1730 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL 40, NO 10, OCTOBER 1993

Simulation of Temperature and Bias Dependencies of and VTo of GaAs MESFET Devices

J. Rodriguez-Tellez and B. P. Stothard

Abstract-A new dc and temperature nonlinear GaAs MES- FET device model is presented. This offers improved accuracy over existing models by simulating the bias dependency of the device transconductance (p) and pinch-off point ( VTo) param- eters. The effect of these bias dependencies becomes more im- portant as a departure from room temperature is made. New expressions for simulating the temperature dependency of VTo and fi are also presented and these provide improved accuracy over existing techniques. The new model effectively couples to- gether the bias and temperature dependency of the device.

I. INTRODUCTION CCURATE simulation of circuits utilizing GaAs A technology requires the use of an accurate device

model. Much of the work in the past for the GaAs MES- FET device has concentrated on the simulation of dc, ac, and noise behavior [1]-[3]. The effects of temperature on the dc characterization of the device has by contrast re- ceived little attention. In this paper, we consider the de- ficiencies with the current approach for simulating the ef- fects of temperature on the dc characteristics of the device. This is carried out by considering the dc characteristics over a wide temperature range. The Curtice Quadratic model [l] and the way in which this model can simulate temperature effects is used as a vehicle for this assess- ment. This is then compared with a new dc and temper- ature model for the device. The results to be presented later show that the behavior of the device is affected most at low temperatures and under low bias conditions.

11. CURTICE DC AND TEMPERATURE MODEL Most nonlinear dc MESFET models are based on the

Curtice Quadratic model so that much of the comments made in this paper for this model are also applicable to other models [2], [4]. The Curtice model predicts the drain current ID of the device [ l ] as

ID = P(VGS - VTO)2(1 - AVD.7) t a d (aVDS) (1) where

transconductance parameter, VTo threshold voltage,

Manuscript received September 21, 1992; revised May 11, 1993. The review of this paper was arranged by Associate Editor M. Shur.

The authors are with the Department of Electronic and Electrical Engi- neering, University of Bradford, West Yorkshire, BD7 IDP, United King- dom.

IEEE Log Number 92 1 1 103.

X modulation factor, CY saturation voltage parameter.

These fodr parameters are assumed to be bias-indepen- dent but later [5] it was found that this was not the case. In particular, the dependency of VTo on bias was shown to significantly affect the accuracy of the model under low drain currents [6], [7].

For this model, only two parameters are normally as- sumed to be temperature-dependent. These are and VTo, which are simulated as [8]

VTO(T) = VTO + VTOT(T - Tnom) (2) where

VTo room temperature value of VTo ( T ) , VToT simulates the change in VTO with temperature, T measurement temperature, T,,, room temperature.

The transconductance parameter is simulated as

(3) p ( ~ ) = p x 1.01&%(T-Tnom)

where

p pFK T measurement temperature, T,,, room temperature.

value of p at room temperature, simulates dependency of P on temperature,

The only other dc model parameter which is normally [8] assumed to be temperature-dependent is the saturation current (Is) of the diodes shown in Fig. 1 . The current contribution from these diodes to ID with a normally biased device (reversed-bias junctions) is, however, min- imal and need not be taken into account. The effects of temperature on these diodes can also be neglected if this condition exists. This was the case for the results pre- sented here. In enhancement-mode devices or in those ap- plications where the diodes are forward-biased the tem- perature dependence of these components will be important and needs to be taken into account.

111. NEW DC AND TEMPERATURE MODEL

0018-9383/93$03.00 0 1993 IEEE

RODRIGUEZ-TELLEZ AND STOTHARD: DEPENDENCIES OF (3 AND Vro OF GaAs MESFET'S

__

1731

h RD

bso"rte Fig. 1. Basic dc FET nonlinear model.

This has the same form as the Curtice expression, but now the dependency of P and VTo on VDs is simulated as

(5)

and

The nonlinear dependency of P and VTo on VDs is there- fore described by a third-order polynomial with coeffi- cients K1 to K3 and K4 to K6, respectively. 0 and VTo rep- resent the minimum parameter value. The above expressions differ from our previous results [9] in that VTo was defined as linearly dependent on VDs. Although this is satisfactory at room temperature, the assumption be- comes more tenuous as the temperature is lowered [9]. In our previous work it was also assumed that the depen- dency of P on VDs was sufficiently small to be neglected. Again, as the temperature is varied, this assumption is no longer valid and this bias dependency needs to be in- cluded in the model.

