Using Modified GaAs FET Model Functions for the Accurate Representation of PHEMTs and Varactors Josef Dobeˇs Czech Technical University in Prague, Department of Radio Engineering, The Czech Republic
[email protected] Abstract— In the recent PSpice programs, several GaAs FET models of various classes have been implemented. However, some of them are sophisticated and therefore very difficult to measure and identify afterwards, especially the realistic model of Parker and Skellern. In the paper, simple enhancements of one of the standard models are proposed. The resulting modification is usable for the accurate modeling of both GaAs FETs and pHEMTs. Moreover, its updated capacitance function can serve as a precise representation of microwave varactors, which is more important.
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Schottky junctions
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I NTRODUCTION The Sussman-Fort, Hantgan, and Huang [1] model equations can be considered a good compromise between the complexity and accuracy (they are updated from [2]). However, both static and dynamic parts of the model equations must be modified when using them for the suggested pHEMT and varactor modeling. All the model modifications defined below have been implemented into the author’s program C.I.A. (Circuit Interactive Analyzer).
Vg Cg
frequency dispersion
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I. M ODIFYING THE S TATIC PART OF THE M ODEL The primary voltage-controlled current source of the GaAs FET model can be defined for the forward mode (Vd = 0) as VT = VT 0 − σVd , (1a) ( 0 for Vg 5 VT , Id = n β (Vg − VT ) 2 (1 + λVd ) tanh(αVd ) otherwise, (1b) and by the mirrored equations for the reverse mode (Vd < 0) (2a) VT = VT 0 + σVd , ( 0 for Vg0 5 VT , ¡ 0 ¢n2 Id = β Vg − VT (1 − λVd ) tanh(αVd ) otherwise, (2b) where Vg0 = Vg − Vd – see the current and voltages in Fig. 1. The model parameters VT 0 , β, n2 , λ and α have already been defined in [1], the parameter σ used in the “boxed” parts of (1) and (2) represents an improvement of the classical simpler models. The ParkerSkellern “realistic” model contains similar dependencies [3] – (1a) and (2a) can be considered as their base.
Fig. 1. Simplified diagram of the GaAs FET model, which includes the frequency dispersion. For modeling the gate delay, a precise method based on the second-order Bessel function (in frequency domain) and associated differential equation (in time domain) is suggested in [7]. (It uses the way defined in [8], but with another model function.)
Although the equations (1) and (2) are relatively simple, they contain an improvement in comparison with the classical Curtice model [2] (n2 which characterizes gate voltage influence more precisely), and also in comparison with the classical Statz model [4] (σ which characterizes drain voltage influence more precisely). The importance of the modifications (1a) and (2a) can be demonstrated by the identification of the model parameters for DZ71 [5] GaAs FET – see the results in Fig. 2. The C.I.A. [6] optimization procedure has provided the values of the model parameters VT 0 = −1.36 V, β = 0.0346 A V−2 , n2 = 1.73, λ = −0.082 V−1 (negative value arises if σ used), α = 2.56, σ = 0.141, rD = 2.88 Ω, and rS = 2.62 Ω (rD and rS have already been estimated in [5]). To compare, the same FET has been identified by the classical Statz model [4] – the suggested model is more accurate, especially for the lesser values of the gate-source control voltage.
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Fig. 4. Suggested GaAs FET model function for the varactor representation.
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measurement. Embedding the frequency dispersion can be also performed in another precise but more complicated way, see [3].
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III. M ODIFYING THE DYNAMIC PART OF THE M ODEL
Fig. 2. Comparison of the GaAs FET model identification using the suggested and classical Statz equations (rms = 2.73 % and δmax = 8 % for the C.I.A. model). The measured data including rD and rS estimations are taken from [5]. .2 0.5 .175
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V D (V) Fig. 3. Results of the pHEMT identification using the C.I.A. model (1) and (2) (rms = 2.38 % and δmax = 8.24 %). The measured data are taken from [9].
