 5859 1988 . Phys. N. G. P. Jpn. Phys. G. W. Part 2 36. Soc. 73. Rogalski and K. A. 60. Mani. W. Appl. Stringfellow and P. S. Santos. Phys. 965 1991 . R. and M. Appl. A. 3256 1992 . 13. T. 659 1985 . 3929 1989 . C. 1995 . A. I. Jpn. Ozaki. Sass. G. H. 529 Yu. Wang. 61. 2025 1999 . 11. Sato. V. Phys. Robinson. T. I. 524 N. A. 22. D. G. C. Semicond.-Peterburg 5. Geddo. N. Vol. D. Dawson. Bellani. B 47.: Vurgaftman. Hrivnak. Dawson. T.31. B 59. Bolognesi.-Peterburg 23.aip. p. Appl. R. O’Reilly. and S. Lett. Vinter. 2684 1991 . A. Sonomura. and B. 52. 2091 1978 . Appl. A. 526 H. Najda. J. and T. Doyle. and M. 1378 1988 . A. B. Leibiger. D. Chem. O. A. Lacroix. R. 549 S. Tekh. J. Kinder. 519 K. Delvin. 3412 1995 . H. 418 2000 . 523 S. 537 J. Deboeck. Phys. B 34. 405 2000 Fiz. Liedenbaum. R. 73. 170 1997 . Walther. K. Makino. D. O. J. N. 26. G. Patel. J. Yamaguchi. I. Phys. Mel’nik. 1909 1992 . Cerny. 505 D. Y. Woolley. R. 2. A. 508 ¨ M. Rheinlander. M. Morkoc. D. Ohtsuka. J. Kean. T. 93 1998 . and P. C. and N. 42. Phys. 522 Ya. J. and J. T. Guizzetti. M. D. Chen. J. Poluprovodn. Proceedings of the 22nd Conference on Physics of Semiconductors World Scientific. Kumagawa. Phys. Ryzhikh. K. B. Hopkinson. L. 77 1974 . Lett. B. and J. M. L. Lin. D. Phys. Rev. Rev. Chyi. 12272 1999 . 561 Y. and R. and W. Appl. Appl. Rodriguez. Merkel. Karouta. Dedegkaev. R. Gong. Nicholas. Chung. 4706 1999 . Prins. Appl. T. 11. Dawson. 12039 1995 . Lett. 439 1996 . Duggan. and R. 543 R. 517 N. L.8. K143 1971 . Valster. Pullin. Hopkinson. 34. H. 29. Meyer. and Yu. Zunger. K. Makino. I. and A. F. Semicond. 743 1981 . Phys. Appl. 2638 1986 . Tekh. 499 Yu. Naito. Zitouni. 9. V. J. C. 79. Filion and E. Phys. 63. 502 S. Y. L. H. and N. Girault. Skolnick. Shaw. 89. M. Raymond. A. D. 560 H. Schmitz. C. C. R. 534 R. A. Manasreh. Aulombard. L. D. E. E. Electrochem. Technol. S. and N. Tsang. A. Groves. Woollam. C. 35 1989 . and M. 521 I. J. Y. Plaskett. Bouzehouane. P. S. A. 43. S. P. and Ram-Mohan 528 5869 J. S. K. C. Phys. Ihm. Appl. 3132 1998 . Kean. R. Drechsler. Klem. Otsuka. Manasreh. B. Appl. Dev. J. R. Borghs. Ohtsuka. Lett. Phys. 213 1974 . Valster. Franchi. Levine. Hafich. E. Phys. 58. 1847 1996 . Krijn. Hengehold. Greene. Appl. J. Y. Phys. P. W. 62. 2165 1970 . and V. J. Krier. Koidl. and J. M. Mowbray. and M. 532 N. Bhan. R. Appl. J.. 46. 805 1971 . M. 744 1991 . B. P. T. T. Marciniak. Y. O. Robinson. G. L. M. 512 J. 211 1996 . M. Phys. Dunstan. Phys. A. P. E. Prins. Gottschalch. Inoue. Lett. Semicond. 58. Stotz. D. Phys. Nelson. 535 M. and A. P. Woodall. and G. Thomas. Chen. Solids 56. J. Brown. Semicond. Technol. E. 603 1995 . Appl. Chung. Cardona. 552 X. Res. and R. 65. Quantum Electron. M. Ditzenberger. 2101 1998 . 77. B. T. Sov. D. G. 551 X. 944 1997 . Laugt. James. Phys. Kunakin. Woolley. J. 1330 1972 Fiz. Phys.jsp . Follstaedt. Baraldi. J. Y. 530 G. Alibert. Lett. Aourag. U. and G. and M. and M. and S. Lett. Phys. C. Gong. Adachi. X. C. Mani. 518 M. C. Aoyama. 11190 1994 . and J. 3251 1997 . Hart. 513 J. R. 493 M. A. Mebarki. L. J. Thompson. Huang. S. Phys. Menoni. Phys. Suzuki. Adams. W. O’Reilly. H. T. 61. Semicond.org/japo/japcr. Appl. M. Phys. Robert. Stradling. K81 1975 . Kumagawa. Can. Joullie. Rev. Dawson. 118. Phys. H. S. Cleverley. V. Norman. ’t Hooft. Miyauchi. 1177 1995 . Herzog. A. Status Solidi B 199. P.-H. D. and S. V. D. G. Appl. P. Woolley. L. M.105. Rev. L. 503 S. and J. Status Solidi B 65. J. Appl. I. S. 511 H. F. L. Marcadet. Wong. 559 A. Boukredimi. Kurtz. Semicond. E. Phys. M. Stutz. Appl. P. Choi. K. Appl. S. Kadri. S. IEEE J. Germini. J. 557 1989 Fiz. Y. M. and A. Chang. Kuo. see http://ojps. Chin. J. F. Technol. Sov. and G. Phys.-Peterburg 11. X. Phys. S. and K. Lorenz.-H. M. Tu. Sites. and M. 538 D. 30. E. Mertens. N. Status Solidi B 68. 10. Massies. D. Anwar and R. 541 J. J. Phys. J. H. IEEE Photonics Technol. R. Lett. Shmartsev. M. Williams. Hua. S. 12598 1993 . M. M. C. Woolley. J. Syassen. Shaklee. J. Duggan. 349 1995 . Rakovska. Morkoc. C. Dovzhenko. 492 G. C. Michels. J. Kozlovskii. Appl. 1607 1977 . Ahlswede.J. Mowbray. Balkanski. Dobbelaere. I. O. Lett. Phys. Goni. Sci. Vurgaftman. Adams. G. M. Phys. Appl. Sakai. Nakadaira and H. Nishida. 82. Appl. 604 J. Cryst. Stolz. 75. P. Tu. 1928 1998 . S. Uomi. Appl. Y. S. Shimomura. 4452 1998 . T. Bahng. Perkins. C. 2630 1998 . 65. J. 637 T. 59. 605 S. P. Phys. H. Phys. Sota. Poluprovodn. S. and Yu. K. Appl. Y. Phys. Lett. G. Phys. V. Phys. 36 2000 . 574 M. N. 603 J. A. and R. Mascarenhas. R. 578 M. Phys. Y. J. 610 L. M. Rev. 569 H. Semicond. T. J. 71. M. 2048 1977 . Lett. and S. Nakajima. C. B. J. O’Donnell. Phys. Bergman. Koch. 5084 1972 . T. and A. Rubio and M. A. S. Appl. Heuken. D. 611 M. N. Pollak. Aumer. Phys. Ivanov. Appl. Lett. 76. Semicond. A. Redistribution subject to AIP license or copyright. 10568 1995 . Le Corre. R. F. Phys. G. H. Nicholas. W. Guo. Sov. Lett. Anan. Sawaki. S. H. Phys. Phys. Sik. J. B. Mascarenhas.-H. 10233 1997 . X. T. 148 1997 . 342 1988 . Phys. Terauchi. L. G. Bi and C. Nicholas. Shmartsev. Phys. and J. C. Phys. and C. 59. J. Zhang. Part 2 33. V. 135 1999 . 2725 1998 . H. F. A. V. Sakai. Phys. 646 J. S. Kato. Mater. S. Ogawa.5870 566 567 J. Klar. P. Nordgren. R7861 2000 . and E.-H. 11. S. 70. 3830 1998 . Ougazzaden. Appl. Bellaiche. Lett. 2984 1997 . Appl. T. A. V. Ni. Appl. B. Appl. Cohen. C 12. Araki. S. Appl. Kobayashi.. 2720 1997 . Choe. 112. G. A.: Vurgaftman. 800 1997 . 596 M. Jen. J. E. Z. 84. Appl. Saxler. S. Mattila. Jr. B 60. Camassel. Appl. 89. Razeghi. Shim. 77. 462 1995 . Jpn. 2024 1994 . Khan. 74. Phys. Salzman and H. 2832 2000 . Phys. Nelson. 606 M. B. V. Jpn. Phys. Lischka. 3558 1997 . G. Zahn. Davis. M. Kistenmacher. Lett. B. Electron. Tu. and Y. Phys. Mascarenhas. Phys. V. and G. M. Sci. C. Lett.. 575 R. 76. J. and Ram-Mohan Y.-J.-C. S. D. K. Khan. M. Xin. E. Phys. Makimoto. Shan et al. 579 M. C. Phys. 587 1981 . Koide. 20. 76. Appl. Amano. L143 1978 . and G. Cryst. Lett. H. Lett. 43. Kuroiwa. 76. B 54. H. 635 L. A. T. E. Kim. Reihlen. Stringfellow.31. 