Modeling Intermodulation Distortion in HEMT and LDMOS Devices Using a New Empirical Non-Linear Compact Model
Toufik Sadi and Frank SchwierzDepartment of Solid-State Electronics,
Technische Universität Ilmenau, D-98684 Ilmenau, Germany
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Objectives Motivation Non-linearities in semiconductor devices Non-linear FET models Compact modeling of III-V HEMTs and LDMOSFETs
Motivation New in-house model Validation
Summary
Outline
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Framework: Within the COMON (COmpact MOdelling Network) project funded by the European UnionAim: Development of improved universal HEMT models Objectives:
Efficient current-voltage, charge and noise models GaAs, GaN HEMTs and other high-power devices
Focus: Non-Linearities in HEMTs Intermodulation distortion (IMD)
Included Effects: Self-heating; frequency dispersion; etc..
Compact Modeling of III-V HEMTs
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Current-Voltage (I-V) Model Accurate modeling of I-V characteristics and derivatives
Inclusion of electrothermal & frequency dispersion effects Applicable to GaAs and GaN HEMTs, and to Si LDMOS FETs Effective parameter extraction and fitting routines Modeling of IMD figures of merit using Volterra series analysis
Charge (C-V) Model Correct modeling of C-V characteristics is sufficient
Using simple/existing models
Non-linear HEMT Models Design of modern microwave circuits and systems
Minimization of Intermodulation Distortion
Motivation
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Non-Linearities in Electron Devices
Non-linear I-V characteristics Distortion of the output signal shape New frequency components appear
2nd order: 2xf 3rd order: 2xf, 3xf nth order: 2xf, 3xf,…,nxf
0.0 0.5 1.0 1.5 2.0-15
-10
-5
0
5
10
15
Dra
in c
urre
nt (a
.u.)
Time
0.0 0.5 1.0 1.5 2.0-20
-10
0
10
20
30
40
Out
put (
a.u.
)
Time
Output Signal
Linear output Non-linear output
Almost everything in semiconductor electronics is nonlinear !!!
cos( )GS PV V t
1( )
d GSI t K V
2
1 2
3 4 5
3 4 5
( )
d GS GS
GS GS GS
I t K V K V
K V K V K V
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Intermodulation in HEMTs
Two-tone Input Input with two frequency components f1 and f2
Signal (Intermodulation ) components at new frequencies are generated
1 2 1 1 2 2
cos cos inV t V t V t A t A t
Example: 3rd order transfer characteristics
1 2 1 2
1 2 1 2
2
1 2
1 2
1 2
th
st
nd
1
rd
0 :
1 :
2 :
( ), ( )
(2 ), (2 ),
3 :
,
2 , 2 ,
(2 ), (
3 , 3 ,
2
out
f f
DC
f f
f f
f f
V
f f
f f f f
f
t
f
2 1)
f f
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Compact Models for III-V FETs
Physics-based Analysis of effect of physical parameters (gate length, mobility, etc…) No parameter optimization Rigorous mathematical formula Technology-dependent Discontinuous (using of conditional functions)
Table-based Storing parameters at several biases in a table No parameter optimization Technology-dependent Discontinuities in the model elements or their derivatives
Empirical Simple Flexible Continuous Technology-independent Good model formulation Parameter optimization
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Non-Linear Empirical III-V FET Models
Curtice Model (1980) Quadratic/cubic dependence of ID on VGS
First empirical time-domain simulation model Tajima Model (1981) Exponential dependence of ID on VDS and VGS
First empirical frequency-domain simulation model Materka Model (1985) Quadratic/hyperbolic dependence of ID on VGS
Including drain-bias dependent pinch-off potential Statz Model (1987) Hyperbolic/cubic dependence of ID on VGS/VDS
Temperature scalability TOM Model(s) (1990) Exponential/cubic dependence of ID on VGS/VDS
Spatial/temperature scalability ADS EEFET/EEHEMT Model(s) (1993) Rigorous formula
Charge-based C-V model Chalmers Model (1992) Hyperbolic dependence of ID on VGS/VDS
First to provide a good fit for transconductance and derivatives Auriga Model (2004) Enhanced version of the Chalmers model