II. U SING THE M ODEL AS PHEMT S R EPRESENTATION The modifications (1a) and (2a) also enable the model to be used for the pHEMT modeling – see the results in Fig. 3. The identification has set the model parameters to VT 0 = −1.64 V, β = 0.102 A V−2 , n2 = 0.991, λ = −0.0288 V−1 , α = 1.16, σ = 0.00797, rD = 0.3 Ω, and rS = 0.2 Ω. The representation of pHEMT using (1) and (2) is very precise (rms ≈ 2 % only) and is slightly more accurate than the TriQuint model in [9]. (See [10] and [11] for exhaustive TriQuint model definitions.) The model is able to form a negative differential conductance, which is illustrated in Fig. 3. On the other hand, at very high frequencies, the s22 parameter has mostly a positive real part. Therefore, a corrective current source Id0 must be added identified by the s parameters
In general, the GaAs FET gate capacitance is highly nonlinear as seen in Fig. 4. The definition splits into the three parts (similar to those in Statz model [12], [13]) s φ0 − VT for Vg 5 VA , ²W arctan VT − Vg " µ ¶ −m VB V − V g A CJ0 1 − + V − VA φ0 B # r ²W φ0 − VT π + − ²W arctan Cg = 2 VT − VA r φ0 − VT ²W arctan for Vg > VA ∧ VT − VA Vg < V B , µ ¶ −m ²W Vg π + CJ0 1 − for Vg = VB , 2 φ0 (3) where the transitional region is determined empirically [1] VA = VT − 0.15 V,
VB = VT + 0.08 V.
(4)
All the model parameters have been defined in [1] with the exception of the “boxed” m. This parameter can be found in the recent PSpice tables of the advanced model parameters – all the classical models always use − 12 instead of −m. IV. U SING THE M ODEL AS VARACTORS R EPRESENTATION The microwave varactors are highly nonlinear with observed dependencies similar to those in GaAs FET gate capacitances. Therefore, the functions in (3) can be used after replacing Cg and Vg with the external ones, i.e., CG and VG . A. Testing the Varactors from Texas Instruments Firstly, let’s demonstrate this idea by identifying Texas Instruments EG8132 gate and source [14] varactors – see the results in Fig. 5 and 6. The identifications confirm that the usage of (3) enables more accurate approximation than the 6th order polynomial in [14].
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Fig. 5. Comparison of the EG8132 gate varactor model identification using the updated GaAs FET and classical polynomial functions (rms = 4.52 % and δmax = 13.7 % for the C.I.A. model). The measured data are taken from [14], where the original polynomial approximation a0 + a2 (VG − Va )−2 + a3 (VG − Va )−3 + · · · + a6 (VG − Va )−6 has been also tested with the inaccurate results (dashed curve) shown here. (In [14], the parameters Va = −8 V, a0 = −0.54 pF, a2 = 2.3 nF V2 , a3 = −87.938 nF V3 , a4 = 1.4 µF V4 , a5 = −10.458 µF V5 , and a6 = 30.48 µF V6 were used.)
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Fig. 6. Comparison of the EG8132 source varactor model identification using the updated GaAs FET and classical polynomial functions (rms = 4 % and δmax = 6.87 % for the C.I.A. model). The measured data, and the polynomial approximation a0 + a2 (VG − Va )−2 + a3 (VG − Va )−3 + · · · + a6 (VG − Va )−6 are taken from [14] again (Va = −6 V, a0 = −0.09 pF, a2 = 0.4783 nF V2 , a3 = −14.703 nF V3 , a4 = 0.18351 µF V4 , a5 = −1.0475 µF V5 , and a6 = 2.3177 µF V6 were used with the inaccurate results shown by dashed curve here). 8
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(ident, C.I.A.) (meas) CG , CG ( ) (pF)
For the gate varactor, the C.I.A. optimization procedure has provided the values of the model parameters ²W = 0.15711 pF, CJ0 = 1.0771 pF, VT = −2.7569 V, φ0 = 23.451 V (!), and m = 12.827 (!). The last two parameters do not have “physical” values, which illustrates the necessity of using the general −m-power in (3). From the physical point of view, the varactor is not defined for VG > VB by the classical junction capacitance function – however, this formula is flexible enough to characterize it. For the source varactor, the C.I.A. optimization procedure has provided the values of the model parameters ²W = 0.13587 pF, CJ0 = 0.66625 pF, VT = −2.6026 V, φ0 = 13.251 V (!), and m = 8.1457 (!) with a little more precise device characterization – compare the values rms and δmax .
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B. Testing the Varactor from International Laser Centre
Fig. 7. Results of the ILC varactor identification using the updated GaAs FET C.I.A. model function (rms = 6.21 % and δmax = 23.7 %). The measured data are granted by the authors of [15].