3696 1998 . Loualiche. Sci. Downes. Growth 162. 211 1988 Fiz. 27. 22. 123Õ124. M. Deibuk. 581 S. Kobayashi. Phys. Hasegawa. J. Antypas and T. 114. Sletov. Foster. I. 2566 1999 . 62. Lett. Patriarche. Wada. C. Zheleva. G.. 588 K. 580 G. Lett. As. G. 4604 1990 . Phys. D. Zunger. T. J. Omoto. 600 C. Monemar. V. de Mierry. Huang and J. Rev. Hai. 75. A. R. Zubrilov. Misawa. Minamino. Leibiger. Rao. V. R. Phys. Akasaki. Askenazy. Appl. 76. R. H. J. Nitta. J. Sov. Lett. Appl. Kim. A. S. Portal. B. C. K. Zunger. R. 52.-Peterburg 34. L. 644 L. 596 1982 Fiz. Perry. Growth 133. A. Y. Phys. 619 K. Appl. Zhang. J. Martin. R. Gibart. 624 M. Katoh. 634 A. Qiu. D. V. Phys. D. 1158 1998 . Phys. Solid State Commun. Lett. Kozhevnikov. Caulet. and I. Phys. Liu. Cherng. Lett. Nelson. Appl. 70. J. Lindsay and E. W. Phys. Gershenzon.jsp . M. 585 E. Sci. F. Lett. Uesugi. K. Kohler. 323 1987 . Akasaki. Nagatomo. Kurtz. see http://ojps. Behres. Kariya. 647 L. 291 2000 . Temkin. Semicond. 69. Saito. Yep. 582 H. Appl.-Peterburg 16. N. and K. 3439 2000 . W. 70. 2587 1999 . P.aip. Koide. Weyers and M. Parker. Asahi. O’Reilly.. Schulze. Shokhovets. Appl. Yoshida. S. Neugebauer and C. Lett. 602 M. H. D. Appl. J. 625 R. Yu. Li. Res. Chaldyshev. Phys. Stradling. R7 1998 . J. Bryden. J. Sov. Bellaiche and A. and I. 549 1988 . H. B 58. W. 705 1995 . and A. P. H. Romano. Kudou. Growth 195. V. J. 640 J. F. M. 84. Metcalfe. and T. Rev. 572 R. F. Rev. 1396 1993 . H. 650 C. McCluskey. H. J. El-Masry. and B. Johnson. 72. N. Phys. Phys. Rev. 632 M. M. 1608 1997 . 237 1999 . G. G. C. Yamaguchi. R. Deveaud. Phys. 651 Y. and S. Vicente. Vol. Gil. L. 84. K. Asami. Phys. 1843 2000 . A. Phys. Lett. and T. Wright and J. P. Phys. Skiebriszewski et al. Stringfellow. 68. and D. 599 W. A. 618 Q. 76. Appl. Itoh. Appl. Ivanov.. Appl. Faleev. Appl. Cryst. Werninghaus. Olson. Phys. Van de Walle. and A. B. Holst et al. Lett. E. 2861 1997 . J. 576 V. J. Desjardins. M. Wright and J. G. Takeuchi. Phys. Thordson. Matsuoka. Yoshimoto. Beaudoin. G. J. Akasaki. D. Scheiner. Nakamura. Phys. F. 623 M. 643 B. Y. S. Bargeron. T. MRS Internet J. R. 615 S. R. and T. 598 C. 589 T. Amus’ya. 1990 1996 . and E. Y. B 56. 72.-X. 620 T. 76. D. Lett. 443 1999 . D. H.-H. H. Kung. 631 T.8. Mozume. Growth 93. Van de Walle. 746 1998 . Rev.105. Schubert. G. Hofmann. V. 66. and J. Appl. Status Solidi B 205.-Peterburg 22. Part 2 28. Lett. and C. V. Mathieu. Part 1 32. 641 K. Master. A. L853 1992 . Lett. 4425 1998 . and H. S. Merle. V. R. Lett. and Y. Y. W. Robins. Wetzel. Zunger. L1334 1989 . T. 570 Y. 1951 1994 . Phys. Phys. F. M. and I. Appl. Phys. Hosomi. S. H. Peng. J. 3390 1996 . Min’kov. Itoh. Appl. Duda. C. and R. M. Cherng. 66. Appl. 568 A. Meyer. Phys. Lett. Weyers. Phys. I. 613 G. 509 1986 . Eng. 82. 664 1996 . M. and G. Morooka. Schubert. C 12. 7479 2000 . 601 H. F. B 61. Zunger. Jpn. 17568 1996 . and W. Aspnes. P. W. Appl. M. Phys. J. S. 614 T. Cryst. Gonzalez. Rev. Heimbrodt. Gauneau. T. P. Ueta. Phys. Masut. 61. 16. 4433 2000 .-H. Juhel. Appl. J. G. Phys. Jen. Sato. Bellaiche. Humlicek. H. Nam. Phys. 928 1982 . and P. 1254 1999 . 2439 1997 . Rev. Lett. Stringfellow. Rev. S. 621 S. A. 594 R. P. 597 T. Zhang. Voznyi. Akutagawa. 4413 1993 . M. and I. Appl. Biefeld. Isnard. B. Amano. Appl. Beaumont. M.. 636 L. 2251 1991 . Amano. Tu. Moustakas. N. Wickenden. H. 492 1983 . Appl. V. P. Phys. Appl. M. Phys. Ueda. Suemune. V. Lett. G. Akasaki. Phys. and K. Meyer. 645 K. 4540 1987 . and S. J. Xin. 70. Fang. 484 1998 . Leprince. Solid State Commun. Yoshida. D. 623 2000 . Lee. Phys. 583 T. 642 P. M. Parikh. Guo. Semicond. Onton and L. A. 593 W. No. K. Appl. 627 M. and L.. 42. A. Miragliotta. and L. and D. and T. 1653 1979 . 577 C. Cryst. Phys. B 61. J. Suemune. K. Part 2 36. Xin. J. M. Bhat. M. Amano. 70. 622 A. Lett. Kondow. Zhang. P. Khan. Appl. K. Lett. Antipov. 590 N. Takeuchi. Umezawa. T. M. Rev. Piprek. A. T. K. Phys. Chennouf. and J. 629 J. J. Friedman. and I. 592 S. P. Phys. A. L. K. Hagen. L. Clark. L. Rev. and M. Surf. and O. Appl. Lim. Gottschalch. J. 616 A. Biryulin. 2. H. Wickenden. H. Lett. J. Zunger. and O. Katsui. Schrenk. A. Lett. S. 10. Phys. 584 V. Geisz. Status Solidi B 216. J. Swann. S. Armelles. J. Mascarenhas. Takeuchi. Appl. K. Pozina. Jou. Rev. 60. LeBoeuf. W. B 50. Schneider. Wei. S. and P. Wei. 6844 1982 . Narayanamurti. 630 A. Sato. B 61. Mater. Appl. Xin. Malikova. 423 1991 . 649 P. M. Andersson. Phys.org/japo/japcr. Appl. B 51. and S. Growth 146. Follstaedt. Fukui and Y. P. Horikoshi. Uesugi. Stringfellow. J. Wei. and A. J. Mater. B 53. Ando. A. Jou. P. R11245 1999 . 43... Lett. Wei. and J. Solid State Commun. 595 L. and H. Phys. Phys. Jou. E. and G. 626 S. Akasaki. P. Electron. G. 38 1993 . M. J. Part 2 31. Kruzhaev. J. Tu. Bedair. 586 R. U. H. Phys. Y. Jpn. K. Appl. 66. J. Lett. S. 34. L177 1997 . Kirpal. Gonda. R. S. O. 628 G. N.-Chr. J. Downloaded 05 Dec 2002 to 140. Appl. B. Appl. and A. Hohnsdorf. C. 4343 1995 . and S. 639 W. Bellaiche. K. H. Akasaki. Phys. Tu. A. 1. H. Appl. J. Baucom. McIntosh. B 57. Wei and A. Phys. Novikov. 1641 1979 . Middleton. Roberts. 638 A. Gonda. J. Sugou. Nakamura. T. Amano. Phys. Le Bellego. 3315 1999 . Sci. T.. and B. V. J. Heime. S. 587 D. Wetzel. 609 D. Nikishin. Rut. 648 Y. Buyanova. 2859 2000 . 73. Sotomayor Torres and R. and K. Phys. Appl. Ameziane. J. Leonelli.-H. M. and G. 62 1988 . H. W. Temkin. 8 1996 . Tekh. T. 573 M. Phys. O. C. J. C 11. Bremser. D. and T. N. W. M. Bedair. Rev. Stradling. 571 G. A. and N. L1056 1994 . Tekh. 3028 2000 . Fujimoto. H. T. K. Poluprovodn. J. and N. Smith. and A. S. Yamaguchi. Zunger. 3201 1971 . Lett. B 15. Laugt. F. A. H. M. and I. Gruning. I. Lett. 53. A 13. J. Lambert. C. O. Kubota. and I. J. and C. Lett. D. Unruh. Golubev. Tanaka. Phys. Jpn. Rev. Akasa. Phys. B. J. 1285 2000 . Steude. W. 591 A. T. Gonzalez. Leroux. Phys. 919 1981 . Lecrosnier. S. 73. J. H. J. Appl. Stradling. W. Tekh. 617 K. Salaun. Phys. Appl. 633 J. Poluprovodn. Takeuchi. Olowolafe. Phys. Edwards. F. Phys. and I. Stagarescu. J. B 51. Vac. Rev. I. Jpn. Appl. 2984 1989 . and M. M. Kurtz. F. Ramage. 