p11 Sadi Mos-Ak Paris 2

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Modeling Intermodulation Distortion in

HEMT and LDMOS Devices Using a NewEmpirical Non-Linear Compact Model

Toufik Sadi and Frank SchwierzDepartment of Solid-State Electronics,

Technische Universitt Ilmenau,

D-98684 Ilmenau, Germany

[email protected]

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


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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



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Framework: Within the COMON (COmpact MOdellingNetwork) 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



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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 systemsMinimization of Intermodulation Distortion

Motivation



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Non-Linearities in Electron Devices

Non -l inear I-V characteris t ics Distortion of the output signal shape

New frequency components appear

2nd order: 2xf

3rd order: 2xf, 3xf

nthorder: 2xf, 3xf,,nxf

0.0 0.5 1.0 1.5 2.0-15

-10

-5

0

5

10

15

Draincurren

t(a.u.)

Time

0.0 0.5 1.0 1.5 2.0-20

-10

0

10

20

30

40

Output(a.u.)

Time

Output Signal

Linear output Non-linear output

Almost everything in semiconductor electronics is nonlinear !!!

cos( )GS P

V 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



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Intermodulation in HEMTs

Two-tone Input

Input with two frequency components f1and f2

Signal (Intermodu lat ion ) compon ents at new

frequencies are generated

1 2 1 1 2 2

cos cosin

V 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



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Compact Models for III-V FETs

Physics-based

Analysis of effect of physical parameters (gate length, mobility, etc)No parameter optimizationRigorous mathematical formulaTechnology-dependentDiscontinuous (using of conditional functions)

Table-basedStoring parameters at several biases in a tableNo parameter optimizationTechnology-dependentDiscontinuities in the model elements or their derivatives

EmpiricalSimple

FlexibleContinuousTechnology-independentGood model formulation

Parameter optimization



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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/VDSTemperature 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 modelMOS-AK/GSA Workshop Paris - 7th & 8th April 2011


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Chalmers Model for HEMTs Advantages

Infinitely differentiable hyperbolic functions

Inherent reconstruction of the bell-shape ofGm(VGS) for GaAs HEMTs

Reliable modeling of the higher order

derivatives ofGm(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, 1992MOS-AK/GSA Workshop Paris - 7th & 8th April 2011


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Chalmers Model for HEMTs Limitations

max 1 max

1

Drain current at (at ) /

(

[1 tanh{ ( )}] tanh( )(

1

) ( )

)

PKPK GS PK

n i

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 2IPK

Improved model to provide much moreindependent 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



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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 GS SAT

GS GS DS DS

f V Vf V V

V VV V

F V I f V

EC g ECEC g EC

F V I I f V

I F V F V V V

f(VGS) f(VDS)



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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



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EC:more flexibility forI-Vcurves & derivatives

ISAT:IMAX=2IPKVTN:fine-tuning

parameters

Fager et al., IEEE MTT, p. 2834, 2002MOS-AK/GSA Workshop Paris - 7th & 8th April 2011


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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)



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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 = 0.1V

0.35m gate length GaN HEMT[2]

VGS : -4V to 0V Step = 1V

LDMOS FET from[3]

VGS : 3 and 5V

Pulsed (300K)

Static DC



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Volterra Series Analysis

Two-tone excitation input

1 2cos( ) 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 Ohm

Plin, PIM2, PIM3: linear, 2ndand 3rdorder power

IP2, IP3: 2ndand 3rdorder interception points

Modeling the contribution of the current source to non-linearities



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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)



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Conclusions

New flexible empirical non-linear modelMinimized 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

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