Secondly, the nonlinear capacitance of the nonstandard SACM APD layer structure MO457/4 [15] has been identified – see the results in Fig. 7. The C.I.A. optimization procedure has provided the values of the model parameters ²W = 1.51155 pF, CJ0 = 5.30894 pF, VT = −6.17455 V, φ0 = 204.491 V, and m = 30.4842 (the last two parameters have again exceptional values).
using the modified GaAs FET capacitance function. It is important that all the model parameters can be easily identified from the measured data.
C ONCLUSION The proposed model has been verified for the approximation of both GaAs FETs and pHEMTs with the precision of several percent. The new unusual way is suggested for the accurate modeling of the microwave varactors
ACKNOWLEDGMENTS This paper has been supported by the Grant of the European Commission FP6: Expression of Interest for a Network of Excellence called TARGET (Top Amplifier Research Groups in a European Teamwork), and by the Czech Technical University Research Project No J04/98:212300016.
A PPENDIX The root mean square and maximum deviations computed for the results in Figs. 2–5 are defined naturally v ! u np à (ident) (meas) 2 uX y − yi i u u (meas) t i=1 yi rms = × 100 %, np ¯ ¯ ¯ (ident) − y (meas) ¯ np ¯ y ¯ i δmax = max ¯ i ¯ × 100 %, (meas) i=1 ¯ ¯ yi (ident)
(meas)
are the identified and yi respectively, where yi and measured values, and np is the number of all points. R EFERENCES [1] S. E. Sussman-Fort, J. C. Hantgan, and F. L. Huang, “A SPICE model for enhancement- and depletion-mode GaAs FET’s,” IEEE Trans. Microwave Theory Tech., vol. 34, pp. 1115–1119, Nov. 1986. [2] W. R. Curtice, “GaAs MESFET modeling and nonlinear CAD,” IEEE Trans. Microwave Theory Tech., vol. 36, pp. 220–230, Feb. 1988. [3] A. E. Parker and D. J. Skellern, “A realistic large-signal MESFET model for SPICE,” IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1563–1571, Sept. 1997. [4] H. Statz, P. Newman, I. W. Smith, R. A. Pucel, and H. A. Haus, “GaAs FET device and circuit simulation in SPICE,” IEEE Trans. Electron Devices, vol. 34, pp. 160–169, Feb. 1987.
[5] A. K. Jastrzebski, “Non-linear MESFET modeling,” in Proc. 17 th European Microwave Conference, 1987, pp. 599–604. [6] J. Dobeˇs, “C.I.A.—a comprehensive CAD tool for analog, RF, and microwave IC’s,” in Proc. 8 th IEEE Int. Symp. High Performance Electron Devices for Microwave and Optoelectronic Applications, Glasgow, Nov. 2000, pp. 212–217. [7] ——, “Expressing the MESFET and transmission line delays using Bessel function,” in Proc. 16 th European Conf. Circuit Theory Design, vol. I, Krak´ow, Sep. 2003, pp. 169–172. [8] A. Madjar, “A fully analytical AC large-signal model of the GaAs MESFET for nonlinear network analysis and design,” IEEE Trans. Microwave Theory Tech., vol. 36, pp. 61–67, Jan. 1988. [9] J. Cao, X. Wang, F. Lin, H. Nakamura, and R. Singh, “An empirical pHEMT model and its verification in PCS CDMA system,” in Proc. 29 th European Microwave Conference, Munich, Oct. 1999, pp. 205–208. [10] A. J. McCamant, G. D. McCormack, and D. H. Smith, “An improved GaAs MESFET model for SPICE,” IEEE Trans. Microwave Theory Tech., vol. 38, pp. 822–824, June 1990. [11] D. H. Smith, “An improved model for GaAs MESFETs,” TriQuint Semiconductors Corporation, Tech. Rep., 2000. [12] G. Massobrio and P. Antognetti, Semiconductor Device Modeling With SPICE. New York: McGraw-Hill, 1993. [13] E. Sijerci´c and B. Pejcinovi´c, “Comparison of non-linear MESFET models,” in Proc. 9 th IEEE Int. Conf. on Electronics, Circuits and Systems, vol. III, Dubrovnik, Sep. 2002, pp. 1187–1190. [14] C.-R. Chang, B. R. Steer, S. Martin, and E. Reese, “Computeraided analysis of free-running microwave oscillators,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1735–1744, Oct. 1991. [15] M. Klasovit´y, D. Haˇsko, M. Tom´asˇka, and F. Uherek, “Characterization of avalanche photodiode properties in frequency domain,” in Proc. 5 th Scientific Conference on Electrical Engineering & Information Technology, Bratislava, Sep. 2002, pp. 63–65.