Since the dependency of 0 and VTo on VDs changes in a nonlinear fashion with temperature, the coefficients of the above polynomials are defined as

For this case, T i s the temperature of interest, T,,, is the maximum temperature over which the analysis is to be camed out, and a , b, c are parameters which describe the dependence of the coefficient on temperature. d is a tem- perature-dependent parameter which, for this case, has a fixed value of 0.05 (K-I) . K 1 , K 3 , K4, and K6 are defined with the expression for K , whereas K2 and K5 are defined as 1 / K . It should be noted that the a , b, and c parameters are specific to each coefficient and are not global param- eter values used for all six coefficients. Work is currently in progress to understand the temperature and bias depen- dencies of the parameters so that a physical model may be developed in place of the empirical approach presently used.

Although measurements indicate that X and CY are also bias- and temperature-dependent, these dependencies are not included in the model. This is because the resulting improvement in accuracy is small and the increase in the model complexity large. This will be demonstrated later in the paper. These two parameters therefore have the normal room-temperature values.

IV. MEASUREMENTS

For the results presented in this paper, 4-finger 75-pm gate-width, 0.5-pm gate-length 1-V pinch-off MESFET devices were employed. These devices are fabricated using ion implantation into LEC semi-insulating sub- strates. A multilevel process with the option of either blanket or selective implantation is employed. A variety of profiles are supported which can be selectively im- planted. FET's are normally of 0.5-pm gate length with Ti/Pt/Au gate metallization and silicon nitride passiva- tion to give high performance. Through-GaAs vias mini- mizes FET source inductance.

These devices were cut from the wafer, bonded onto packages, and sealed to prevent the ingress of moisture. The devices were then inserted in a temperature-con- trolled chamber where the input (dZD versus VGs versus VDS) and output ( I D versus VDS versus VGs) dc character- istics were measured over a temperature range from +50"C to -75°C. The measurements were camed out with an HP4143 semiconductor analyzer. These data en- abled the model parameter values to be estimated and plotted as a function of temperature [5], [9]. Self-heating effects arising from the dc biasing conditions were not found to be a problem [9]. The results presented are typ- ical of those achieved for a large and varied number of different MESFET devices [9].

V. VARIATION OF 0, VTo AND CY WITH TEMPERATURE

The measured value of VTo with temperature for differ- ent values of VDs is shown in Fig. 2. It shows that the dependency of VTo on VDS increases in a nonlinear fashion as the temperature is lowered. At a given temperature this dependency is nonlinear. In the Curtice model, it is clearly assumed that at room temperature this bias dependency is small enough to be ignored. However, previous results [5] have indicated that up to an 18 % improvement in ac- curacy could be achieved if this is taken into account. Clearly, this becomes more important as the temperature is lowered, since this bias dependency increases. Notice from these data that (2) is only valid over a small tem- perature range and that the bias-dependency component is not incorporated in the model. Similar results for the vari- ation of VTo with temperature has been reported by others [ 101. The available physical models which attempt to sim- ulate such behavior are only suitable for devices with long gate lengths (> 1 pm). Even then the accuracy is rela- tively poor due to the complicated parameter estimation process. In addition, the coupling between the tempera-

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 40, NO. 10, OCTOBER 1993 1732

- 8

-9

- 2 -10 >

11

-1 2

B---+ vds=30 e------@ vds=2 5 +- -- + vds=20

-90 -60 -30 0 30 60

Temperature (C) Fig. 2. V,, versus temperature and bias.

0275 I . ,

0150 I -90 -60 -30 0 30 60

Temperature $)

Fig. 3 . 0 versus temperature and bias.

5 -90 -60 -30 30 60

Temperature fC)

Fig. 4. cy versus temperature and bias.

2 5x10 Q-----€ VgS= 00 o-----E vgs=-o2 F--T vgs=-o4 e----+ Vgs=-O6 Q..

10x103 I I -90 - 60 -30 0 30 60

Temperature @)

Fig. 5 . X versus temperature and bias.

ture and bias dependency of the parameters are not ac- counted for.

The dependency of /3 on temperature and VDs is shown in Fig. 3 . This again shows fi to be nonlinearly dependent on V,, across all temperatures and this is not included in existing work. Notice also that the bias dependency is af- fected by temperature.

The dependence of CY on temperature and V,, is shown in Fig. 4. The normal assumption that this parameter is both bias- and temperature-independent is clearly not cor- rect, especially at the higher temperatures. The same is also true of X which is shown in Fig. 5 . In the new model, the bias and temperature dependency of these two param- eters are not included for the reasons stated.