1 June 2001 608 Appl. D. Skogman. R. 76. N. 71. 612 V. A. H. H. L’Esperance. 121 1996 . Rev. Goldhahn. Appl.. A. Appl. 76. Lett. Harris. Hiramatu. H. 3465 1995 . Omnes. Vorob’eva. Kuboyama. and S. Iwata. 35 2000 Fiz. 309 1998 . Frey. Chen. M. Korakakis. M. Kim. Phys. D. S. Bensaada. 75. Technol. J. 2722 2000 . Reddy. W. Reed. Nitride Semicond. K. 3051 1995 . R. Drews. 607 M. 3312 1999 . H. Technol. R. 1994 1998 . Arnold. 715 T. I. and Y. Phys. M. and H. P. 97 2000 . Holonyak. 3576 2000 . Z. Ivanov. Appl. D. M. B. K. E. Kurtz. Daniels-Race. S. Mars. 2931 1997 . 295 and references therein. Lett. Bi and C. Bohrer. N. J. P. Phys. Sherstnev. 635 1974 . 70. Sirota. 702 M. Bouarissa. 714 M. V. Young. Lett. Jr. A. Subramanya. and G. Solid State Phys.-C.. Phys. Xin. Mater. L. Hsu. Phys. B. Appl. Thompson. J. 639 1981 . D. Kruger. A. Baillargeon. A. B. W. C. Ya. 709 P. Chamberlain. Wiegmann. 33. 8480 1993 . and G. Poluprovodn. Kisker. J. J. 75. 725 J. 30. Bimberg. Henderson. Appl. A. DeWinter. V. Hofler. B 16. A. 17. 77. Mauk. 671 E. H. Beresford. M. 669 G. S. Stringfellow. and G. G. J. 732 E. 978 1993 Fiz. 791 2000 . Appl. Yu. Mascarenhas. Lett. Tekh. Menendez. Sherstnev. E. P. 89. 692 J. K. and S. W. Siegle. P. 1161 2000 . 699 M. Pollack. Kurtz. in GaInAsP Alloy Semiconductors. Phys. 724 P. 6116 1992 . Macksey. Phys.-C. K.-Peterburg 24. M. and references therein. 39. M. A. Matevosyan. Moon. Appl. 33 1989 . M. J. Sci. and T. Zyskind. Mater. Tit and M. N. B. N. 2540 1992 . and M. 2891 1999 . 688 J. L. L. M. 706 S. and J. J. 24. Zhou. and J. Chin. and H. S. Phys. Coleman. Hill. J. 41 1986 . and L. J. 1314 1999 . Semicond. Shan. 423 1999 . K. Electron. N.. 276 1991 . H. 1780 2000 . and J. and C. G. Semicond. Cryst. 681 R. S. Mater. J. H. and K. X. and M. Tiwald. No. W. A. D. Lett. B. Phys. M. Appl. Bishop. 685 D. and S. Yeh. B 60. 697 L. Asami.: Vurgaftman. 655 S. 12. Poluprovodn. Shin.. Technol. L. 75. J.-K. H. Phys. Cheng. Phys. C. and N. 667 1998 . J. Semicond. J. 1 June 2001 652 Appl. N. M. 1397 1990 . E. 717 E. Mou. Tu. Wu and C. Alibert. L. Tournie.. Phys. Voronina. J.. and Yu. Lett. J. R. Glisson. Rev. and Z. Y. S. T. 5340 1985 . Shan. 730 Q. T. Phys. R. Y. 2409 2000 . Lu. Wu. W. A. Chen. and S. 139 1981 . Wilson. R. Asif Khan et al. Rev. Astles. A. S. Mikhailova. Cryst. Petersen. edited by J. 704 M. Alferov. Gonda. Tozer. 1 1992 . R. Poluprovodn. Phys. Hauser. 4134 1992 . Phys. D. Appl. 675 M. Appl. Poluprovodn. Jiang. G. IEEE J. K. and A. and E. S. and R. D. C. 77. K. Dmitriev. S. Korb. 299 1986 . Growth 179. Sipovskaya. G. Phys. A. Poluprovodn. Shellenberger. Tekh. Appl. Appl. Sov. N. 674 L. T. 36. M. C. Prokof’eva. Phys. 719 H. 14. 117 1988 . Bellaiche. H. 658 W. Littlejohn. V. K135 1976 . L320 1997 . Williams. 279 1999 . Klem. W. 676 C.. 684 J. Nishino. S. 667 K. 76. 26. 217 1987 . A. G. and S. W. Lett. Patel. Surf. and H. E. J. A. p. R. 73. H. 208 1993 . E. Kawamura. L. 876 1990 Fiz. Growth 216. Watanabe. Y. E. Bajaj.. 1237 1984 . Redistribution subject to AIP license or copyright. Ianno. Aourag. Gossard. Koteles. G. and L. Chap. Lett. Thin Solid Films 313–314. 664 C. Xin. 314 1996 . 419 1986 .-W. J. Parayanthal and F. 76.. F. 543 1983 . E. A. Joullie. Phys. W. 680 J. and S. Y. Baillargeon. N. Mashita. Hegde. and W. Tekh. Jpn. Finkelstein. Lin. 9. Jpn. D. 59. 729 1985 . McGill. 726 M. T. Weber. W. Chen. Shiraki. 74. 77 1972 Fiz. Appl. B21 1992 . E. Appl. A. R. E. Williams. Phys. Sakai. and Z. Tekh. Zhong. W. Y. Hsieh. Ager III. X. Sov. 2180 2000 . Ketterson. C. M. 721 R. Ababou. 711 R. Dharma-wardana. Dawson. G. Pollack. 657 H. Semicond. Dore. N. Lagunova. H. M. B. J. Asahi. Moiseev. Kroemer. Li. G. Growth 145. N. 63. S. 87. Phys. Bouarissa. and Y. Y. Appl. J. C. Phys. Gossard.-C. V. Yakovlev. A. L. Voronina. Kazaryan. and A. T. A. Phys. 76. Wu. M.org/japo/japcr. A. Ager III. W. Phys. 683 P. J. Geisz. Phys. Henry. R. Mater. C. Appl. Jaw. and C. 708 W. Stillman. J. Pearah. Appl. Tome. 1287 1999 . L. Huang. 712 C. Lazzari. Sov. Yaguchi. A. Phys. Appl. Quantum Electron. S.8. Yassievich. Bodnar. Phys. Phys. Smirnova. W. Lahtinen and T. Lagunova. V. M. Phys. Bi and A. B 28. T. Chen. Avdzyan. S. and D. D. Lett. Growth 121. L. Jones. Emanuel. P. F. L. Part 1 38. J. 62. Modine. J. J. T. Appl. Abid. J. N. 689 V. Leite. 713 M. I. Kuo. 6. James. A. 737 1993 . and G. J. Oder. Phys. Tu. S. 18. J. H. A. Garbuzov et al. J. Semicond. K. and Ram-Mohan 5871 J. K. Mou. 404 1987 . and X. 7. Yu. 1221 1999 . J. W. Sci. Zhu. Sci. 698 T. A. and S. Lett. Walukiewicz. 639 1978 . 705 M. 132. Sherstnev. N. Pinczuk. 76. K. Tamulaitis et al. A. Phys. W. D. Part 1 37. Xin. Wei. Yu. Li. Lett. C. 48. 11. Surf. J. Phys. Tekh. 48. Shapiro. 74. Phys. 1 1997 . 723 D. 679 Y. J. W. Dingle. Afrailov. Jones. Phys. 661 T. Patel. H. B 33. Werder. Sov. Phys. M. 733 Q. Lett. F.-Peterburg 25. Voronina. Tu. Mirzabekyan. 1279 1994 . Stringfellow. Phys. P.. 1934 1996 . T. Semicond. Sci. Lett. T. and M. 710 N. Haller. 716 G. J. 73. 75. H. Rev. 2578 1999 . 71. and A. P. Sorokin. Weiser. Pearsall. D. Lambert. Woodhouse. Yakovlev. 72. Part 1 31. Blue. P. N. Zyskind. S. 53 1992 . S. N. H. Kurtz. A. Lagunova. Electron. 419 1980 . J. Sov. Appl. 238 1999 . J. Appl. A. Rev. Perlin. 63. Chang. H. Xin and C. Phys. E. A. 720 R. Logan. Sov. and K. and M. Hamarakawa. and T. Phys. 2935 1981 . Dingle. G. 1918 1993 . Mani. 40. Phys. 827 1974 . R. Electron. Lett. Lett. Srivastava. Eng. Haller. W. 666 P. 16. J. Semicond. Phys. Laufer. 977 1992 . J. A. 76. O. Friedman. and Yu. Sov. T. J. Phys.J. Woollam. 694 H. Aleksanyan. 696 H. Appl. Y. C.. P. E. V. 718 H. Lett. 25. and I. 77. T. 82. R. A. C. 11. C. N. J. Sipovskaya. Reeder. A. 15. and A. 50. Antypas. Wei. 70. and J. B 41. 659 H. Lett. Vac. V.jsp . 663 N. Phys. 77. W. Appl. C. 395. Moiseev. G. 3. 63. Liu. Miyoshi. Miller. 656 H. Mater. S. A. Thulke. Freeouf. Charache. Mikhailova. J. J. Appl. Wu. Zhou. Welty. E. Lett. Forrest. Appl. A. J. Jpn. Abul-Fadl. M. and L. and A. Chen. Zhong. Appl. Lett. 910 1977 Fiz. Nakanisi. Haase. 