Using modified GaAs FET model function for the accurate representation of PHEMTs and varactors

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 enhancement of one of the standard models is proposed. The resulting modification is usable for the accurate modelling of both GaAs FETs and PHEMTs. Moreover, its updated capacitance function can serve as a precise representation of microwave varactors, which is more important.

Full text

Using Modified GaAs FET Model Functions for
the Accurate Representation of PHEMTs and
Varactors
Josef Dobe
ˇ
s
Czech Technical University in Prague, Department of Radio Engineering, The Czech Republic
dobes@feld.cvut.cz
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 model-
ing of both GaAs FETs and pHEMTs. Moreover, its updated
capacitance function can serve as a precise representation
of microwave varactors, which is more important.
INTRODUCTION
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).
I. MODIFYING THE STATIC PART OF THE MODEL
The primary voltage-controlled current source of the
GaAs FET model can be defined for the forward mode
(V
d
= 0) as
V
T
= V
T 0
− σV
d
, (1a)
I
d
=
(
0 for V
g
5 V
T
,
β (V
g
− V
T
)
n
2
(1 + λV
d
) tanh(αV
d
) otherwise,
(1b)
and by the mirrored equations for the reverse mode
(V
d
< 0)
V
T
= V
T 0
+ σV
d
, (2a)
I
d
=
(
0 for V
0
g
5 V
T
,
β
¡
V
0
g
− V
T
¢
n
2
(1 − λV
d
) tanh(αV
d
) otherwise,
(2b)
where V
0
g
= V
g
− V
d
– see the current and voltages
in Fig. 1. The model parameters V
T 0
, β, n
2
, 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 Parker-
Skellern “realistic” model contains similar dependencies
[3] – (1a) and (2a) can be considered as their base.
V
G
V
D
I
D
V
d
V
g
r
D
r
S
C
g
frequency
dispersion
Schottky
junctions
I
d
I
d
′
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] (n
2
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 V
T 0
= −1.36 V,
β = 0.0346 AV
−2
, n
2
= 1.73, λ = −0.082 V
−1
(negative value arises if σ used), α = 2.56, σ = 0.141,
r
D
= 2.88 Ω, and r
S
= 2.62 Ω (r
D
and r
S
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.

0
-0.2
-0.5
-1
-1.5
0 1 2 3 4 5
0
.01
.02
.03
.04
.05
.06
.07
V
G
( )V
V
D
( )V
I
I
I
D
D
D
(ident,
C I A ) (ident,
Statz)
(meas)
( )
( ) ( )
. . .
,
,
A
Fig. 2. Comparison of the GaAs FET model identification using the
suggested and classical Statz equations (rms = 2.73 % and δ
max
=
8 % for the C.I.A. model). The measured data including r
D
and r
S
estimations are taken from [5].
-1.5
-1
-0.5
0.5
0
0 1 2 3 4 5
0
.025
.05
.075
.1
.125
.15
.175
.2
V
G
( )V
V
D
( )V
I
I
D
D
(ident)
(meas)
( ) ( )
,
A
Fig. 3. Results of the pHEMT identification using the C.I.A. model
(1) and (2) (rms = 2.38 % and δ
max
= 8.24 %). The measured data
are taken from [9].
II. USING THE MODEL AS PHEMTS
REPRESENTATION
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 V
T 0
= −1.64 V, β = 0.102 AV
−2
, n
2
= 0.991, λ =
−0.0288 V
−1
, α = 1.16, σ = 0.00797, r
D
= 0.3 Ω, and
r
S
= 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 s
22
parameter has
mostly a positive real part. Therefore, a corrective current
source I
0
d
must be added identified by the s parameters
C
G
V
G
V
A
V
B
Fig. 4. Suggested GaAs FET model function for the varactor repre-
sentation.
measurement. Embedding the frequency dispersion can be
also performed in another precise but more complicated
way, see [3].
III. MODIFYING THE DYNAMIC PART OF THE MODEL
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])
C
g
=













































²W arctan
s
φ
0
− V
T
V
T
− V
g
for V
g
5 V
A
,
V
g
− V
A
V
B
− V
A
"
C
J0
µ
1 −
V
B
φ
0
¶
−m
+
π
²W
2
− ²W arctan
r
φ
0
− V
T
V
T
− V
A
#
+
²W arctan
r
φ
0
− V
T
V
T
− V
A
for V
g
> V
A
∧
V
g
< V
B
,
π
²W
2
+ C
J0
µ
1 −
V
g
φ
0
¶
−m
for V
g
= V
B
,
(3)
where the transitional region is determined empirically [1]
V
A
= V
T
− 0.15 V, V
B
= V
T
+ 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 −
1
2
instead of −m.
IV. USING THE MODEL AS VARACTORS
REPRESENTATION
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 C
g
and V
g
with the external ones, i.e.,
C
G
and V
G
.
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 6
th
order polynomial in [14].