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Chalmers Model for HEMTs – Advantages
Infinitely differentiable hyperbolic functions Inherent reconstruction of the bell-shape of Gm(VGS) for GaAs HEMTs
Reliable modeling of the higher order derivatives of Gm(VGS) curves
Continuity – no conditional functions Possibility of readily including several effects, such as temperature effects, frequency dispersion, and soft-breakdown Simple procedure for parameter extraction
Suitability for intermodulation distortion studies Angelov et al, IEEE Trans. MTT, vol. 40, p. 2258, 1992
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Chalmers Model for HEMTs – Limitations
max 1 max
1
Drain current at (at ) /
(
[1 tanh{ ( )}] tanh( )(
1
) ( )
)
PKPK GS PK
ni
GS n GS PK
D PK GS DS DS
i
gm gm II V V P
V P V
I I V V V
V
Limited suitability to model high-power devices and new structures such as GaN HEMTs and LDMOSFETs (Fager et al., IEEE MTT, p. 2834, 2002; Cabral et al., MTTS 2004)
Saturation current (ISAT) is limited to 2 IPK
Improved model to provide much more independent control of the shape of the current and transconductance curves while maintaining the principal advantages of the Chalmers model
Angelov et al, IEEE Trans. MTT, vol. 40, p. 2258, 1992
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
New Current-Voltage Model (1)
( )
( )
( ) (1 tanh
ln(1 exp{ ( ) / })
ln(1 exp{
{ ( ) }) 0
( ) ( tanh{ ( ) }
( / )
0
) }
)
[ ( ) ( ) ] tanh( )(1 )
GS PK
GS P
GS GS
GS G
K
S
GS PK GS
GS PK GSSAT
GS GS DS DS
f V V
f V V
V V
V V
F V I f V
EC g EC
EC g EC
F V I I f V
I F V F V V V
f(VGS) f(VDS)
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
New Current-Voltage Model (2)
1 2 1 2
1 2 1 2
2 2 2 2
2 2 2 2
1
1
( )
( )
( ) (
( ) (
{
{ .
( )
( )
) }
) }PK
SAT PK
TN TN TN TN
TN TN TN TN
GS n GS
GS n GS
GSN GS P
GS
GS
K
ni
i
ni
GSP
GSN GSN
G S
i
SP G P
I
I I
h V V V
h V V V
V
g V P h V
g V P h
V
V
V V
V V V V
V V V V
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
New Current-Voltage Model (3)EC: more flexibility for I-V curves & derivativesISAT: IMAX = 2 IPK
VTN: fine-tuning parameters
Fager et al., IEEE MTT, p. 2834, 2002MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
I-V Model Advantages
Continuous – closed-form expression Accurate modeling of I-V characteristics and derivatives
Simple parameter extraction & fitting procedureApplicable to GaAs, GaN HEMTs; LDMOS FETs;
LDMOS FET (Fager et al., IEEE MTT, p. 2834, 2002)GaN HEMT (Cabral et al., MTTS 2004)
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
I-V Curves
0.25m gate-length GaAs pHEMT [1]
[1] K. Koh et al, in Proc. IEEE IMS, p. 467, 2003 [3] C. Fager et al, IEEE Trans. MTT, vol. 50, p. 2834, 2002 [2] J.-W. Lee et al, IEEE Trans. MTT, vol. 52, p. 2, 2004
VGS : -1.2V to -0.4V — Step = 0.1V0.35m gate length GaN HEMT [2]
VGS : -4V to 0V — Step = 1VLDMOS FET from [3]
VGS : 3 and 5V
Pulsed (300K)
Static DC
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Volterra Series Analysis
Two-tone excitation input – 1 2
cos( ) cos( )Vin Vs t t
Results are from the GaAs pHEMT *
*K. Koh et al, in Proc. IEEE IMS, p. 467, 2003
Pin = -20dBm, RL = RS = 50 OhmPlin, PIM2, PIM3: linear, 2nd and 3rd order powerIP2, IP3: 2nd and 3rd order interception points
Modeling the contribution of the current source to non-linearities
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Accomplished Work (5) IMD analysis in high-power GaN HEMTs and LDMOSFETs
GaN HEMT (Cabral et al., MTTS 2004)
LDMOS FET (Fager et al., IEEE MTT, p. 2834, 2002)
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Conclusions
New flexible empirical non-linear model Minimized parameter fitting Accurate calculation of higher-order derivatives Suitable for intermodulation distortion modeling Applicable to a wide range of devices
AcknowledgmentsThis work is funded by the European Union, in the framework of the COMON project.
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011