3251 2000 . Poluprovodn. Downloaded 05 Dec 2002 to 140. and H. Lett. Cheng. Yoshida. P. J. M. 21. McCaldin. and Z. Phys. 727 C. 4430 1999 . Yamazoe. Appl. S. Pollack. Mater. Sci. Infrared Phys. 668 N. 690 M. 87 1994 . Lin. D. 654 S. K. Status Solidi B 73. S. A. 12. Tu. Kuphal. A.-C. Iyer. J. Appl. S. 701 J. Miyoshi and K. Y. 700 D. A. 73. F. Lett. P. W. W. Cherng. and Zh. Phys.. P. M. 1991 . Yang. A. Appl. Wang. Vol. Status Solidi B 130. 45. 80. Technol. P. Pollack.-J. Appl. A. Lett. Tanaka. M. 677 T. Wright. Sci. J. 731 S. 728 M. P. Singapore. J.31. Kroemer. Sorokin. A. K. Semenov. J. Scifres. Onabe. 2813 1993 . Rev. Semicond. Temkin. Superlattices Microstruct. 660 W. Olson. 3703 1998 . 678 P. Superlattices Microstruct. 707 K. Meltser. Appl. A.-C. R. G. J. Morkoc. Timchenko. H. Phys. S. Solid State Commun. 60. J. 703 J. K. Ito. 693 N. T. K. Snyder. Hoger. 1777 1993 . L. 662 R. I. Gokhale. Madelon and M. Appl. Chow. Stevens. M. p. Solid-State Electron. F. B. Electron. Appl. A. A. R. Phys. Tu. I. X. V. 163 1992 . E. Su. Rev. Morosini. Krost. E. Wright. Phys. 77. Smith. Batey and S. 541 1986 . B. J. 97 1972 . Tuomi. N. 3958 1993 . 5485 1988 . Meyer. J. Munoz. Electron. Lett. Chaves World Scientific. S. 722 J. Baranov. in Proceedings of the 5th Brazilian School on Semiconductor Physics. Yakovlev. Z. Phys. 25. Onabe. E. R. Appl. Mitchel. Turner. R. Lett. S. Solid State Commun. Jpn. Appl. S. K. R. Phys. 1550 1977 . 1946 2000 . Schwatzman. Sipovskaya. Allerman. 695 T. J. S. Mikhailova and A. P. 672 P. 673 W. A. 1639 1991 . Modine. Appl. A. 463 1992 . Appl. English. Coblentz. Lett. F. Phys. N. and D. Timchenko. Allerman. K. H. F. and W. 729 S. Phys. Phys. Regreny. edited by T. 653 X. Cryst.105. 1293 1998 . C. 670 W. Appl. O. M. Appl. Phys. Technol. Satzke.-W. and W. A. H. 34. 46. Herrera-Perez. D. Lett. A. 27. Zhu. Pearsall. 682 K. Lukomskii.-Peterburg 27. C. Nahory. Phys. W. M. I. Smirnova. Lett. Srivastava. 686 J. C. A. see http://ojps. P. and C. McNeil. 4680 1998 . Hsu. Pollack. D. Phys. S. Lett. J. 57. Wu. 200 1986 . Wu and C. Yu. R. Technol. P. Benchimol. and B. 2136 2000 . Appl.aip. 167 1991 Fiz. Part 2 36.-Peterburg 11. Cryst. J. A. Chen. 989 1991 Fiz. and Yu.-Peterburg 6. 687 M. Skierbiszewski et al. A. 1327 1975 . C. Rev. W. S. Yakovlev. Houston. 2514 1992 . J. N. Phys. Smorchkova. J.-W. C. Quantum Electron. 4541 1995 . Tekh. Zhang. I. 1267 2000 . L. Wang. Li. 174.-Peterburg 25. T. H. 3632 1983 . Titkov. Appl. 665 R. T. L. Hojo. Lyon and C. T. Ho. C. Burnham. Rezki. Fazzio. G. Solid State Commun. L. H. Menoni. Wei. Popova. I. Phys. W. Wiegmann. J. I. Mater. J. 9. 691 T. R. S. Guillot. Sci. V. 8863 1986 . Tu. C. Walukiewicz. R. 637 1985 . Wright. Nakajima. 7. J. Vac. A. J. J. Tabata. W. R. K.org/japo/japcr. Letartre. Rev. Leymarie. Recio. S. 58. 524 1992 . Phys. M. Superlattices Microstruct. Benyattou. Vasson. 766 C. A. 62. 1997 . 809 T. M. Rev. Bhargava. Kraut. Phys. Phys. 813 R. and T. v. P. E. F. 705 1982 . Phys. Bohrer. and F. 801 J. A. Mater. P.-I. and D. 754 I. D. M. and T. and E. F. Luth. Waldrop. Sputz. Kirchner. Wicks. K. 69. Takahashi. Electron.-M. P. and R. and E. Narayanamurti. Tu. 69. Pinczuk. 10. and Y. 79. S. L6 1996 . Rev. Phys. Y. Iwamoto. Y. H. Appl. 74. 744 N. Zekentes. Hirakawa. E. 743 A.-H. and F. M. P. Kraut. C. Massies. K. Lugagne-Delpon. and Y. R. Forster. S. J. Technol. Arias. Appl. Andersen.-C. Krebs. Stievenard. Rev. Desjardins. J. Syassen. Rev. G. Masut. M. 755 Y. M. E. Appl. Rev. W. Phys. Appl. and L. 83. J. 7. H. Appl. 59. Ghiraldo. B. and P. 753 K.. and H. W. Proceedings of the 23rd Symposium on Compound Semiconductors IOP. Lu. Beaudoin. P. Ilg. A. J. Jr. 742 M. J. Huang. Welch. P. V. and P. Priester. Schneider. Y. Esquivias. 745 W. B 8. P. 922 1997 . 792 W. F. P. 738 A. Cryst. UK. Phys. B 55. J. 757 L. 796 G. D. Appl. Spicer. 127 1995 . 800 L. and L. Burkner. G. 789 V. V. 772 L. Monier. Semicond. Phys. S. Shih. B 45. J. A. Phys. Rev. Hybertsen. Massies. Morris. Holzbrecher. 58. G. J. H. and T. M. A. Bristol. Hrivnak. No. Woodall. T. Alonso. O’Shea. F. Sci. Lugagne-Delpon. 889 1991 . 3176 1984 . Cheong. W. Appl. 18147 1994 . Phys. Shiraki. Lett. 80. Garcia.-C. R. 1632 1987 . M. Appl. Lett. Butov. 736 K. 2893 1994 . Sci. B 59. Hou. W. Sci. R. S. 773 E. J. Venet. 799 E. E.. Chi and Y. Phys. H. B 51. Burnett. Rev. 815 1989 . P. Technol. Sci. d. J. Sorensen.-Peterburg 33. J. Wei and A.-H. Shen. and B. and P. 768 J. and L. Phys. J. Rev. J. and K. K. Pikhtin. 791 J. F. V. 4673 1994 . H. Nakamura. C. B 56. Phys. 752 D. Lett. Kraut. Monteil. and R. K. 766 1996 . Appl. B 44. 63. 477 1993 . Phys. 86. Rosenzweig. R. N. and J. Rev. O. Electron. T. Phys. 8083 1992 . Menendez. and A. Bugge. W. C. 778 J. M. Maurel. Rev. and H. 8.-Z. K. Rev. Mater. Li. J. Sci. Gendry. F. Forrest. Aristone. Luth. I. Pollak. 1241 1992 . A. Phys. Weisser. 767 C. Davies. Moneger. Vac. Tidemand-Petersson. 2292 1997 . Grant. Forster. Grandjean. V. Hopkins. 70. 740 J. 76. M. B 38. Jogai. Appl. Stolz. 6968 1985 . J. 749 W. 147 1997 . Lett. Barbarin. Hashimoto. Pao. B 47. 85. Veje. M. K. D.aip. C. Shen. and G. 20. 76. Xu. B 35. Foulon and C.-H. Elliott. Lett. and J. Rev. J. Andersson. 6182 1987 . Z. Yang. Mel’nik. 65. 785 B. and G. J. 746 S. Palmier. Lett. Phys. 5056 1999 . L. Hirtz. Voisin. J. Holtz. Smith. E. Phys. Muraki. 748 M. 1010 1994 . V. Appl. C. J. Appl. J. 815 P. E. and Z. Rev. W. Leymarie.-M. Phys. Phys. Technol. Huang. Y. Phys. J. Kraut. O. Szmulowicz. J. Semicond. Vasson. B. A. T. Waldrop. 1117 1991 . C. Wang. Solid State Commun. Andre. T. S. Naudzius. B 50. Briones. Technol. Kulakovskii. M. W. and H. M. Van de Walle and R. and J. and J. Zheng. Kochman. Fekete. Tabata. A. 2406 1997 . Vasson. S. 51. B 49. 760 J. H. 774 E. Wessels. 1734 1991 . M. Appl. 2274 1997 . J. Rev. Rev. J. Tit. 70. M. Beltram. and G. 2050 1991 . J. Vleuten. Rev. 747 J. and J. Z. 758 C. P. 769 Y. 790 W. Miller. 1 June 2001 775 Appl. B 32. Phys. and A. H. Sci. M. A.8. Yu. M. Phys. H. Phys. Sci. I. M. S. Hwang. Lett. Daniels. 2011 1998 . 782 J.jsp .-Z. 779 J. Appl. Farley. Eastman. and R. 33. Segall. G. 79. 7864 1998 . Phys. Eng. 1 1993 . N. P. Electron. Joyce. Phys. 2813 1990 . Satzke. Phys. 55. 