MEASUREMENT OF THE EXTRINSIC SERIES ELEMENTS OF A MICROWAVE MESFET UNDER ZERO CURRENT CONDITIONSF. Diamand, M. Laviron ABSTRACT A new measurement method of the parasitic series impedances of a microwave MESFET is presented. The basic point of the method is that the MESFET is polarized under zero drain voltage, resulting in a simple analytical model. Comparison with experiment is discussed. INTRODUCTION A MESFET with an unbiased drain is a fairly simple system in contrast to the case of normal operating conditions. For zero drain voltage, the region under the gate can be described by a distributed, uniform, R-C transmission l'ine [1], leading to a simple analytical model which can be expected to be of good accuracy. It will be shown that this model, combined with the lumped c'ircuit model of the extrinsic part of the MESFET, is very su'itable for comparison with experiment and lead to a straightforward measurement method of several device parameters, in particular the parasitic source, gate, and drain resistances and reactances. The analytical form of the model will be derived and the related measurement method outlined. Then it will be compared with experiment and its validity discussed. DESCRIPTION OF THE MODEL Fig. 1 shows the equivalent circuit for the zero drain voltage condition. The region under the gate is modellized with distributed elements, the extrinsic region with lumped elements. Parallel lead parasitic capacitances are neglected. The (Z) matrix of this 2-port in the common source configuration is derived. With a concern of clarity, the inter-electrode capacitances C , C d Cd are first neglected. Then the (Z) matrix is further smpl iiedj,using the low frequency -and- open channel condition, an approximation which is consistent with our measurement conditions. Final ly the inter-electrode capacitances are taken in account. 1)C gs' C gd C sd neglected nelcd the (Z) matrix is then given by Thomson-CSF, Laboratoire Central de Recherches, ORSAY, FRANCE. 451 Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply. 12 (Z) = ( 9 \ Z s + + rl jC c rI thFl ,. Zs + rl (chrl-1) jwC c shf l J 2rl s C.Wsc i@C~~~~~ic S Z 9 (chrl-l) = ZS + jL w Zd Z d JjwCc shl /I + (chrl-1) r1 (1) where Z = + s s jLgw, = d jLc cF'cc = (jwR C ) 1/2 the gate r is the propagation constant of the R-C transmission line, length, R the channel resistance, C the geometric depletion layer capacitance. cc c 2) Low frequency - and - open channel limit Sti I I neglecting Cgs9 Cgdc oRC Cc Cds, we assume that <<1 112 1 2 1 = (2) this condition is related to the low frequency, open channel limit. It is general ly met with an X-band FET for frequencies up to about 10 GHz and for a channel opening higher than 20 %. This can be checked with the FET which has been used for experiment. Expressing condition (2) with the help of practical device parameters gives rr F 12 (3) <<1 (S.f. units) b ( 4) (V I212i2= (-V + + where F is the frequency, pthe mobility, V the barrier a = c)/(V height, + p b/a= 14 Taking a 1-ca'/2 the = 0,8 chanRel p, the pinch-off voltage, openi p = 0,4 m ng, where V 1 s 1 Vp + - 2,35 V, F < 10 GHz, b > 20 %, Condition (3) gives 1F2121 < O013 Assuming the condition (2) to be met, expression (1) reduces to /Z 9 s +-R + 3 R c R JCcW . Z S + 2 Rc) (4) (Z) = Z + Zd + RcJ 3) Influence of capacitances C9S, Cgd' Cds The influence of capacitances C in the low frequency - open channel assumed that: w gppro C dJ Cds will be estimated imation. It is further c Cx 1 (5) 452 Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply. or Cds' but these capacities are in general smaller where Cx = C , C than Cc, so Fhat Sondition (5) is weaker than condition (2). Then the impedance matrix is given by (Z) = (R) + j(X), with P R P s 9 +1 CC c + C 3Cds + 3Cd ds dR ~~gs gd RR s c CC + 2Cgd gs + (R) - ( s +2 + R C gd Cs Cgd g U) w R~~ c + ~ P s + R d + R c Ls +L9 (X)= X)Ls+L9 dc+gs w(cc + C9 1 Cgd +gd~ L sw@ 6 ) Ls w gd (Ls +Ld (6) COMPARISON WITH EXPERIMENT The (Z) matrix (6) involve some interesting features which provide straightforward mean of checking the validity of the model and of determining the parasitic elements : a -each matrix element Z.. - is a linear function of Z , Zs Zd Rc. the real part of the matrix is independent of frequency ; X 12X X21X22 are independent of V and are simply related to Ls and Ld1 -1 so that Grebene's for a flat doping profile, RP = Rco (l-ctl/2) to R.. elements in order to measure method [2] can be extended the