Using Modified GaAs FET Model Functions for
the Accurate Representation of PHEMTs and
Varactors
Josef Dobeš
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.
VD
ID
Schottky
junctions
VG
rD
Vd
Id
I d′
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
rS
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.
CG
0
.06
-0.2
.05
-0.5
.04
V G (V )
(meas)
(ident, C.I.A.)
(ident, Statz)
ID
, ID
( ), I D
( ) (A)
.07
.03
VA VB
Fig. 4. Suggested GaAs FET model function for the varactor representation.
-1
.02
.01
measurement. Embedding the frequency dispersion can be
also performed in another precise but more complicated
way, see [3].
-1.5
0
0
1
2
3
4
5
V D (V )
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
(meas)
(ident)
, ID
ID
( ) (A )
VG
0
.15
.125
-0.5
.1
.075
V G (V)
-1
.05
.025
-1.5
0
0
1
2
3
4
5
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].
1
.5
0
-13 -12 -11 -10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
(meas)
(ident, C.I.A.)
(ident, polyn)
CG
, CG
( ), CG
( ) (pF)
(meas)
(ident, C.I.A.)
(ident, polyn)
CG
, CG
( ), CG
( ) (pF)
1.5
1
.9
.8
.7
.6
.5
.4
.3
.2
.1
0
-14 -13 -12 -11 -10 -9
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.)
-8
-7
-6
-5
-4
-3
-2
-1
0
V G ( V)
VG (V)
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
7
(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 .
6
5
4
3
2
1
0
10
20
30
40
50
60
−V G ( V)
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. Dobeš, “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, Kraków, 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. Sijercić and B. Pejcinović, “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. Klasovitý, D. Haško, M. Tomáška, 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.