Vol. 34, No.5 Journal of Semiconductors May 2013 Extraction of interface state density and resistivity of suspended p-type silicon nanobridges Zhang Jiahong(张加宏)1; , Liu Qingquan(刘清惓)1 , Ge Yixian(葛益娴)1 , Gu Fang(顾芳)2 , Li Min(李敏)1 , Mao Xiaoli(冒晓莉)1 , and Cao Hongxia(曹鸿霞)1 1 Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044, China 2 College of Physics & Opto-Electronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China Abstract: The evaluation of the influence of the bending deformation of silicon nanobridges on their electrical properties is crucial for sensing and actuating applications. A combined theory/experimental approach for determining the resistivity and the density of interface states of the bending silicon nanobridges is presented. The suspended p-type silicon nanobridge test structures were fabricated from silicon-on-insulator wafers by using a standard CMOS lithography and anisotropic wet etching release process. After that, we measured the resistance of a set of silicon nanobridges versus their length and width under different bias voltages. In conjunction with a theoretical model, we have finally extracted both the interface state density of and resistivity suspended silicon nanobridges under different bending deformations, and found that the resistivity of silicon nanobridges without bending was 9.45 mcm and the corresponding interface charge density was around 1.7445 1013 cm 2 . The bending deformation due to the bias voltage slightly changed the resistivity of the silicon nanobridge, however, it significantly changed the distribution of interface state charges, which strongly depends on the intensity of the stress induced by bending deformation. Key words: interface state density; resistivity; silicon nanobridges; bias voltages DOI: 10.1088/1674-4926/34/5/052002 PACC: 7300; 7320; 7360F 1. Introduction Semiconductor and metallic nanostructures, particularly those widely used in further miniaturization of electronic devices, sensing and actuating applications, such as silicon nanobeams and nanowires, have gained tremendous attention due to their unique properties. Until now, they have shown unique electrical, mechanical, thermal, electromachanical and photonic properties as compared to their bulk counterpartsŒ1 8 . Due to the high surface-volume ratio of nanostructures, these unique behaviors are generally attributed to their surface properties. Recently, experimental and theoretical studies have confirmed that surface states would have a significant impact on the electrical properties of silicon nanostructuresŒ1; 9 15 . For example, depending on the electrical activity of the silicon nanostructure, its conductance can vary by a few orders of magnitudeŒ1 , and theoretical calculations recently confirmed the importance of surface states on nanowire conductanceŒ9; 10 . More recently, VauretteŒ11 and IslamŒ12; 13 have investigated the influence of the surface states on the resistance of silicon nanowires, and extracted their surface charges and the resulting depletion layer thickness, which are obviously very important for MOS field effect transistors and sensors for optimal operationŒ14; 15 . However, on the one hand, the silicon nanowires used in their experiments were fabricated by a metal-catalyzed chemical vapor deposition growth process or electron beam lithography, and the effects of the surface states on electrical properties of silicon nanostructures fabricated by standard CMOS manufacturing technology is still lacking understanding at present. From the perspective of large-scale production, the related study is necessary and meaningful. On the other hand, in order to make the sensing and actuating applications reliable, the exact evaluation of the influence of bending deformation of silicon nanostructures and the resulting stress on their surface states and electrical behaviors is essential and critical. Therefore, in the present paper, we determine the surface state density of a suspended p-type silicon nanobridge (SiNBs) fabricated by a standard CMOS process, as well as their resistivity under different bias voltages. For that, we needed a set of suspended SiNBs with different lengths (L/ and widths (W /, and we measured the resistance of SiNBs of varying cross section and length under different bias voltages, which result in different bending deformation. Our research might be useful for determining the optimum doping concentration and surface treatment of SiNBs for fabricating SiNB-based NEMS devices. * Project supported by the National Natural Science Foundation of China (No. 41075026), the Natural Science Foundation of Jiangsu Province (No. BK2012460), the Special Fund for Meteorology Research in the Public Interest (No. GYHY200906037), the Universities Natural Science Research Project of Jiangsu Province (No. 12KJB510011), and the Priority Academic Program Development of Sensor Networks and Modern Meteorological Equipment of Jiangsu Higher Education Institutions. † Corresponding author. Email:
[email protected] Received 27 August 2012, revised manuscript received 18 October 2012 © 2013 Chinese Institute of Electronics 052002-1 2 is the piezoresistive doped region. (b) Three-dimensional tapping-mode AFM image of a SiNB. the current–voltage (I –V / characteristics of the SiNBs without bending deformation at room temperature were measured by simultaneously applying DC voltage Vs2 between the electrodes. 2. However. the lengths and widths of SiNBs are accurately determined by scanning electron microscopy (SEM) and atomic force microscopy (AFM). the scanning voltage step is 0. the BOX underneath SiNBs was etched using a buffered oxide etcher (BOE) solution and SiNBs were then released using critical point drying in liquid carbon dioxide (post-CMOS process). SiNBs and their anchor regions were intentionally heavily doped with about 1019 cm 3 boron impurities to form piezoresistors by the ion implantation method.J. 1(a). 2.1. Electrical properties test with a MOS model Fig. reactive ion etchings were used to etch the silicon device layer and the exposed BOX until reaching the silicon substrate. and the effect of the undercutting can be included into the nanobridge effective length by adding a correction length of 4 m to the original nanobridge length. Experimental details 2. the SiNBs exhibit different electrical properties from the bulk silicon. the SiNB will be bent downwards due to the effect of electrostatic force. 2. The inset is top view of the schematic SiNB with piezoresistor. Fabrication of single-crystal p-doped SiNBs Based on the SMIC 0. 1(a). the SiNBs released in this way did not collapse. and we take the 100 sets of I –V data fitting for the resistance of each SiNB. 3 is the Al metal electrode. it is noted that as the width and thickness of the SiNBs in this work are much larger than 10 nm. The first step of the fabrication process was defining patterns of h110i oriented SiNBs of different lengths and widths onto the silicon surface device layer by standard photolithography. the resistance and interface state density of the SiNB may be changed. cutting on the mechanical response of the SiNBs. On this basis. 1. 1(b). 2. The schematic diagram of a MOS model for measuring I –V characteristics of the suspended SiNB with different lengths and widths under different bias voltages. Theoretical model and analysis 3. and the doped thickness hPR is in the order of 60 nm. Semicond. we have investigated the effect of under- As sketched in Fig. thus. In this case. So it is very important to study the impact of the surface or interface charge distribution on the electrical properties of SiNBs. (a) Typical SEM image for a suspended p-type SiNB with its contacts. which results in the different bending deformations.02 V. In order to get accurate data. and 1 is the SiNB. 34(5) Zhang Jiahong et al. Finally. 2013. However. Then the anchor regions were sputtered by 600 nm Al metal as the top electrode (pad). The case without bias voltage The influence of the surface properties can be ignored in macroscopic conditions due to the very small surface–volume ratio. and Vs1 is similar with the gate voltage in the MOS model. On the other hand. the influences of any quantum confinement effects on defect energy levelsŒ17 and the nature of the defectsŒ10 are safely negligible because theoretical calculations predict a modification of the nature of the defects (surface reconstruction) only for nanowires less than 052002-2 . if we consider the influence of different bending deformations on electrical behaviors of suspended p-type SiNBs.1. the double clamped SiNBs with the same thickness (t/ were fabricated from (100) silicon-on-insulator wafers with a 200 nm buried oxide (BOX) and a 200 nm single-crystal silicon surface device layer with a resistivity b of 10 cmŒ16 . Fig. In our previous articleŒ16 .18 m CMOS process. 3. In general.2. and a typical tapping mode AFM image of a SiNB is given in Fig. on the one hand. the bias voltages Vs1 should be connected between the SiNB and the substrate. However. When the gate voltage Vs1 increases from 0 V. After that. Photoresist was then spinned on the metal pad region in order to prevent corrosion of the Al metal in the release process of SiNBs. A typical SEM image of a SiNB is given in Fig. the sacrificial wet etching resulted in the undercut at the base of the SiNBs. and the current through the SiNBs was measured by using a Keithley4200SCS semiconductor parameter analyzer. the surface properties of SiNBs play a key role in their physical properties at the nanoscale because the weight of the