parasitic resistances. In p54ticular the plot of R versus (l-a /2)c' must give the same straight line, whatever 4e frequency, and its intercept with the ordinate axis gives R + Rd The same procedure, applied to RP1 and R12, gives respectively R + R and R . In these latter cases, the slope of the line deviates slightly from a constant (because C depends on a), but this does not affect notably the extrapolated values of the parasitic resistances. - - identifying X11 with a resonant circuit for a given value of V allows L + L must be i&depen+ C to determine l + L and C = C + C dant of V . For a flat doping profie, pl8#tins C vgrsus a -4 gives C c (V ) w9ich must be consistent with Nd. d g The method was tested on a MESFET realized in the laboratory, giving = 8.5 dB. l1dB gain at 10 GHz, a noise figure NF = 2.4 dB with G Device parameters are : ND = 1.6 1017 cm3, layer thicnes = 0.3p, channel thickness under recess = 0.15}p, gate length = 0.,8p gate width = 300p, source-drain space = 4p. The S-parameters of the MESFET were measured with an automatic network analyzer in the 2GHz - IOGHz range, the terminal planes of the 2-port being very close to the chip, but the gate and drain lead connections are included in the 2-port. Then the Z-parameters are computed. 453 Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply. Figures 2,3,4 represent respectively the plot of R22, 1 (R12 + R21) and R P versus (1-al/2) , for several frequencies. Good linearity is obi4ined in all cases. For figures 2 and 3, the dependency on frequency is very weak, allowing to measure R = 2Q, and Rd = 3,2Q, with a good accuracy. Poorer agreement is obtained for the RP plots which show a more pronounced dependence with frequency, resulting in a spread of 10 % for R + R when F varies from 7GHz to 10GHz R = 3,2Q is obtained for F 9 10GHz. RP decreases with frequency4 The question arises if there is some error In the 1-heoretical model or the experimental procedure, or if R is really frequency dependent. It should be noted also that the valug of R de,uced from Wolf's formula [3] is nearly two times smaller : R /39n2 - 1,5 Q. Fig. 5 shows the plot of L5, Ld, and L versus V . For each V value L was determined by : 9 9 9 5 L - z (X1 + X21 )/w, for several frequencies (F - 3,4,5,6,7,8 GHz) and tdking the mean. Simi larly, using X22, Ls + Ld and therefore Ld was computed. The standart deviation is typically .01 nH . The inductance values are weakly dependent on Vg for IV 1< 0,6v, then they decrease more and more strongly when pinch-off is approached. L + L + C d` for each V vatue, was determined together with C = C + C by identifying X 1 with a resonant circast foF different frgquencies (F = 3,4,5,6,7,8 Hz), then using the least square method, to compute L and C. Fig. 6 shows the plot of C versus Of z , from which C has been deduced. From C (V ) we found Nd = 1,68 1017 cm-3 which agreSs welI l i er va l ue. w i th the nom na4 suop CONC LUS ON In spite of some slight discrepancies which we are trying presently to solve, the experimental procedure described here offers a convenient mean of characterizing the extrinsic model which is usually characterized together with the intrinsic model by sophisticated computer optimization methods. We believe that the independent measure of the extrinsic model will result in increased accuracy for these parameters. On the other hand, by reducing the number of unknown parameters, it contributes to simplify the computer optimization method. REFERENCES 1. K. Lehovec. Appl. Phys. Lett. 25, N0 5, 279 (1974) 2. A.B. Grebene. PIEEE Lett. 2031, (nov. 1967) 3. P. Wolf. IBM Journ. Of Res. and Der. 14 N0 2 (1970) 454 Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply. 11 R1 16 C36 ds~~ Figure 1. Equivale-nt circuit model for Vds 0 RA 25 4 ,; I/ / S i - . E + GHz I- 9 40 0 + 9 + t -b . 4 .40 A 45 4 4 , i a~ ADI /1 a I a -- A S 4 i (I -.4)4 ,, 9 (4 )K-~ - Figure 3. Determination of R Figure 2. Determination of Rs + Rd 455 Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply. All R,4 (It e .. * Figure 4. Determination R s + Rg of AAOS Il .- :- : . : a *; t a A 4 r 5- .(.1 -,is - 4 -f io L F* °03 I I L0. W- LA Figure 5. Gate voltage sensitivity of L ,L ,Ld 0,4 0 C~~~~~~ * 3d C = Crs t Ce Cc + 48° 2j33v r / Figure 6. Determination of the geometrical depletion capacitance *1 1i" 456 Authorized licensed use limited to: BHABHA ATOMIC RESEARCH CENTRE. Downloaded on June 01,2010 at 05:30:21 UTC from IEEE Xplore. Restrictions apply.