Capacitance and RF-Conductance/Transconductance Look-up Table Based pHEMT Model

Capacitance and RF-Conductance/Transconductance Look-up Table
Based pHEMT Model
Ce-Jun Wei1, Yu Zhu, Hong Yin , Oleksiy Klimashov, Cindy Zhang, and Tzung-Yin Lee
SKYWORKS SOLUTION INC., 20 SYLVAN ROAD, WOBURN, MA 01801, USA
1
[email protected]
ABSTRACT
—
A capacitance and RF-conductance/RFtransconductance look-up table based large-signal pHEMT
model is presented based on an ensemble of bias-dependent
small-signal equivalent circuits. The model is capable of
accurate simulation of small-signal S-parameters as well as
large-signal performance over the data-acquisition bias range.
In addition to the dc current sources, the model contains two
capacitive current sources and two dynamic RF current sources,
which fit RF-DS conductance and transconductance
respectively. By introducing the dynamic RF current sources,
the problem of path-dependence which occurs in modeling
large-size devices and devices with dispersion is resolved. The
model is symmetric and swappable between drain and source.
The model has also accurate leakage model and can be used for
either amplifier or switch applications. The validity of the model
is demonstrated by comparing the simulation of DC curves,
leakages, and small-signal S-parameters over a wide bias range,
by comparison of the measured data. Large-signal
power/harmonics simulation shows good comparison to the
measured data.
Index Terms — look-up table modeling, Emote PHEMT.
I. INTRODUCTION
For modern communications, design of pHEMT amplifiers
and switches with accurate bias-dependent S-parameters and
large-signal performances prediction are critical and
challenging. Unfortunately, due to complex trapping effects
in MESFETs and pHEMTs, it is almost impossible to develop
a physics-based model and empirical models and look-up
table-based model are widely used. The applicability of
empirical models depends on if the equations adequately
cover the trapping effects that are normally very tough to do.
Look-up table based model or Root model s are considered to
be most accurate since it is based on measurement data and it
is technology independent.
There are a couple of traps when using the look-up table
based model. First, the accuracy depends on if the measured
data is sufficient to cover all important physical features of
the devices. The Root model uses charge-based look-up
tables and it has the advantages of good convergence and is
very robust. However, due to complex trapping effects, the
charges based on integration of 2D-CV functions are not
always path-independent. The trans-capacitance near pinchoff may result in unphysical small-signal response. Also the
conventional Root model does not take into account the
difference both between DC and RF Gm and Gds. Also it is
required to be symmetric between drain and source that is
important for switch applications and that the conventional
look-up table based models do not satisfy.
In this paper we present an extended and improved look-up
table based model. Instead of a charge-based model, we use
capacitance based look-up tables that do not contain transcapacitances. The model contains two RF-currents, one based
on RF-Gm current that sets into play when there is gatevoltage swing, and the other RF-Gds based current that
comes into play when there is RF-swing of drain-source
voltage. The intrinsic model is symmetric between drain and
source and they are swappable. Plus with the accurate leakage
look-up tables, the model is capable of switch applications.
Systematic extraction to extract two RF-IVs and CV
functions is described. Following is the validation of the
model in terms of fitting of IV, S-parameters in wide range,
as well as power/harmonics for typical sizes of devices. The
overall model including noise model is illustrated.
II. EQUIVALENT CIRCUIT OF THE MODEL
The equivalent circuit of intrinsic part of the model is
shown in figure 1. Extrinsic model contains, as usual, access
resistances Rg, Rs, and Rd and access inductances, Lg, Ls,
and Ld and possible some parasitic capacitances, not shown
here. In the figure, there are three currents between drain and
source, Idc is the dc current, Id_gm is the RF current
integrated from RF-Gm. and Id_Gds integrated from RF-Gds.
Id_gm
Idc
Id_Gds
Ctrap
Rtrap
D
S
Ids_leak
Igd_leak
Cgd
Cds
Dgd
Cgs
Dgs
Igs_leak
G
Figure 1. Equivalent circuit of the intrinsic part of the model
Due to large value of CtrapRtrap time constant, that
corresponding to trapping effects, the DC current will be Idc
and Id_Gm and Id_Gds are shunted by Rtrap. At RF, the
current will be Id_Gm and Id_Gds that flow out to circuit via
Ctrap and Idc is shorted by the large capacitance Ctrap.
The integration path of Irf-Gm starts from far-below
pinchoff at any Vds as initial point, at that the Ids is supposed
to be zero, the current will be the integration of RF-Gm with
respect to Vgs.