surface becomes very large. As shown in the inset of Fig. ANSYS finite element simulation results indicate that the piezoresistor along the length direction of the SiNB will 052002-3 . Thus. (2) . we can get Ld : 2kT "s Nb ln. 3. (2) and (5). and NS . which can trap free carriers and create a depleted region in the SiNBs. the thickness of SiNB in our experiment is about 200 nm. Semicond. where positive charges are sketched at the interface between the oxide layer and a p-type SiNB (the oxide layer and lightly doped region in the SiNB are not reported). HF defects may have less influence. and this layer contains numerous interface charge states. (3) V where NS is the interface charge density and NA is the doping concentration. In addition.. and (4). (7) where k is the Boltzmann constant.J. therefore. and its cross section APR is given by APR D . Ld is the width of the depleted region of the piezoresistor due to the doping concentration difference. However. and the validity of this initial hypothesis is verified thanks to the self-consistence of the deduced values of both the resistivity and the interface states density. unlike the parallel plate actuator.NA C Nb / 1=2 .e. this assumption is reasonable). Schematic diagram of a p-type heavily doped region (piezoresistor) of the SiNB. T is the measurement temperature. combining Eqs. Z S NS dS D Z NA dV . APR (1) where is the resistivity of the piezoresistor. 2013.NA =Nb / Ld D q 2 NA . thus modifying their resistanceŒ11. (5) SWPRi WPRi SWPRj WPRj : 2. we give an intentional doping concentration NA D 1 1019 cm 3 . the resistance RNB of the SiNB equals to the resistance RPR of the piezoresistor. The charge state of the defects due to a variety of reasons is a priori assumed to be positive. With the SiNBs used in this work. according to the reference of GB/T 13389-92. Equation (3) leads to NS D NA hd : (4) To determine Ld . Therefore. i. we finally determine NA through the iterative solution. For that. WPR is the width of the piezoresistor. we need a new relationship. Therefore. the electrostatic force causes a position dependent deflection along the SiNB axis.SWPRi SWPRj / (6) On the other hand. the SiNBs are generally covered by a native oxide layer on their surface. based on the knowledge of semiconductor physicsŒ21 . for a given resistivity b . the developed electrostatic force attracts the SiNB toward the fixed silicon substrate. (9). the doping level assuming that the mobility in the SiNB is equal to the bulk.e. This is illustrated in Fig.2. the precise nature of the defects is not the main objective of this work and has no consequence on the following analysis. 19 . as described later. we can write the following relationship Fig. we get Nb based on Eq. the slope SWPRi of the curve RNB versus L is equal to =APRi . After this. Assuming a uniform interface charge density and depletion charge density. 34(5) Zhang Jiahong et al. In a word. 3. hd is the thickness of the depleted region of the piezoresistor due to interface states. as shown in Fig. hd . q is the elementary charge. Based on the experimental initial settings.WPR 2Ld /.54:56/1:105 (8) In this case. there is a nonuniform stress distribution in the SiNB.hPR 2hd ˛Ld /: (2) To satisfy charge neutrality. These defects became visible as pinholes during HF-etching and influenced the effective Young’s modulus and thermal conductivity of the SiNBŒ18. it was observed that the fabrication-induced defects abruptly increased when SiNB was thinned to below 100 nmŒ18 . 14. (8) N D 1:330 1016 1:082 1017 C : Œ1 C . from the slopes of the linear fit for different SiNB widths. (1) . SWPRi APRi D SWPRj APRj : Combining Eqs. 20 . we measure the resistance of SiNBs versus their length and width. D 1:305 1016 1:133 1017 C N N Œ1 C . For a given resistivity and a set of widths i and j .2:58 10 19 N / 0:737 : (9) According to Eqs. based on Eq. we get Ld : Ld D 6 nm in diameter. which can be written as RNB D RPR D L . L is the length of the piezoresistor. based on the knowledge of semiconductor physics. we subsequently obtain (i. The case with bias voltage When actuated by a bias drive voltage Vs1 . 3. (6) and (7). For a given width WPRi . we established a theoretical model for investigating the resistivity and the density of interface states of SiNBs without considering the quantum confinement effects. As both ends of the SiNB are fixed. At the same time.. As we all know. hd and NS have also been determined. 4. "s is the dielectric constant of silicon. the positive interface charges are balanced by the negative space charges in the depletion region of the SiNB. and ˛ is a scale factor. In view of the very large resistivity of the depleted and lightly doped region in the SiNBs. and Nb is the initial doping concentration of the silicon surface layer. 