762 K. Badolato. Bhattacharya. Leroux. J. 2026 1997 . Tersoff. Farley. Cardona and N. Phys. A. Solid State Commun. Lugand. Downloaded 05 Dec 2002 to 140. Phys. J. F. A. Munoz. 764 W. 765 J. 741 V. G. J. Harada. 807 S. and J. Werder. Technol. 26. Grant. 75. 739 D. Phys. Rev. First. H. Laureto. 768 1990 . Brafman. 1437 1993 . 8165 1987 . K. Vasson. M. Duarte. A. Phys.5872 734 J. G. and B.: Vurgaftman. 1628 1994 . Rev. J. Appl. Williams. C. Solomonov. Marcinkevicius. and D. 776 J. Appl. Zhou. C. 788 Y. K111 1991 . S. Wang. and M. 253 1998 . 781 C. and E. Phys. 808 J. J. D. M. Ghosh. Phys. 11. Voos. Waldrop. Phys. V. Lambrecht and B. J. Hou and C.: Condens. B. T. Dias. Karunasiri. Appl. Appl. Ke. Vac. 786 M. Appl. Ge. and R. Huang and T. M. W. B 55. Harmand. 761 J. and J. Goldys. 2571 2000 . P. Sci. Huang. A 16. H. G. and R. Meyer. M. Aina. Garcia-Moliner. Nelson. Zubkov. 842 1991 . S. 79. Wang. M. Y. Leymarie. Voisin. Di Mauro. 2263 1991 . 372 1991 . K. D. Massies. H. M. 7723 1988 . 13820 1996 . 763 M. A. W. Lambrecht. Solid State Commun. P. Gal. C.-M. W. 49 1995 . Technol. R. Phys. Phys. W. Guillot. Wang. and G. Phys. Marsal. and R. 1878 1989 . R. Dosanjh. Phys. W. 4528 1988 . Moers. 2728 1994 . B 54. and Y. B 38. Hollinger. Technol. Solomonov. Phys. Clarke. Lett. 2832 1990 . Finkelstein. Toginho Filho. G. Lett. Vaughan. Martin.: Condens. Paul. C. and M. P. Vieren. Phys. Armelles. A. Vol. L. Phys. Mazzer. R. J. E. Stragier. Barnes. R. G. E. Phys. J. Landesman. 1620 1988 . Christensen. 977. Appl. 750 R. Feng. 10315 1999 . E. Saxena. A. B 43. Sci. W. Disseix. and Ram-Mohan E. 811 J. Luth. Guillot. Phys. Forchhammer. Harris. 7775 1996 . J. T. 770 C. Kowalczyk. Singh. 804 J. Barnham. I. C. Piazza. 291 1993 . Phys. Ohler. Glytsis. A. Zuo. 76. P. B 59. Vac. Westwood. 14693 1995 . Y. G. and K. 797 P. J. Dugay. Krost. Langer. Velasco. Appl. R. F. 54. A. Rev. Guthrie. 795 G. Grandjean. R. Georgakilas. R. Matter 4. Phys. Schaffer. 805 1998 . Wang. 1759 1991 . Appl. 1047 1991 . Courboules. G. 858 1999 Fiz. 6259 1992 . Wessels. Matter 9. Segall. B 7. Voisin. Appl. Phys. Souliere. 784 X. A. Lett. B 44. Sauncy. Ploog. Rev. Qiang. Delerue. B 50. B 58. Abraham. R. and H. Baltagi. Baltagi. A. L. Roberts. Seidel. N. J. Chin. Phys. S. K. Grant. 780 K. Grant. Tekh. Waldrop. F. 72. Zheng. 812 R. Redistribution subject to AIP license or copyright. Bosh. S. Pate. L. A. Tansley. C. 13274 1995 . Williams. S. and A. Rezki. W. J. Zubkov. A. Disseix. Phys. 76. A. B 41. W. M. I. J. 771 J. C. 759 J. E. 814 H. K. and V. 4071 1999 . G. Mattingly. and U. Technol. Halkias. J. 439 1997 . F. J. 777 S. 71. Phys. C. Lett. Ohler. 3144 1991 . B 44. Leuther.-C. Andre. Mater. 20. 1146 2000 . R. R. Leonelli. L. T. W. A. 201 2000 . Technol. Ikoma. A. Menendez. Phys. Tang. Semicond. Phys. Appl. B 52. W. Phys. 53.. Lett. P. J. Kraut. Kotera. Poluprovodn. C. Phys. M. 806 R. and J. Pettit. Status Solidi A 124. P. Appl. Mater. Deparis. 803 M. 793 J. S. G. Lett. Breuer. 6439 1993 . W. Arriaga. Monier. L’Esperance. Heinrich. 11. A. E. 787 S. W. Rubin. Bru. Phillips. Rev. I. Contessa. 2093 1998 . O. Phys. Monier. J. Sivco. J. Jezequel. 405 1991 . Lett. Vasson. S. T. 75. Zunger. S. J. 8154 1987 . Lopez-Villegas. Gossard. M. Growth 150. Leibenguth. B 41. M. Rodriguez. Leitch. Lideikis. and D. Lett. S. 113. 4184 1999 . 8121 1996 . 60. E. 26. Pikhtin. Appl. Phys. Vasson. Phys. Phys. Jr. p. Semicond. Silov. Moneger. Benyattou. B 43. Goni. Appl. Weiser. Appl. Stecker. Sov. Phys. J. A. R. M.-H. Lee and S. H. Sci. Jr. M. Cho. C. Appl. 10444 1994 . Freitas. Rev. L. Surf. M. Grant. and J. 737 T.105. Melnik.31. E. Halkias. Georgakilas. Brazel. S. 846 1996 . 1329 1991 . Rev. 735 H. P. Phys. Phys. Wolf. Appl. Alnot. Vac. 783 L. N. 6305 1988 . and K. Bimberg. B 37. Phys. Y. and P. Phys. 940 1999 . A. 172 1993 . Appl. Colombelli. Wolter. Fukatsu. N. Rev. Ambrazevicius. Semicond. Shen. J. R. P.-M. H. Sci. Tanaka. Rev. 751 C. Morante. 342 1991 . 85. Schneider. and O. C. J. Rev. B. G. J. Brubach. Guillot. Appl. 776 2000 . Lannoo. S. Larkins. R. 1728 1995 . and A. R. Zekentes. S. B 36. Haverkort. 802 T. 810 J. M. Gray. R. J. D. Lazzarino. and G. 58. L. M. Y. Ragot. Benyattou. Andersson. D. N. J. N. Appl. W. 23. 1077 1994 . C. 805 N. and F. 89. Y. Y. D. Rev. A. 7537 1991 . Wang. Botha and A. B 35. Ploog. Lourenco. Phys. Forster. J. 798 J. 77. R. 756 S. Pianetta. and F. Barbier. and L. A. B 13. 794 J. H. Castrillo. Gaylord. R. A. Patillon. J. T. Q. Brown. W. N. Phys. M. F. B. Chang. see http://ojps. E. V. Christensen. Leroux. 855 S. Omaggio. W. C. Zhang. 825 M. and K. M. H. L. and M. 69. M. 887 N. Ota. Sci. 866 J. Shiraki. 868 X. 14. Y. Hou. K. G.-Z. A. M. 49. Qteish and R. Rev. Phys. 822 T. Nuovo Cimento D 17. M. 63. Kilahara. M. Rev. Semicond. Part 1 32. E. Tejedor. J. J. Ishitani. and J. Govorkov. J. K. Babic. 892 L. R. Matter 102. 832 G. 944 1997 . Faleh. Growth 188. F. 862 X. S. 871 W. P. G. J. Lett. Ke. Semicond. and C. Phys. 69. Li. and R. J. 828 S. Islam. J. Downloaded 05 Dec 2002 to 140. K. Sci. J. H. 838 K. C. and T. Nishi. 836 M. B. Fujii. Phys. 1754 1992 . M. 849 H. 886 A. Rev. Kroemer. Surf. M. J. A. and F. J. 54 1996 . Chelakara. F. S. Phys. R. Jpn. Valster. 2112 1993 . Fukushima.. C. G. and Y. A. Y. and W.jsp . V. Lett. J. Katnani and G. A. H. H. W. 2522 1983 . J. 1317 1992 . Kita. 853 J. Kowalski. 1037 1986 . McCaldin. Sci. Ito. Hopkinson. 66. J. Sci.. Sites. Di FortePoisson. Appl. L279 1997 . Pistol. J. Y. and A. S. Jpn. Jr. Phys. 873 A. G. A.-C. P. Kawai. 857 A. R. and M. Phys.. J. 869 X. see http://ojps. Y. Esaki. 861 J. J. and E. 643 1987 . Jpn. and J. Appl. 821 M. and F. A. McGill. Eng. Yamamoto. G. Technol. Stillman. and A. Pollard. Appl. Lett. and D. J. J. Kuo. 58. J. Phys. Haase. Phys. R. Hill.-P. Ito. Appl. Mater. 834 M. Chua. B 37. Inoue. Technol. 6465 1993 . M. 878 G. M. Wang. Technol. L. 474 1992 . Pinczuk. and W. Xu. K. Sci. M. Phys. J. 882 H. A. Cadoret. Lett. R. and R. Zhang. Appl. J. Koshihara. Rev. 81. A. 1744 1992 . Minagawa. J. Chen. S. Vac. L. 1098 1998 . 8. Biefeld. 16299 1993 . 