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Modeling Intermodulation Distortion in HEMT and LDMOS Devices Using a New Empirical Non-Linear Compact 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. [email protected] de MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Outline v Objectives v Motivation v Non-linearities in semiconductor devices v Non-linear FET models Outline v Objectives v Motivation v Non-linearities in semiconductor devices v Non-linear FET models v Compact modeling of III-V HEMTs and LDMOSFETs ü Motivation ü New in-house model ü Validation v Summary MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Compact Modeling of III-V HEMTs ü Framework: Within the COMON (COmpact MOdelling Network) project Compact Modeling of III-V HEMTs ü Framework: Within the COMON (COmpact MOdelling Network) project funded by the European Union üAim: Development of improved universal HEMT models ü Objectives: Ø Efficient current-voltage, charge and noise models Ø Ga. As, Ga. N HEMTs and other high-power devices ü Focus: Non-Linearities in HEMTs Ø Intermodulation distortion (IMD) üIncluded Effects: ØSelf-heating; frequency dispersion; etc. . MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Motivation Non-linear HEMT Models v Design of modern microwave circuits and systems Ø Minimization Motivation Non-linear HEMT Models v Design of modern microwave circuits and systems Ø Minimization of Intermodulation Distortion Current-Voltage (I-V) Model v Accurate modeling of I-V characteristics and derivatives Ø Inclusion of electrothermal & frequency dispersion effects Ø Applicable to Ga. As and Ga. N HEMTs, and to Si LDMOS FETs Ø Effective parameter extraction and fitting routines Ø Modeling of IMD figures of merit using Volterra series analysis Charge (C-V) Model v Correct modeling of C-V characteristics is sufficient Ø Using simple/existing models MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

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

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

Compact Models for III-V FETs v Physics-based þ Analysis of effect of physical parameters Compact Models for III-V FETs v Physics-based þ Analysis of effect of physical parameters (gate length, mobility, etc…) þ No parameter optimization ý Rigorous mathematical formula ý Technology-dependent ý Discontinuous (using of conditional functions) v Table-based Storing parameters at several biases in a table þ No parameter optimization þ Technology-dependent ý Discontinuities in the model elements or their derivatives v Empirical þ Simple þ Flexible þ Continuous þ Technology-independent ý Good model formulation ý Parameter optimization MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

Non-Linear Empirical III-V FET Models v Curtice Model (1980) Quadratic/cubic dependence of ID on Non-Linear Empirical III-V FET Models v Curtice Model (1980) Quadratic/cubic dependence of ID on VGS Ø First empirical time-domain simulation model v Tajima Model (1981) Exponential dependence of ID on VDS and VGS Ø First empirical frequency-domain simulation model v Materka Model (1985) Quadratic/hyperbolic dependence of ID on VGS Ø Including drain-bias dependent pinch-off potential v Statz Model (1987) Hyperbolic/cubic dependence of ID on VGS/VDS Ø Temperature scalability v TOM Model(s) (1990) Exponential/cubic dependence of ID on VGS/VDS Ø Spatial/temperature scalability v ADS EEFET/EEHEMT Model(s) (1993) Rigorous formula Ø Charge-based C-V model v Chalmers Model (1992) Hyperbolic dependence of ID on VGS/VDS Ø First to provide a good fit for transconductance and derivatives v 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 v Infinitely differentiable hyperbolic functions v Inherent reconstruction Chalmers Model for HEMTs – Advantages v Infinitely differentiable hyperbolic functions v Inherent reconstruction of the bell-shape of Gm(VGS) for Ga. As HEMTs v Reliable modeling of the higher order derivatives of Gm(VGS) curves v Continuity – no conditional functions v Possibility of readily including several effects, such as temperature effects, frequency dispersion, and soft-breakdown v Simple procedure for parameter extraction Suitability for intermodulation distortion studies MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011 Angelov et al, IEEE Trans. MTT, vol. 40, p. 2258, 1992

Chalmers Model for HEMTs – Limitations Angelov et al, IEEE Trans. MTT, vol. 40, Chalmers Model for HEMTs – Limitations Angelov et al, IEEE Trans. MTT, vol. 40, p. 2258, 1992 v Limited suitability to model high-power devices and new structures such as Ga. N HEMTs and LDMOSFETs (Fager et al. , IEEE MTT, p. 2834, 2002; Cabral et al. , MTTS 2004) v 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 MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

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

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

I-V Model Advantages ü Continuous – closed-form expression üAccurate modeling of I-V characteristics and I-V Model Advantages ü Continuous – closed-form expression üAccurate modeling of I-V characteristics and derivatives Ga. N HEMT (Cabral et al. , MTTS 2004) LDMOS FET (Fager et al. , IEEE MTT, p. 2834, 2002) ü Simple parameter extraction & fitting procedure üApplicable to Ga. As, Ga. N HEMTs; LDMOS FETs; MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011

I-V Curves Pulsed (300 K) Static DC 0. 25 m gate-length Ga. As p. I-V Curves Pulsed (300 K) Static DC 0. 25 m gate-length Ga. As p. HEMT [1] VGS : -1. 2 V to -0. 4 V — Step = 0. 1 V 0. 35 m gate length Ga. N HEMT [2] VGS : -4 V to 0 V — Step = 1 V [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 - 7 th & 8 th April 2011 LDMOS FET from [3] VGS : 3 and 5 V [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 Volterra Series Analysis Modeling the contribution of the current source to non-linearities Two-tone excitation input – Results are from the Ga. As p. HEMT * Pin = -20 d. Bm, RL = RS = 50 Ohm *K. Koh et al, in Proc. IEEE IMS, p. 467, 2003 MOS-AK/GSA Workshop Paris - 7 th & 8 th April 2011 Plin, PIM 2, PIM 3: linear, 2 nd and 3 rd order power IP 2, IP 3: 2 nd and 3 rd order interception points

Accomplished Work (5) IMD analysis in high-power Ga. N HEMTs and LDMOSFETs Ga. N Accomplished Work (5) IMD analysis in high-power Ga. N HEMTs and LDMOSFETs Ga. N 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 v New flexible empirical non-linear model v Minimized parameter fitting v Accurate calculation Conclusions v New flexible empirical non-linear model v Minimized parameter fitting v Accurate calculation of higher-order derivatives v Suitable for intermodulation distortion modeling v 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