4.2965 D 0. and the inset is the distribution curve of the axial stress values corresponding to 16 points in the axis of the upper surface of the SiNB. the whole thickness of the depletion layer due to surface states along the length direction of the bending SiNB remain unchanged (2hd /. Furthermore. W (nm) WPR (nm) SWPR (/m) 1500 450 9370. we can see the surface potential is reduced under compressive stress while it is enhanced under tensile stress. Semicond. Fortunately. Results and discussions First. we can calculate this change.0683 nm ˛ D 0. 5. we must first consider that the metallic contacts are placed far away from the SiNBs. Subtracting R from Rc . In this case.89 /m for a 1000 nm wide piezoresistor. Based on the semiconductor physicsŒ21 . which indicated that the SiNB made good electrical Ohmic contact to the silicon electrodes.89 Results hd D 18. the offset exists between the tensile stress and compressive stress. (4). However. according to the Ref. (10). we discuss the case when no voltage is applied.20 /m for a 450 nm wide piezoresistor. Figure 5(b) shows the measured resistance R of various SiNBs versus their lengths and widths. and consequently a resistance Rc . (b) Resistance versus length for SiNBs with different widths. according to Eq. [23]. Ld is shown to remain unchanged. contributes to the whole resistance R. Values of depletion width (hd . obtained from the variation of the resistance of the SiNBs versus their length based on the theoretical method. and it can only be obtained by self-consistently solving the coupled Lagrangian BIE/Poisson/Schrödinger equationsŒ22 . along the axial direction of the heavily doped SiNB. Finite element simulation of the bending deformation dependence on the stress distribution of the SiNB (L W t D 25 m 4 m 200 nm) under the bias voltage.8191 nm Ld D 0. This occurs mainly because the magnitude of the stress along the thickness direction is symmetry equivalent. but opposite in sign. The I –V characteristics of the SiNBs without bending deformation at room temperature were plotted in Fig. Obviously. Furthermore.27 Ns D 1. Table 1. 2013. resulting in a small equivalent axial stress. resistivity (/. we can know that the interface charge distribution will become non-uniform. we deduce contact resistance Rc of 5091 ˙ 172 . and 9370.X/j: q 2 NA (11) The compressive stress will lead to a thinner depletion layer along the thickness direction. 24 . 24 . Fig. the influence of the large compressive or tensile stress on the magnitude of charge density of p-type heavily doped silicon nanostructure is very small and can be basically negligible.21 3000 1000 4215. 4. which strongly depends on the doping concentration. 23 . the relationship was linear. between the electrodes and the SiNB ends. and the existence of this nonuniform stress distribution may result in a more complex carrier charge distributionŒ22.00945 cm NA D 9. which leads to changes in interface charges. To determine the resistance of the SiNBs. Based on the I –V characteristics of the SiNBs. it is noted that the stress will change surface potential and therefore change the magnitude of the depletion layer (hd / along the thickness direction. based on Fig. we de- 052002-4 . linear relationships can be clearly found from the distribution of the measured data points. The impact of stress on the surface potential is simply modeled proposed by Rowe who investigated the giant piezoresistance effect in silicon nanowires using the very simple approach of transportŒ23. as can be seen. while the tensile stress will result in a thicker depletion layerŒ23 . (7). The solid lines show the lines fitted straight. (a) The I –V characteristics for SiNBs with different lengths and widths. inevitably experience a complex stress transformation process (the tensile stress ! zero ! the compressive stress ! zero ! the tensile stress). The stress essentially modulates the thickness of the depletion layer. the slope of the fitted straight line is 4215. and interface state density (Ns / for p-type SiNBs. in series with the resistance RNB of the SiNBs. 5(a). 23.7445 1018 cm 3 1013 cm 2 Eq. hd D ˙ s 2"s j . By further extrapolating the linear curve to L D 0. which should have a small effect on the hole mobilityŒ4. However. the surface potential varies according to the law d D 0:5 meV=MPa: dX (10) From the Eq. Ld /. In this case. doping level (NA /. 34(5) Zhang Jiahong et al.J. For a uniaxial stress X . and the impact of this non-uniform stress on the surface state charges can be investigated by the simplified theoretical model. Next.5 m 450 nm 60 nm. The inset is a schematic of the charge distribution in the bending SiNB. which results in a non-uniform interface charge distribution. resulting in a small equivalent axial stress. Semicond.8191 nm for SiNBs doped to 9. while the tensile stress lead to an increase in the interface state density. 