833 1990 . S102 1993 . Morii. and H. Cryst. Monier. N. X. Davis. Andreani. Leroux. T. Phys. Brylinski. 61. B 45. 1763 1987 . Fan. M. J. Spain. Xu. Omnes. Chelnyi. 13379 1992 . Appl. A. J. Staehli. D. S. 371 1997 . B 39. Meseguer. Solid State Commun. E. Lett. 2317 1992 . B 11. Lee. 6278 1988 . J. A. Piffault. Phys. Sci. C. Inoue. A. Chem. Grant. DenBaars. 73. Lott.. M. No. R. D. and W. L. Donchev. 84. Phys. S. J. 895 R. E. 2852 1995 . Vasson. G. Appl. H. Technol. M. B. J. Priester. N. Hemstreet. Peressi. Shanabrook. Calleja. Appl.-H. Peressi. Yow. Muto. Adams.. S. K. M. J. Landesman. Onabe. L. P. Rudra. 906 1987 . Phys.-E. Kukimoto. Pistol and X. M. 1763 1987 . 577 1998 . H. Lim. Blanck. and Y. Y. J. B. and J. Jones. A. Landesman.-C. Wu. P. S. 410 1999 . Onabe. J. Chin. Margaritondo. Teissier. Hafich. R. Rao. J. Appl. Appl. Minami. 62. Lett. Bourgoin. Harrison. Banvillet. and M.-A. Hara. L. Onabe. Phys. Zhang. 4898 1989 . 1367 1995 . Kawamura. E. Semicond. A. Shen. Katayama. Taira. F. Sunder. S. 8. Jogai. Pollack. A. Appl. Garcia. 860 M. Appl. M. Rev. Hopkinson. McGill. 61. J. J. Lett. Disseix. 1016 1977 . and H. 891 L. Lett. S. M. Gualtieri. Appl. Armelles. A. 848 A. Chen. C. Phys. Lett. Kroemer. Phys. Shiraki. D. E. Technol. Y. Appl. and A. F. Jpn. Munoz. 830 T. A. C. Biswas. J. Anderson and S. J. D. G. Watanabe and Y. Kraut. U. 70. Nakata. Zhang.-E. 843 H. M. C. 863 H. 881 E. M. and C. M.. and G. 50. I. Schwarz. 883 J. p. J. Appl. J. J. Jones. and J. Appl. Appl. Lett. J. Carlin. W.-P. Cho. S. 703 1987 . Appl.-H. Appl. Schulman. Solids 56. and H.-D. Yang. A. A. 817 T. Hafich. 56. J. D. H. Phys. Hang. Mendez. and A. Appl.-S. Appl. 4342 1991 . 1617 1993 . Freiburg. Tokutome. Phys. B. Appl. 3218 1996 . Yang. Solid State Commun. Takasaki. 889 A. Cebulla. Gualtieri. 749 1984 . Fertitta. Takikawa. P. J. Rev. Phys. Dandrea and C. and W. Phys. Technol. Phys. and X. 11. L. G. C. A. 856 S. O. 894 M. Fan. X. P. H. Q. Peter. Leng. Wakita. 890 R. K. K. Vac. Bhattacharya.-Q. Yaguchi. H. Cho. J. Lindell. Waldrop. Long. G. Sci. Jeong. X. 65. Silveira. 1944 1983 . S. C. J. Vilela. T. 67. 361. Griffiths. Yang. Garmire. Robinson. P. Appl. 423 1995 . D. J. Chua. 5691 1996 . Pistol. 865 W. Phys. 859 M. Mater. and W. Ichii. V. 875 C. P. 885 W. Chang. 837 J. 872 A. Lett. Phys. Y. T. D. Phys. Technol. Lett. Garcia. 847 D. Phys. Kobayashi. Hoshino. Claxton. A. Liu. K. Razeghi. 591 1989 . S. N. B 32. Mader. P. D. Ozeki. Technol. Kwamura. Paalanen. H. J. Appl. 70. Waterman. Subbanna. Massies. M. M. M. A. B. J. S106 1993 . 45. Phys.: Condens. Arnaud. Phys. Shiraki. P. A. T. and J. 879 J. Polyakov. 3449 1997 . B 46. P. 54. F. Chu. 18031 1993 . Yang. R. Shiraki. Pessa. Leroux. 58. Bitz. T. and L.-C. P. Briones. 1417 1997 . M. Appl. R. 66. Kumar. Y. O’Reilly. 2127 1998 . A. 74.J. Dupuis. Phys. and M. J. W. 1718 1995 . Patel. Hopkinson. N. J. Zhang. 540 2000 . W. J. Liu. J. Y. Proceedings International Symposium On GaAs and Related Compounds. W. Ley. M. Wang. Armelles. J. 1240 1993 . Tsang. Esaki. 844 R. Asahi. 819 A. 858 P. 831 J. B 28. and M. X. 884 M.8. L127 1986 . B. J. 60. T. Appl. Appl. Lett. J. Y. and R. Bryan. B 45. D. J. and S. Sci. 833 M. Phys. 50. Y. Phys. K. A. J. Huang. Serdiukova. and G. B 11. J. H. Lin. Leys. Phys. 1993. Phillips. 5303 1985 . Part 1 37. Lett. Rev. B 54. B 30. Phys. 1886 1992 . P.105. Jpn. H. I. V. 826 M. S121 1993 . Electron. Molinari. Nelson. 363 1989 . Robinson. G. 61. 61 1997 . D. and E. F. Mujica and A.org/japo/japcr. O. H. I. 3374 1997 . J. 823 Y. and S.-M. I. B 47. Montanari. 820 P. 3022 1996 . I. Nuzzo. Superlattices Microstruct. Nagahara. Y. and R. Lett. 867 M. Ohba. Valladares. and V. L1161 1992 . 854 S. Phys. O. M. 89. Lett. Vac. Growth 209. Gil. Schwarz. Collins. J. H. Dehaese. R. J. G. Di Ventra. R. P. 961 1992 . Lett. 880 U. R. Phys. J. F. A. K. Appl. Z. L. Appl. and Ram-Mohan 852 5873 C. S. S. and A. Phys. J. Phys. E. Phys. Phys. J. Duke. Menendez. Phys. Castrillo. Chua. 840 A. Nagao. 61. Sugou. J. Rev. Part 2 31. H. 3915 1998 . Yu. B. 68. Y. J. Narayanamurti. 841 O. Foulon. Part 2 30. Fille.: Vurgaftman. Tu. 8. C. Reynolds. Gotoh. A. Skolnick. Appl. Gil. B 37. 74. F. 69. Vasson. Ciuba. Bachem. B 46. C. M. Phys. Margaritondo. Rev. Ito. 1 June 2001 816 Appl. 845 O. Krynicki. B 10. W. A. Kim. X. Choe. 5. Hwang. Growth 95. L. N. H. Phys. Freundlich. Takano. Houston. K. Wang. Ito. 1666 1993 . D. N. Tanaka. Sci. Baldereschi. H. Tasselli. S. Bernardini. Wang. Nakamura. B. T. 80. Phys. Phys. K. T. J. Nitta. Appl. 888 B. J. 4874 1984 . Appl. M. Sunder. J. Wallart. A. Lett. R. Chow. Yaguchi. Cockburn.. Lett. Phys. Neff. H. M. 874 G. Nojima. Lett. 818 P. C. Meney. Munoz. Gourley and R. and F. and R. and G. 1693 1993 . 8.aip. Reaves. P. L. 870 J. Phys. C. Gil. O’Shea. Trankle. B 47. V. 8. Iwai. D. 744 1991 . and M. Appl. Germany. Dunstan. Leiferov. Bailbe. Shan. Appl. Loehr. 332 1998 . Houston. Garcia. C. 69. P. Tersoff. 4592 1996 . 79 1996 . 824 K. Chow. D. Yano. Technol. J. Appl. 839 H. Phys. Appl. and T. G. Semicond. E. Fujimoto. Sci. and C.31. and A. Milnes. Appl. 850 A. Phys. Prieto. Sci. Prins.. H. Phys. Lett. Landesman. Zhang. Nieminen. Rev. M. J. B 48. Phys. H. M. Aluev. 1713 1987 . K. Furuse. Boring. M. Caine. M. 877 L. 842 Y. J. Feng. Smirnov. Menoni. A. Defour. L1631 1991 . and M. Phys. Forchel. Sugiyama. Phys. Fukatsu. Winkler. and N. T. Meyer. Werder. 68. Y. Xu. 835 S. 79. Fong. Appl. and E. Song. Jordan. Y. and L. Alonso. C. Z. Mowbray. Growth 145. R. Cryst. I. S. M. A. B 10. Matter 10. W. 619 1995 . B. J. Wagner. Phys. Anan. Di Ventra.-E. Debbas. J. Okagawa. Alaya. Robinson. Lan. N. Vac. H. 864 Y. Appl.-D. Appl. Phys. W. 876 G. 746 1994 . and H. Hafich. 544 1993 . Onabe. Vol. Hara. Phys. 3451 1990 . Gu. 851 Y. Nuzzo. Rev. Ishikawa. Tomita. G. G. Baroni. and S. Technol. Kodama. H. 829 D. Phys. 893 J. Sly. and P. and L. 616 1991 . Phys. J. Chen. C. Part 2 25. 1288 1996 . Fuchs. Nishino. Hemstreet unpublished . P. M. Y. Phys. Ziem. J. Sci. B: Condens. Wagner. Schuler. Matter 9. 82. Chang. Phys. Vac. Lett. Kuo.-H. Marty. Yu.: Condens. C. Samuelson. Phys. Salokatve. Yoshino. K. 827 T. 81. E. G. Chiu.