VI. ASSESSMENT OF CURTICE PERFORMANCE To determine whether the Curtice expression for ZD is

applicable at any temperature point, the basic room-tem- perature equation was applied to the output characteristics of the device at different temperatures. At each tempera- ture the four parameters of the model were optimized in an unconstrained fashion to achieve the best possible ac- curacy. The worst results were achieved at -75°C and this is shown in Fig. 6 . For higher temperatures, a much better fit to the measured data is achieved. This indicates that, providing the temperature dependency of the param- eters are properly taken into account, for this case reason- ably good accuracy should be achieved. The reasons for the poorer accuracy of the model at low temperatures is due to the greater bias dependency of the parameters which is not accounted for in the model.

When the four parameters of the model were retained at their optimized room-temperature values and (2) and (3) were applied at different temperatures, the results were highly inaccurate. The results at -75°C are shown in Fig. 7 , where the values used for CY and X are the optimized room-temperature values and /3 and VTo have been com- puted with (2) and (3). These results clearly show that the present approach of simulating the temperature depen-

RODRIGUEZ-TELLEZ AND STOTHARD: DEPENDENClES OF /3 AND VTo OF GaAs MESFET'S 1733

calculated I vgs= O O A

03 1

02 - Q n

01

n 0 1 2 3

Vds (V)

Fig. 6 . Optimized Curtice model at -75°C.

0 1 2 3

Vds (V)

Fig. 7 . Comparison of measured data and Curtice model at -75°C

dence of V,, and 0 is incorrect, and that the bias depen- dency of these parameters must be incorporated in the model. As shown in Fig. 7, most of the errors arise from the incorrect modeling of 0 and V,, with respect to tem- perature and bias. Comparing Fig. 6 with Fig. 7 we see that 0 and VTo are the most affecting temperature-depen- dent parameters while cx and X have a small effect which can be neglected. Improvements in accuracy would be gained by modeling the bias and temperature dependen- cies of these two parameters but due account must be made between model complexity and improvement in accuracy.

VII. ASSESSMENT OF NEW MODEL

The measured and computed output characeristics for the same device at -75°C are shown in Fig. 8 when the new model is employed. The conditions used here are the same as those employed in Fig. 6 . That is, the effects of temperature are implicitly included in the normal param- eters of the model. For this case, only (4)-(6) were ap-

calculated measured

Vds (V)

Fig. 8. Optimized new model at -75OC

- 8

t- -- + measured

1 0 -30 30 60

-1 2 -60 -90

Temperature (C)

Fig. 9. Comparison of measured and calculated V , versus temperature and bias.

plied. It is seen that these results are better than achieved previously.

The measured and computed results for VTo and 0 as a function of temperature and bias are shown in Figs. 9 and 10. In both cases, reasonably good agreement with the measured data is achieved.

The measured and computed output characteristics of the device at -75°C and at +50°C are shown in Figs. 11 and 12. For this test, the parameters of the model have been kept fixed and only the temperature value has been altered. The parameter values used for the calculations are shown in Table I. The parameters employed for cx and X are the normal optimized room-temperature values. This test therefore employs the same conditions which were applied to the Curtice model in order to obtain the results of Fig. 7. It is seen that the agreement with the measured data is considerably better than that achieved with the pre- vious model.

1734 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 40, NO. 10, OCTOBER 1993

0275

0250

0225 e Q m c 0)

0200

- modelled t- -- + measured

+ .

Vds= 30V

0150 L ’ ’ I

-90 -60 -30 0 30 60

Temperature (C)

Fig. 10. Comparison of measured and calculated 0 versus temperature and bias.

04

03

- s. 02 0

01

0

modelled measured

Vas= OOV

/- vgs= -08V / _----- --

0 1 2 3

Vds (V)

Fig. 1 1 . Comparison of measured data and new model at -75°C.

03

02

- d 0

01

0

vgS= -06V

/ vgs= -08V

. . . . . . . . . . . . . . . . . . . . . 0 1 2 3

Vds (V)

Fig. 12. Comparison of measured data and new model at 50°C

TABLE I

lO-’( l /V); a = 1.861 ( l /V); f i = 2.137 X lo-’ (A/V’); VTo = -1.017 (V)

PARAMETER VALUES U S E D FOR CALCULATED DATA WITH = 7.228 X

a b C

KI -9.05 x 1 0 - ~ 0.1505 -2.408 K2 -4.755 x 6.034 4 -1.068 X 0.1405 - 1.465 K4 -7.188 x 0.1618 -0.9702 KS -5 .56 X lo-’ 0.368 6.045 X IO-’ K6 -5.292 X IO-’ 0.1361 -0.8676

3.367 x IO-^

04

03

- 5 02 0

01

measured modelled

-75°C

0 0 1 2 3

Vds (V)

Fig. 13. Measured and calculated data at -75’C, 20”C, and 5OOC.

