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 Ilmenau, Germany MOS-AK/GSA Workshop Paris - 7 th & 8 th 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 - 7 th & 8 th April 2011

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.. Compact Modeling of III-V HEMTs MOS-AK/GSA Workshop Paris - 7 th & 8 th 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 - 7 th & 8 th April 2011

Non-Linearities in Electron Devices Non-linear I-V characteristics  Distortion of the output signal shape  New frequency components appear 2 nd order: 2xf 3 rd order: 2xf, 3xf n th order: 2xf, 3xf,…,nxf Linear output Non-linear output Almost everything in semiconductor electronics is nonlinear !!! MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Intermodulation in HEMTs Two-tone Input Input with two frequency components f 1 and f 2 Signal (Intermodulation ) components at new frequencies are generated Example: 3 rd order transfer characteristics MOS-AK/GSA Workshop Paris - 7 th & 8 th 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 - 7 th & 8 th April 2011

Non-Linear Empirical III-V FET Models  Curtice Model (1980)  Quadratic/cubic dependence of I D on V GS  First empirical time-domain simulation model  Tajima Model (1981)  Exponential dependence of I D on V DS and V GS  First empirical frequency-domain simulation model  Materka Model (1985)  Quadratic/hyperbolic dependence of I D on V GS  Including drain-bias dependent pinch-off potential  Statz Model (1987)  Hyperbolic/cubic dependence of I D on V GS /V DS  Temperature scalability  TOM Model(s) (1990)  Exponential/cubic dependence of I D on V GS /V DS  Spatial/temperature scalability  ADS EEFET/EEHEMT Model(s) (1993)  Rigorous formula  Charge-based C-V model  Chalmers Model (1992)  Hyperbolic dependence of I D on V GS /V DS  First to provide a good fit for transconductance and derivatives  Auriga Model (2004)  Enhanced version of the Chalmers model MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Chalmers Model for HEMTs – Advantages  Infinitely differentiable hyperbolic functions  Inherent reconstruction of the bell-shape of G m (V GS ) for GaAs HEMTs  Reliable modeling of the higher order derivatives of G m (V GS ) 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 - 7 th & 8 th April 2011

Chalmers Model for HEMTs – Limitations  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 (I SAT ) is limited to 2 I PK 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 - 7 th & 8 th April 2011

New Current-Voltage Model (1) f (VGS) f( VDS) MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

New Current-Voltage Model (2) MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

New Current-Voltage Model (3) EC: more flexibility for I-V curves & derivatives I SAT : I MAX = 2 I PK VTN: fine-tuning parameters Fager et al., IEEE MTT, p. 2834, 2002 MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

I-V Model Advantages Continuous – closed-form expression Accurate modeling of I-V characteristics and derivatives Simple parameter extraction & fitting procedure Applicable 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 - 7 th & 8 th April 2011

I-V Curves 0.25  m 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 V GS : -1.2V to -0.4V — Step = 0.1V 0.35  m gate length GaN HEMT [2] V GS : -4V to 0V — Step = 1V LDMOS FET from [3] V GS : 3 and 5V Pulsed (300K) Static DC MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Volterra Series Analysis Two-tone excitation input – Results are from the GaAs pHEMT * *K. Koh et al, in Proc. IEEE IMS, p. 467, 2003 P in = -20dBm, R L = R S = 50 Ohm Plin, PIM2, PIM3: linear, 2 nd and 3 rd order power IP2, IP3: 2 nd and 3 rd order interception points Modeling the contribution of the current source to non-linearities MOS-AK/GSA Workshop Paris - 7 th & 8 th 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 - 7 th & 8 th 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 - 7 th & 8 th April 2011