-J. Appl. A. Delage. S. L. and E. K. Rev. Miles. Leymarie. Tsou. Allan. Katnani and G. N. J. and J. F. and J. Needs. C. Mollot. J. 50. 4312 1992 . 2092 1993 . 26. Semicond. J. R. 387. 4664 1988 . Miyauchi. Leroux and J. 846 X. 3154 1991 . J. S. Cryst. Schneider. 2162 1996 . Yaguchi. Stutz. and M. Rev. R. Cryst. 2078 1993 . and F. Yaguchi. H. G. C. G. Redistribution subject to AIP license or copyright. Zhang. J. Nasu. Rev. F. Herres. : Vurgaftman. Walker. 913 R. 13080 1997 . T. 949 P. Johnson. P. Bennett. 3495 1999 . Nakao. J. Sci. Yang. Bewley. J. Omaggio. M. Anson. 918 1990 . 3483 1997 . Lett. 144. M. 906 D. S. J. 11. R. P. J. M. Lett. 8379 1996 . 72.-H.-R. Phys. M. R. S. Davis. Schwarz. Lett. Phys.-H. 13. Samoska. Voisin. Lett. C. and T. Lu. Semicond. Cuminal. 34. W. T. and G. 801 1990 . R. C. 783. and S. 71. Santos. Lett. Ralston. S. J. Narayanamurti. Rezek. 944 S. J. J. 934 H. Wessels. Grein. Lett. R. 2501 1996 . 11. R. 891. 58. 31. 929 H. Yoshida. Technol. R. Proceedings of the 22nd International Conference on Physics of Semiconductors. P. M. R. Nicolas. H. Howard. E. Appl. Appl. R. R. C. Kost. H. Quantum Electron. Jang. 63. Phys. J. 53. G. Phys. Rev. Chow. E. Meyer. G. L. C. Zhang. T. A. Semicond. Walker. W. Fan. B. Phillips. Lett. 70. Boggess. W. A. 927 C. S.8. Li. J. Twigg. J. G. Nakagawa. R. McGill. C. A. Lett. Olesberg. Freeman. 938 S.-J.org/japo/japcr. Khodaparast. Falcon. 45. 3833 1998 . Soucail. Pei. Zhang. K. and R. D. Kurtz and R. Murry. Meyer. IEEE Photonics Technol. Phillips. Mebarki. D. 897 D. J. B 53. IEEE Photonics Technol. Appl. Klingert. Phys.-H.. Grein. Miles. H. H. and C. J.jsp . N. Pei. and C. Gonda. Osbourn. H. see http://ojps. Lin. J. Grant. Rev. D. Phys. Li et al. Lett. S. Arch. Appl. T. 69. Su. M. 5852 1998 . Redistribution subject to AIP license or copyright. M. 56. Chung. R. Brown. Lazzari. 916 T. D. J. Vancouver.. Chow. M. R. Srivastava. West. R. Appl. B 10. Chow. A. and P.. Shiao. Rev. Xu. J. Sci. and W. Brown. Sci. 953 T. Campbell. D. D. G. A. p. Kurtz and R. Ducroquet. Nicholas. Phys. S. and S. Flatte. 663 1984 . 962 M. Phys. Lett. Mason. Rev. Phys. 3473 1998 . 27. Phys. Phys. 1 June 2001 930 Appl. A. Chang. Technol. J. Picozzi. 812 1994 . P. W. M. R. W. Holonyak. Dunlap. F. E. Appl. D. 1573 1997 . Le. Lin. Ryu. R. 207 1992 . J. 937 A. and P. T. C. C. Lett. H. Herres. 5337 1987 . 66. 917 L. Lett. 66. Walker. Ploog. Baranov. Phys. Baumgratz. Goldberg. and S. Sai-Halasz. Olivier-Martin. Flatte. Lu. T. Phys. J. Miles. H. 912 B. Lett. and J. H. Lin. I. J. Kadri. M. Physica B 184. Wagner. Miles. M. Chapman. and E. K. Appl. I. O. 1921 1995 . K. J. Razeghi. Johnson. Appl. Ser. McGill. L. Solid-State Electron. Golding. Y. G. Michel. 966 F. Jang. 971 1997 . Solid State Commun. D. 71. Bertru. 33. W. Phys. 54. Sugawara. 902 M. Phys. Wicks. B 55. J. Appl. Phys. Olesberg. Voos. Appl. C. Hasenberg. Hasenberg. R. Lett. Flatte. C. 8. 72. B. Phys. Q. Bennett. Proceedings of the 22nd International Conference on Physics of Semiconductors. H. B. G. H. Bennett. Felix. R. Appl. Bewley et al. Yuen. B 47. Y. S.-J. Sci. and W. Yang.-H. C. 10852 1996 . C. L. H. 915 F. 89. M. B. J. 922 T. 64. Esaki. Wagner. Phys. J. Jr. M. T. and H. Pei. and B. Bewley et al. F. B 11. G. Lim. Paul. and V. p. Biefeld. Lakrimi. J. S. Moore. Yang. 899 M. 5. Phys. Lum. Stradling. Ababou. Phys. and D. W. R. and K. Gualtieri. L. R. Hasenberg. Phys. A. A. Phys. and R. 1773 1992 . A. Phys. Phys. 216 1988 . 1116 1996 . Freeman. Koidl. Barvosa-Carter. Chin. Waterman. 66. R. and J. 920 ´ H. R. Boggess. and J. Omaggio. G. Kim. C. 69. Phys. and L. D. and F. H. A. Wagner. 1893 1989 . N. 940 J. Hall. V. Collins. H. T. Feenstra. Yang. W. J. 969 J. W. M. McDaniel. Chang. J. Rev. Daly. C. J. and J. J. R. J. Lett. L. and M. R. Vigliante. Continenza. 846 1991 . L. Sci. Lett. W. J. C. Wu. H. Phys. Gossard. Sci. 823 1996 . Tonaue. Boggess. J. and P. 956 A. C. and L. P. H. Weimer. N. and T. Appl. 945 S. Vac. Shanabrook. Giraudet. P. Lett. West. Appl. M. 1075 1999 . and M. 904 G. Schmitz. and P. Lett. Appl. Phys. B 59. H. M. and R. C. 61. A. 270 1998 . R. Shanabrook. Baucom. L. Cho. 66. Picozzi. A. 8192 2000 . R. R. Kroemer. Appl. Yang. 275 1995 . Boissier. K. Y. 1796 1999 . L. 69. Proceedings of the 22nd International Conference on Physics of Semiconductors. Malik. L. Appl. 2237 1996 . Le. C. P. and Ram-Mohan ´ M. V. 73. Chang. 74. 903 J. 3764 1997 . Moore. 1143 1991 . Meyer. and J. C. Y. Kosai. Chung. Shanabrook. 941 R. E. Phys. A. Nicholas. Felix. Symons. I. Vaughan. H. 935 1978 . Bolognesi. No. Appl. Phys. Biefeld. Appl. Chow. and W. M. 919 H. Phys. J. H. Yan. Sci. McCahon. R. Mater. Wang. J. J. Sci. B 55. B. P. H. Appl. R. K. Grant. A. and A. Qian and B. S. Symons. 49.-A. D. A. R. 41 1986 . Dandrea and C. 2135 1996 . Yang. R. N. 1185 1996 . H. Chow. L. R. 79. Davis. Electron. J. Murry. B. R. Electron. 71. 907 D. Chin. Jang. S. L. Schmitz. J. H. B. Appl. J. Moss. J. Phys. Walker. 71. Gossard. 935 M. R. J. 963 R. Chang. A. Technol. J. Rev. V. H. and R. C. R. 86.. Harrison. T. R. Chow. Miles. Lett. R. Biefeld. Anson. 37. de Cremoux. 74. 589 1981 . J. H. and H. 1994. Waterman. R. V. J. 947 P. Phys. Rezzoug. Technol. M. Mazuelas. A. 901 A. J. 921 F. and A. Phys. Lee. Waterman. J. M. 1743 1999 . Ahlswede. C. D. 1795 1993 . 968 C. J. L. Semicond. 795 1989 . 900 G. Semicond. C. Zhang. 955 L. B. J. 3700 1995 . J. 939 M. Meyer. 967 X. J. J. Lett. Y. Fuchs. Rondi. J. F. Zhang. M. Phys. Brewer. and E. B. Razeghi. Soderstrom. H. B. 118 1995 . Vac. Chang. J. B. Phys. Cho. R. Lett. S. 733 1994 . Pletschen. P. 67. Mitchel. K. Lin. J. Phys. and L. E. 898 M. 72. Phys. 910 J. Selvig. W. Stradling. Wagner. R. Phys. C. Lin. Phys. D.-H. J. D. H. A. Lett. and M. 965 B. L. Phys. D. L. V. Yan. 49. Mason.. J. Walther. Lett. Appl. S. 9. Solid State Commun. Cross. Lin.-L. H. W. Whitman unpublished . L. Lett. 1994. Kurtz. F.aip. R. and J. Kirchoefer. T. M. 862 1979 . Chua. K. M. Yang. Bhargava.31. A. H. Blank.. J. B.5874 896 J. 5745 1999 . 1199 1984 . 