25 . the compressive stress causes the interface state density to reduce. we find RPRi =RPRj D 0:7845 and ˇi =ˇj D 0:7826 for two different SiNB piezoresistors with dimensions L WPR hPR D 20 m 1000 nm 60 nm and LWPR hPR D 11.5 meV/MPa is likely to lead to slight deviations in final simulation results. The distribution of interface state charges of the top and bottom surfaces along the length direction of the SiNB under different stresses. For example. the value of 1013 cm 2 is consistent with the expected one for a Si(100) wafer after RCA treatmentŒ11. and the maximum relative change of resistivity is less than 4%. the greater the amplitude variations of the interface state density. We find the two values are in a good agreement for those SiNB samples we used in the experiment. Figure 6(b) shows the variations of the resistivity with different voltages. 6. 7. At this time. we discuss the case when the bias voltage is applied. i. different bending deformations.65% increase in the resistance of the 12 m long and 3000 nm wide SiNB under the bias voltage of 4 V. duce the resistance RNB of the SiNBs and finally the resistivity along with the doping concentrations of the SiNBs based on the above-mentioned theoretical model. Furthermore. the resistivity slightly increases with the bias voltage. Figure 7 shows the distribution of interface state charges of the top and bottom surfaces along the length direction of the SiNB under different stresses. Therefore. For a typical example. The results are summarized in Table 1. the influence of the resulting bending deformation on the electrical properties of SiNBs can be investigated.81 1013 cm 2 /.. (a) Resistance versus voltage for p-type SiNBs with different lengths and widths. which is in agreement with the intentional doping concentration (1 1019 cm 3 /. Figure 6(a) depicts the measured resistance of various SiNBs with different lengths and widths versus the bias voltage. on the whole. If we assume that the involved defects are the ones associated with the Si–SiO2 interface. where ˇ D L=WPR is the aspect ratio. which indicates the influence of the bending deformation induced by the bias voltage on the interface state density is very important and it needs to be carefully evaluated when designing SiNB-based NEMS devices. (b) Resistivity versus voltage for p-type SiNBs with different lengths and widths. all the results are coherent. which also indicates that the above-mentioned uniform doping assumption is reasonable. thus. we get the same density of states (Ns D 1. we report on a combined theory/experiment approach for the extraction of the resistivity and interface state density of the suspended SiNB under different bending defor- 052002-5 . As mentioned above. 2013. Note that the d /dX in our model is the fitting parameter. there is only a 0. the slight simulation error does not qualitatively change our conclusion. we obtain a depletion layer thickness of 18. 34(5) Zhang Jiahong et al. the bending deformation induced by the electrostatic force lead to the non-uniform stress distribution. whose actual value will depend on the density and (piezoresistive) nature of the Si/SiO2 surface states. Conclusions In summary. we extracted Fig.27 1018 cm 3 . Therefore. Because the chemical treatments of the wafers during the technology process (RCA cleaning process) are the same as the Ref. From these results. the resistivity of SiNBs under different bias voltages. but these microscopic details are not addressed in the phenomenological modelŒ24 . 5. We can also see the change is slightly larger for a long and narrow SiNB. 7.e. Similar to the resistance change. The greater the stress. especially for the short and wide nanobeam. Combining the experimentally measured resistance and the previously mentioned theoretical model. One way to check the coherence of the results is to compare the ratio RPRi =RPRj with the ratio ˇi =ˇj . For this doping level. Fig. the resistivity of p-type SiNBs without bending is 0.7445 1013 cm 2 /. as shown in the inset of Fig. As we can see.00945 cm and the corresponding uniform density of interface states is in the order of 1013 cm 2 . the value of 0. these densities are associated with the charge states of the same defects. which slightly changes the hole mobility and the resistivity. [11] (Ns D 1.J. Nevertheless. the bias voltage and the resulting bending deformation have a small effect in the resistance of the SiNB. As we can see. This occurs mainly because of the following fact: the offset exists between the bending deformation-induced tensile stress and compressive stress in the heavily p-doped region of the SiNB. surface traps. 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