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
0
.5
1
1.5
C
C
C
G
G
G
(ident,
C I A ) (ident,
polyn)
(meas)
( )
( )
pF
)
(
. . .
,
,
V
G
( )V
Fig. 5. Comparison of the EG8132 gate varactor model identification
using the updated GaAs FET and classical polynomial functions (rms =
4.52 % and δ
max
= 13.7 % for the C.I.A. model). The measured data
are taken from [14], where the original polynomial approximation a
0
+
a
2
(V
G
− V
a
)
−2
+ a
3
(V
G
− V
a
)
−3
+ · · · + a
6
(V
G
− V
a
)
−6
has been
also tested with the inaccurate results (dashed curve) shown here. (In
[14], the parameters V
a
= −8 V, a
0
= −0.54 pF, a
2
= 2.3 nF V
2
,
a
3
= −87.938 nF V
3
, a
4
= 1.4 µF V
4
, a
5
= −10.458 µF V
5
, and
a
6
= 30.48 µF V
6
were used.)
For the gate varactor, the C.I.A. optimization proce-
dure has provided the values of the model parameters
²W = 0.15711 pF, C
J0
= 1.0771 pF, V
T
= −2.7569 V,
φ
0
= 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 V
G
> V
B
by the classical junction capacitance
function – however, this formula is flexible enough to
characterize it.
For the source varactor, the C.I.A. optimization pro-
cedure has provided the values of the model parameters
²W = 0.13587 pF, C
J0
= 0.66625 pF, V
T
= −2.6026 V,
φ
0
= 13.251 V (!), and m = 8.1457 (!) with a little
more precise device characterization – compare the values
rms and δ
max
.
B. Testing the Varactor from International Laser Centre
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,
C
J0
= 5.30894 pF, V
T
= −6.17455 V, φ
0
= 204.491 V,
and m = 30.4842 (the last two parameters have again
exceptional values).
CONCLUSION
The proposed model has been verified for the approxi-
mation of both GaAs FETs and pHEMTs with the preci-
sion of several percent. The new unusual way is suggested
for the accurate modeling of the microwave varactors
V
G
( )V
C
C
C
G
G
G
(ident,
C I A ) (ident,
polyn)
(meas)
( )
( )
pF
)
(
. . .
,
,
-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1
Fig. 6. Comparison of the EG8132 source varactor model identification
using the updated GaAs FET and classical polynomial functions (rms =
4 % and δ
max
= 6.87 % for the C.I.A. model). The measured data,
and the polynomial approximation a
0
+ a
2
(V
G
− V
a
)
−2
+ a
3
(V
G
−
V
a
)
−3
+ · · · + a
6
(V
G
− V
a
)
−6
are taken from [14] again (V
a
=
−6 V, a
0
= −0.09 pF, a
2
= 0.4783 nF V
2
, a
3
= −14.703 nF V
3
,
a
4
= 0.18351 µF V
4
, a
5
= −1.0475 µF V
5
, and a
6
= 2.3177 µF V
6
were used with the inaccurate results shown by dashed curve here).
0 10 20 30 40 50 60
1
2
3
4
5
6
7
8
−V
G
( )V
C
C
G
G
(ident,
C I A ) (meas)
( ) (pF)
. . .
,
Fig. 7. Results of the ILC varactor identification using the updated
GaAs FET C.I.A. model function (rms = 6.21 % and δ
max
= 23.7 %).
The measured data are granted by the authors of [15].
using the modified GaAs FET capacitance function. It
is important that all the model parameters can be easily
identified from the measured data.
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 Ampli-
fier Research Groups in a European Teamwork), and
by the Czech Technical University Research Project
N
o
J04/98:212300016.

APPENDIX
The root mean square and maximum deviations com-
puted for the results in Figs. 2–5 are defined naturally
rms =
v
u
u
u
u
t
n
p
X
i=1
Ã
y
(ident)
i
− y
(meas)
i
y
(meas)
i
!
2
n
p
× 100 %,
δ
max
=
n
p
max
i=1
¯
¯
¯
¯
¯
y
(ident)
i
− y
(meas)
i
y
(meas)
i
¯
¯
¯
¯
¯
× 100 %,
respectively, where y
(ident)
i
and y
(meas)
i
are the identified
and measured values, and n
p
is the number of all points.
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