71. J. Miles. and B. 924 C. 3281 1997 . Electron. Hoffman. T. Meyer. Lett. J. Phys. R. A. J. H. B 44. Downloaded 05 Dec 2002 to 140. Vac. and W. J. Jacovetti. Youngdale. Technol. B. 936 W. G. Lett. Esaki. and L. 68. Su. Appl. Kaplan. Vurgaftman. L. G. G. S. Y. 34.-S. K. E. Appl. Appl. Lett. Tang et al. Phys. 957 N. 3740 1996 . Appl. A. G. Phys. Kost. Nuzzo. S. A. S. Mason. W. D. Phys. Appl. J. 3434 1998 . 59. 911 J. S. Miles. Q. Appl. S. M. Phys. Hasenberg. and A. 1496. Jack. Forrest. C. Zhang. 1994. 1652 1993 . Chow. J. C. E. Joullie. 74. Yang. Hasenberg. A. Meyer. Flatte. Lett. Kroemer.-H. Lin. R. 1873 1998 . Aggarwal. G. V. D. Quantum Electron. 735 1997 . Technol. R. W. Pei. W. W. Wagner. Lett. 717 1999 . Felix. Phys. Appl. L. P. 1785 1995 . Merz. J. Wilson. Bennett. R. D. H. Lim. Vol. 960 Y. and S. Appl. 76. V. B. IEEE J. R. Appl. O.-D. B 51. Lett. H. Jr. Shiao. Appl. C. L. A. Nicholas. Y. K. Hasenberg. Lett. and R. K. Praseuth. 61. J. 909 I. 3933 1985 . P. Samoska.-M. 961 Y. Mani. U. J. R. and L. 4477 1997 . Lett. and T. M. Phys. Felix. G. van der Burgt. A. L. J. West. Kroemer. Q. 364 1995 . 950 S. Appl. H. Lett. 905 L. T. R. Slivken. 943 S. Jr. Appl. Technol. English. Y.105. Twigg. 951 S. 87. Klann. W. C. and H. A. 959 M. Anson. Sai-Halasz. IEEE J. Pullin. Jaw. Phys. L. K. Welter. D. Appl. and T. C.. 925 C. 914 D. Flatte. Lett. J. 2981 1995 . Kolbas. E. Zborowski. Miles. 4589 1997 . R. 34. J. Appl. H. N. Vurgaftman. 3621 1997 . Wong. 7588 1993 . R. Guzman. L. 1125 1997 . R. 908 R. 3905 2000 . McDaniel. Sandoen. Lee et al. Meyer. A.. Brown. J. Appl. A. Duke. F. S. F. Dawson. J. H. Heber. Kim. H. I. Rev. A. Inst. P. 946 Y. B. Appl. C. 11. L. R. Biefeld. Phys. 918 ´ S. 933 W. S. J. 219 1995 . Cheong. Hardaway. Tang. and H. Schmidt. Lett. C. E. Brandt. Hart. Moore. J. C. Shanabrook. Warburton. Briones. Rev. L. F. 35. Dai. S. H. J. 83. B. Rev.. Lin-Chung. L. and P. Lett. J. 942 S. Appl. Mohseni. 948 Y. 1418 1990 . Guillot. S. J. R. W. Vurgaftman. Vancouver. W. and T. G. 19. N. Chow. Tang. J.-J. D. 958 N. Armelles. Waldrop. Kurtz. Lett. S. H. Phys. Wilson. A. N. Postigo. 932 W. T. Bennett. J. Kost. E. Hasenberg. R. J. Kraut. 926 ´ M. Miles. Phys. J. C. and M. Phys. Appl. A. M. H. 106 1993 . M. M. Conf. Lett. M. 57. and G. P. Choe. Appl. M. T. L. Koidl. 1135 1999 . Appl. 74. Lett. Dutt. J. Vancouver. Smith. Zyskind. D. Phys. 964 S. Utzmeier. Staudenmann. J. and E. 1729 1995 . Hoffman. P. Choe. Sullivan. B. Appl. Jaw. Phys. Continenza. and L. Laurich. Q. J. Sela. Norman. 80. Jelen. 928 C. 970 J. and A. Solid State Commun. B 55. 66. Boggess. S106 1993 . Doezema. Lett. 952 Y. 1403 1997 . 954 S. Fuchs. Fatemi. p. 3251 1997 . Rev. and L. and S. R. Nagle. and C. Technol. R. Olesberg. E. McGill. and C. Alibert. 931 M. 923 ´ D. P. Schulman. T. Shanabrook. S. 1403 1997 . B. Appl. 9. R. B 56. Wagner. C. A. T. T. Lakrimi. J. Bewley. R. M. B 57. Hua. Brandt. Luo. Harrison and J. Li. and A. A. Z. 972 M. Agarwal. S. Appl. Baur. Downloaded 05 Dec 2002 to 140. and N. H. Smirnov. Res. 983 B. 994 E. Binggeli. C. Uomi. 73.J. Ding. J. J. Mater. Lett. Monch.. Tang. Sun. M. X. Pan. P. M. Sci. L. J. Eglash. Vol. Tang. 4153 2000 . R. Xie. Druzhinina. Appl. Benjamin. Lett. D. E. W. 974 A. Polyakov. Sadik. and K. 67. S.8. Vac. 515 1996 . Druzhinina.31. J. Xu. Solid-State Electron. Satta. see http://ojps. 995 X. 980 G. A. 80. V. Zhao. B 12. 649 1993 . C. Meloni. 985 W. Maier. Y. Hu. 998 W. Nemanich. Kaufmann. A. S. Krispin. B. King. Kunzer. Z. 88. Phys. 977 W. P. F. and A. Phys. R. Spruytte. Proc. C. Botchkarev. 68. Li. W. and K. 982 T. Phys. Sci. H. Lett. Lett. 232 1999 . 67. V. J. Grant. A. A.org/japo/japcr. Y.-M. 1377 1996 . 5003 1999 . Soc. 89. 1371 1993 . A. 775 1998 . 973 A. Monti. Boukredimi. 482. Yang. G. 3432 1995 . Appl. Strite. S. Luth. Z. J. G. 993 A. 11. R. Shen. Rev. Rogachev. 2541 1996 . R. Vac. 2086 1998 . K. Rizzi. 65. Kitatani. Superlattices Microstruct. Phys. L. A. A. Yang. B 4. H. J. 36. 76. 1582 1995 . Mater. Phys. Fiorentini. Phys. Ye. Appl. Zhao. Symp. Technol. and J. 2470 1994 . A. 984 P. Phys. M. B. Lugli. Res. S. B 53. Phys. Chang. No. Meyer. 996 A. Symp. Symp. A. and H. R7323 1997 . G. Phys. Phys. Solid-State Electron. Lett. J. 989 G. Chen. 1 June 2001 971 Appl. Technol. and X. Phys. Tunitskaya. Lantier. A. A. Wu. and J. Proc. C. 3322 1995 . B. and J. 4710 1994 . and Ram-Mohan 987 5875 A. G. L. Appl. R. J. Ronning. Sci. U. and W. Jiang. Jpn. Ploog. Okai. Matter 8. Z. Y. J. Y. L. Y. M. Phys. Phys. Martin. Q. Baldereschi. Goddard III.aip. Tunitskaya. 975 A. A. 999 N. Milnes. W. B. B 17. Appl. Phys. S. Barman. 981 X. 911 1998 . E. and B. A. O. Redistribution subject to AIP license or copyright. A. J. Rockett. Govorkov. M. V. N. Mikhailova. Appl. Smirnov. R9427 1998 . C. P. N. Appl. F. Morkoc. J. Murayama and T. Ke. Rev. Lett. Rockett. Appl. Yakovlev. Sci.-D. Bernardini and V. A. and Yu. Milnes. Phys. 375 1990 . A. 4751 1996 .105. Nakayama. C.: Condens. Agrawal. Lett. and I. V. Harris. Surf. 2862 2000 . F. W. Huang et al. Bernholc. Rev. V. Tersoff. 1674 1999 . Mebarki. D. J. Y. 58. R. A. J. A. W. Vac. I. 68. Horn. 988 G. Martin. Proc. Thornton. 976 W. K. G. and R. 997 S. 36. Della Sala. C. 990 J. X. Technol. Shen. 2360 1993 . Strite. Appl. and P. J. Z. Bosin. Soc.-H. 979 S. Morkoc. W. and H. Morkoc. K. L. Botchkarev. Soc. H. 978 M. T. and A. Ploog. Rev. 1000 M. 2407 1997 . Rev. Appl. Lambrecht. and H. A. Schneider. K. L. and K. and R. Polyakov. 482. Y. Appl. Fiorentini.. Yazawa. 395. A. Langlois. 986 B. Martin. M. Appl. 2375 1991 . S. 1068 1986 . Phys. Mater. Vac. B 49. Agrawal. J. 38. Waldrop and R. B 55. D. B. McGill. Lambrecht. Kikawa. Srivastava. Sci. 2211 1994 . 2918 1996 . Technol. 84. Ferrara. Davis.jsp . S. K. J. Bochkarev. and T. Milnes. S. and A. Solid-State Electron. Appl.-M. Zhang. 2879 1996 . Phys.: Vurgaftman. Albanesi. Piquette. S. R. Lett. N. G. V. 525 1995 . Phys. Grant. Beach. Segall. 5076 1996 . Shen. Appl. Shen. 1001 F. and F.. Kondow. Segall. 80. Phys. Li. Nardelli. 8. S. Res. Imenkov. Part 1 38. 992 S. 70. H. W. J. 991 R. Y. Baranov. Z. Phys. Phys. Polyakov. 424. Di Carlo. and R. B 13. Lazzari. Rapcewicz.