The same measured and computed curves for the V,, = 0 V case at three temperatures are shown in Fig. 13. This shows that the computed curves faithfully reproduce the point where the device becomes temperature-indepen- dent. This is the point where the effect of the temperature dependency of @ cancels out the effect of the temperature dependency of VTo. This effect has been noted for MES- FET’s operating at high temperatures (25°C to 400°C) by Shoucair [ 1 11.

VI11 . CONCLUSIONS A new dc and temperature GaAs MESFET nonlinear

model has been presented. This simulates the dependency of @ and VTo on V,, using third-order polynomial expres- sions. This yields substantial improvements in dc simu- lation accuracy at normal room temperature. The new model also effectively couples together the dependency of the model parameters on bias and temperature. Results presented show that the new model provides a large im- provement in accuracy compared with the conventional technique for simulating temperature over a wide range.

REFERENCES

[ I ] W. R. Curtice, “A MESFET model for use in the design of GaAs integrated circuits,” IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 448-456, May 1980.

RODRIGUEZ-TELLEZ AND STOTHARD: DEPENDENCIES OF 0 AND V,, OF GaAs MESFET’S 1735

[2] H. Statz, P. Newman, I. W. Smith, R. A. Pucel, and H. A. Haus, J. Rodriguez-Tellez received the B.Sc., M.Phil., “GaAs FET device and circuit simulation in SPICE,” IEEE Trans. and Ph.D degrees in electncal engineenng in Electron Devices, vol ED-34, pp 160-169, Feb. 1987. 1979, 1982, and 1985, respectively, from Leeds

[3] A. F. Podell, “A functional GaAs FET noise model,” IEEE Trans. and Bradford Universities, United Kingdom. Electron Devices, vol. ED-28, pp. 511-517, May 1981 From 1979 to 1983 he worked for Standard

[4] T. Kacpzak and A. Materka, “Compact dc model of GaAs FETs for Telecommunications Laboratones, Harlow, UK, large signal computer calculations,” IEEE J . Solid State Circuits, as a research engineer in high-speed communica- vol. SC-18, pp. 211-213, Apr. 1983. tion systems. Since 1983 he has worked at the

[SI J. Rodnguez-Tellez and P. J. England, “A five-parameter dc GaAs University of Bradford as a Senior Lecturer His MESFET model for nonlinear circuit design,” Proc. Inst. Elec. Eng., research interests are device, interconnect, and pt. G, vol. 139, no. 3, pp. 325-332, June 1992. package modeling for microwave circuit applica-

wideband circuit design,” presented at the IEE Summer School, Univ. of Guildford, UK, July 1992.

[7] J. Rodnguez-Tellez, M. AI-Daas, and K. A. Mezher, “Comparison of nonlinear MESFET models for wideband circuit design,” submit- ted to IEEE Trans. Electron Devices.

[8] Precise Simulator Manual, Electncal Engineenng Software Inc., 4675 Stevens Creek Blvd., suite 200, Santa Clara, CA.

[9] J. Rodnquez-Tellez and B. P. Stothard, “Ambient temperature ef- fects on dc behaviour of GaAs MESFET devices,” Proc Inst. Elec. Eng., pt. G, to be published 1993.

[ lo] C-H. Chen, M. Shur, and A. Peczalski, “Trapping-enhanced tem- perature variation of the threshold voltage of GaAs MESFET’s,” IEEE Trans. Electron Devices, vol. ED-33, pp. 792-797, June 1986.

[ I I] F S. Shoucair and P. K. Ojala, “High temperature characteristics of GaAs MESFET’s (25-400“C),” IEEE Trans. Electron Devices, vol. 39, no. 7, pp. 1551-1557, July 1992.

161 J Rodnguez-Tellez, “Companson of GaAs MESFET models for tlOnS.

B. P. Stothard received the B.Sc degree in phys- ics and the M Sc. degree in microwave solid-state physics from Leicester and Portsmouth Universi- ties, United Kingdom, in 1989 and 1990, respec- tively .

He is currently pursuing the Ph.D degree at Bradford University, studying temperature effects on GaAs MESFET devices

Mr. Stothard is a student member of the IEE