Id _ Gm =
Vg
∫<<Vp Gm _ rf dVgs =fg(Vgs, Vdso)
where
is
Gm _ rf
measured
bias
dependent
RF
transconductance and the integration assumes Vds is
unchanged and it is the DC component. The Vgs is integrated
from far below pinchoff to the point of required augument of
the function. Similarly, the integration path of Irf-Gds starts
from Vds=0 at any Vgs as initial point, at that the Ids is
supposed to be zero, the current will be the integration of RFGds with respect to Vds.
Id _ Gds =
Vd
∫0
Gds _ rf dVds = fp(Vgso, Vds)
where the DC-Vgso is a parameter and Gds _ rf is measured
bias dependent RF DS-conductance and the integration
assumes Vgs is unchanged and is the DC component.
It is straightforward to verify that the RF-Gm is exactly the
same as measured and the RF-Gds is exactly the same as
measured, too.
Figure 2 shows these two RF currents and how much
difference is between them. The device measured is a
4x75um E-mode pHEMT from Winn-semi.
Figure 2. Plot of Id_gm and Id_gds for a device of 4x75um E-mode
pHEMT.
The charge model is replaced with the capacitance model.
The advantage of the capacitance-based model is direct use of
measured capacitance look-up tables and there is no transcapacitance involved. The charge equations are replaced with
capacitive currents: Icap_gs= Cgs x dVgs/dt and
Icap_gd=Cgd x dVgd/dt. Therefore, the model is fully
consistent with bias-dependent small-signal models.
The leakage look-up table is generated by measuring the
gate leakages at Vds=0 and measuring the leakages with the
drain open and fitting the drain floating voltages.
The model is implemented with a 14 port SSD in ADS, as
shown in figure 3. The model also contains a noise model that
will not be addressed here.
Port
G
Num =2
G
D
S
Port
S
Num =3
Tj
Port
D
Num=1
_dgsdt
R
R44
_dgddt R=1 Ohm
_Gc
_Dc
di
si
ds
_Sc
vdsn
vgmn
SDD14P
SDD14P1
I[1,0]=Ig
I[2,0]=(_v2)/1e15
I[3,0]=(_v3)/1e15
I[4,0]=-ids*(_v2-_v3)
I[4,1]=Cth*(_v4)
F[5,0]=-dvgs_dt
F[5,1]=vgs/f_nom
F[6,0]=-dvgd_dt
F[6,1]=vgd/f_nom
I[7,0]=Igs_cap+Igd_cap
I[8,0]=-Igd_cap
I[9,0]=ids-igd
I[9,1]=qds
I[10,0]=-igs-Idrf
I[10,1]=-qds
I[11,0]=-ids+Idrf
I[12,0]=-Igs_cap
I[13,0]=ids*EnNoise
I[14,0]=idgn*EnNoise
C[1]="Igrf"
C[2]="Idrf"
C[3]="Igdrf"
Cport[1]=
Figure 3. Using SDD to build look-up table model.
III. MODEL EXTRACTION
The model extraction uses a 4x75um E-mode pHEMT
from Winn-semi. ICCAP is used for measurements. The
measurement range from Vgs=-10V up to 0.8V, Vds from 0V
to 6V covers well the linear-saturation region as well as
leakage region. The S-parameters measured from Vds=0 to
6V covering active region and Vgs from -10V to 0.3V
covering below pinch-off region. The later is important when
the device is used for switch or class C and high-power
applications.
An important extraction step is generating bias-dependent
small-signal models with all bias-dependent element values,
Cgs, Cgd, Gm, and Gds….ColdFET technique is used to
extract the extrinsic element values such as Rg, Rs, and Rd
and Lg, Ls, and Ld. After extrinsic elements are extracted, the
intrinsic element values can be calculated. This was done
with our in-house program. The program also generates a
series look-up-table in mdf format that the ADS can read in.
It should be pointed out that all look-up-tables generated
by measurements are with reference to extrinsic port voltages,
Vgse/Vgde, and Vdse. To make the model more robust and
faster converge, the lookup-tables were converted in
reference to intrinsic port voltages, Vgs/Vgd and Vds. This
was done using MATLAB.
IV. MODEL VALIDATION
It is expected that the model should generate DC-Ids
curves as measured. Figure 4 shows indeed the fitting is
perfect, where the lines are modeled and the symbols are
measured. The Vds changes from 0V to 6V and Vgs changes
from 0.3V to 0.8V and the step is 0.05V. It has been also
verified that by swapping DS, it generates the same results
providing Rd is equal to Rs. In real case, Rs is somewhat
smaller than Rd due to the layout, that all source fingers are
connected crossover and grounded.
It is vital to validate the bias-dependent S-parameter fitting.
The model was validated over wide bias range from linear to
saturation, from below pinchoff to active region. They all
show perfect fitting without any unphysical results.
