Modeling Intermodulation Distortion in
HEMT and LDMOS Devices Using a New
Empirical Non-Linear Compact Model
Toufik Sadi and Frank Schwierz
Department of Solid-State Electronics,
Technische Universität Ilmenau,
D-98684 Ilmenau, Germany
Toufik.Sadi@tu-ilmenau.de
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Outline
 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
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Compact Modeling of III-V HEMTs
 Framework: Within the COMON (COmpact MOdelling
Network) project funded by the European Union
Aim: 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..
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Motivation
Non-linear HEMT Models
 Design of modern microwave circuits and systems
 Minimization of Intermodulation Distortion
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
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Non-Linearities in Electron Devices
Almost everything in semiconductor electronics is nonlinear !!!
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
Linear output
V  V cos(t )
15
1
GS
I (t )  K V  K V
d
1
K V
3
GS
GS
3
2
K V
4
GS
GS
4
2

30
5
20
0
-5
-10
K V
5
10
Output (a.u.)
I (t )  K V
d
40
Output Signal
P
Drain current (a.u.)
GS
Non-linear output
5
-15
0.0
GS
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
10
0
-10
0.5
1.0
Time
1.5
2.0
-20
0.0
0.5
1.0
Time
1.5
2.0
Intermodulation in HEMTs
Two-tone Input
Input with two frequency components f1 and f2
Vin  t   V1  t   V2  t   A1 cos 1 t  A2 cos 2 t
Example: 3rd order transfer characteristics
Vout  t   0 : DC
th
st
1 : f1 , f 2
2 : 2 f1 , 2 f 2 , (f1  f 2 ), ( f1  f 2 )
nd
3 : 3 f1 , 3 f 2 , (2f1  f 2 ), (2 f1  f 2 ),
rd
(2f 2  f1 ), ( 2 f 2  f1 )
Signal (Intermodulation ) components at new
frequencies are generated
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
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Angelov et al, IEEE Trans. MTT,
vol. 40, p. 2258, 1992
Chalmers Model for HEMTs – Limitations
I D  I PK [1  tanh{ (VGS )}] tanh(VDS )(1  VDS )
Angelov et al,
IEEE Trans. MTT,
vol. 40, p. 2258,
1992
n
 (VGS )   Pn (VGS  VPK ) i
i 1
I PK  Drain current at gm
max
(at VGS  VPK )
P  gm / I
1
max
PK
 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 2IPK
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
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
New Current-Voltage Model (1)
I  [ F (VGS )  F (VGS )  ] tanh(VDS )(1  VDS )
f(VGS)
f(VDS)
F (VGS )   I PK (1  tanh{ f (VGS )  })  VGS  VPK  0
F (VGS )   ( I SAT  I PK ) tanh{ f (VGS )  }  VGS  VPK  0




f (VGS )   EC ln(1  exp{g (VGS ) / EC })




f (VGS )  EC ln(1  exp{g (VGS ) / EC })
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
New Current-Voltage Model (2)
n
g (VGS )    Pn {h(VGS ) }i
i 1

g (VGS ) 
I PK
I SAT  I PK
n
P {h(V

i 1
n
 i
GS
) }.


2


2
 2
 2
 2
 2
 2
 2
h (VGS )  VGSN  (VGSN  VTN 1 )  VTN 2  VTN 1  VTN 2
h (VGS )  VGSP  (VGSP  VTN 1 )  VTN 2  VTN 1  VTN 2
VGSP  VGSN  VGS  VPK
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
New Current-Voltage Model (3)
ISAT: IMAX = 2IPK
EC: more flexibility for
VTN: fine-tuning
I-V curves & derivatives
parameters
Fager et al., IEEE MTT, p. 2834, 2002
MOS-AK/GSA Workshop Paris -
7th
&
8th
April 2011
I-V Model Advantages
 Continuous – closed-form expression
Accurate modeling of I-V characteristics and derivatives
GaN HEMT (Cabral et al., MTTS 2004)
LDMOS FET (Fager et al., IEEE MTT, p. 2834, 2002)
 Simple parameter extraction & fitting procedure
Applicable to GaAs, GaN HEMTs; LDMOS FETs;
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
I-V Curves
Pulsed (300K)
Static DC
0.25m gate-length GaAs pHEMT [1]
VGS : -1.2V to -0.4V — Step = 0.1V
0.35m gate length GaN HEMT [2]
VGS : -4V to 0V — Step = 1V
[1] K. Koh et al, in Proc. IEEE IMS, p. 467, 2003
[2] J.-W. Lee et al, IEEE Trans. MTT, vol. 52, p. 2, 2004
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
LDMOS FET from [3]
VGS : 3 and 5V
[3] C. Fager et al, IEEE Trans. MTT, vol. 50, p. 2834, 2002
Volterra Series Analysis
Modeling the contribution of the current source to non-linearities
Two-tone excitation input – Vin  Vs
cos( t )  cos( t ) 
1
2
Results are from the GaAs pHEMT *
Pin = -20dBm, RL = RS = 50 Ohm
*K. Koh et al, in Proc. IEEE IMS, p. 467, 2003
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011
Plin, PIM2, PIM3: linear, 2nd and 3rd order power
IP2, IP3: 2nd and 3rd order interception points
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
Acknowledgments
This work is funded by the European Union, in the
framework of the COMON project.
MOS-AK/GSA Workshop Paris - 7th & 8th April 2011