As an example, figure 7 shows the modeled (blue) and
measured (red) S-parameters at saturation region, Vds=3V
and Vgs varying from 0.2V to 0.65V step 0.05V.
0.07
0.06
IDS.i, A
Id_IV
0.05
0.04
0.03
0.02
0.01
2
3
4
5
6
Vd
Figure 5. Modeled (lines) and measured (symbols) Ids curves for a
4x75um E-mode pHEMT. Vgs=0.3V to 0.8V step 0.05V and Vds
from 0V to 6V.
S(4,3)
S(2,1)
The leakage model is verified by comparing Ids and Ig at
and below pinch-off as shown in figure 6. The upper graph
shows the Ids as a function of Vgs with Vds varying from 1
to 4V. The lower graph shows corresponding gate leakage
current. It is shown that the fitting is excellent.
freq (300.0MHz to 10.00GHz) freq (300.0MHz to 10.00GHz)
-20
-10
0
10
S(3,4)
S(1,2)
1
S(3,3)
S(1,1)
0
S(4,4)
S(2,2)
0.00
20
-0.4
-0.2
0.0
0.2
0.4
freq (300.0MHz to 10.00GHz)
freq (300.0MHz to 10.00GHz)
Modeled and measured Ids
0.000025
Figure 7. Modeled (blue lines) and measured (red lines) Sparameters from 0.3 to 10GHz for 4x75um E-mode pHEMT.
Vds=3V Vgs=0.2V to 0.65V step 0.05V.
0.000020
0.000015
0.000010
Figure 8 shows another example, the modeled (blue) and
measured (red) S-parameters at linear region, Vds=0.5V and
Vgs varying from 0.2V to 0.65V step 0.05V.
0.000005
0.000000
-0.000005
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Vg
S(3,3)
S(1,1)
2E-2
1E-2
1E-4
freq (300.0MHz to 10.00GHz) freq (300.0MHz to 10.00GHz)
1E-6
1E-10
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-20
-10
0
10
S(3,4)
S(1,2)
1E-8
S(4,3)
S(2,1)
Modeled and measured Ig
S(4,4)
S(2,2)
(a)
20
-0.4
-0.2
0.0
0.2
0.4
0.5
Vg
(b)
Figure 6. Modeled (lines) and measured (symbols) Ids leakage (a)
and Ig leakage curves (b) for a 4x75um E-mode pHEMT. Vgs=-3V
to 0.25V and Vds from 1V to 4V step 1V.
freq (300.0MHz to 10.00GHz)
freq (300.0MHz to 10.00GHz)
Figure 8. Modeled (blue lines) and measured (red lines) Sparameters from 0.3 to 10GHz for 4x75um E-mode pHEMT.
Vds=0.5V Vgs=0.2V to 0.65V step 0.05V.
The model shows good convergence for a device 4x75um
and input power up to 3dBm. Figure 9 shoows the simulated
power performance and harmonics with input power
sweeping and its comparison with measured data. In
harmonic simulation, the real test-set termiinations have been
carefully calibrated and the impedancess as function of
frequency have been taken into account. The
T model predicts
very well the output power and 2nd/3rd harm
monics. The model
shows the small-power gain to be 19.22dB vs measured
19.35dB and the 1dB compression is at Pin=-7.3dBm vs
measured -8.5dB, slightly off. The 2nd andd 3rd harmonics as
function of input power are in very goodd agreement with
measured results.
Figure 9. Modeled (lines) and measured (sym
mbols) output power,
2nd/3rd harmonics and power gain as function of input power for
4x75um E-mode pHEMT. Vds=3.5V Vgs=0.5V Pin=-20 to 3dBm.
VII. CONCLUSION
A new lookup-table based model is deveeloped. The model
is based on capacitance, RF transconducttance, and RF DS
conductance as a function of intrinsic gate and
a drain voltages.
Two RF currents, one based on RF-Gm annd the other based
on RF_Gds, are used to solve the path-deppendence problem
due to dispersion. There is no trans-capacitance involved that
makes the model perfectly compatible wiith bias-dependent
small-signal models.
Leakage is incorporated into the model.
m
Plus the
symmetric feature, the model is appliicable to various
applications. The model has been implemennted as design kits
at Skyworks Solutions, Inc. The new modeel shows exact DC
fitting and excellent bias-dependent S-param
meter fitting at the
wide bias range. Large-signal simulation also shows it is
robust. The model extractioon is fast and technologyindependent.
The model validation was shown also by the excellent
bias-dependent S-parameter fitting
f
over wide bias range.
Large-signal simulation also shows to be robust and the
model predicts very well the power and harmonic
performances. The model extrraction is fast and technologyindependent.
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