an angelov large signal model and its parameter …...curticemodel: in 1980, walter r. curtice first...

TSINGHUA UNIVERSITY

An Angelov Large Signal Model and its Parameter Extraction Strategy for GaAs HEMT

Yan Wang Wenyuan ZhangTsinghua University

OutlineMotivation

Large Signal Model

Parameter Extraction Strategy

Model verification

Conclusion

2

OutlineMotivation

Large Signal Model


Model verification

Conclusion

3

Device modeling is to find a suitable equivalentdescription of the transistor and accurate models playan important role in the success of IC design.

A good modelaccurate within a certain frequency rangeas simple as possibleThe parameters in the model should be easily extractedThe model should be able to reflect the temperature effectThe parameters should have clear physical meaning scalableThe model should have good convergence The model should ensure high-order derivative of the

expression , especially for the large signal model in order toaccurately predict harmonic components.

Motivation

4

A good model is a good trade off

OutlineMotivation

Large Signal Model


Model verification

Conclusion

5

the number of papers on the research of transistor modeling

You can find from the published papers that the number oftransistor modeling show a significant growing trend

Large Signal Model

6

numbers of research papers on different types of transistor modeling

HEMT Modeling had an obvious down times, but in recent years, with the advantagesof high electron mobility, high linearity and low noise, It has become a hot spot in theresearch of modeling. The modeling work in this talk will also aim at GaAs HEMT.

Large Signal Model

7

Statistics of research papers on HEMT large signal nonlinear modeling

Transistors will exhibit obvious nonlinear effects when working under large signalconditions. We can see that the number of articles related to nonlinear large signalaccounts for nearly half, and the proportion increases year by year

Large Signal Model

8

For RF and microwave applications, transistors often work inlarge signal states. The nonlinear behavior of transistors ismore important.

As early as eighty in the last century, the large signalempirical model of microwave devices was established.

Over the past thirty years, there have been many excellentlarge signal models, such as: Curtice Model Tajima Model Materka Model Statz Model TOM Model Angelov Model EEHEMT1 business Model

Large Signal Model

9

Curtice Model:In 1980, Walter R. Curtice first proposed an FET large signalempirical model and simulated it through Spice, which includethe drain current Ids、 gate capacitance Cgs and parasiticparameters, but the model does not take into account theprinciple of charge conservation.

Statz Model:In1987. A large signal transistor model is put forward by Statz,and considering the conservation of charge, a two dimensionalcapacitance model is established.The gate charge and drain charge are unified as gate charge,which is determined by gate voltage and drain voltage. Theprecision of the model is further improved.

Large Signal Model

These two models are proposed for MESFET, None of the models can bedirectly applied to HEMT Device

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Angelov model

In 1992, Sweden professor ( in Chalmers）Angelov put forwarda new large signal model, based on the empirical formula of theexponential function and the current-voltage relationship is ahyperbolic tangent function. This form is more applicable tolarge signal modeling of MESFET and HEMT.

Large Signal Model

From the first HEMT model to present，the most widely usedmodels are Curtice and Angelov Model and EEHEMT1 businessmodel. Many later scholars are based on these three models toconsider the improvement of thermal effect, frequency migrationeffect and charge conservation.

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Tajima ModelIn 1981, Tajima proposed the model applied to the frequencydomain, based on the model GaAs FET. A large signalmodel is established for DC characteristics of the device andwas successfully applied to the design of the oscillator.

Materka modelIn 1983, Materka proposed a simple large signal modelbased on DC characteristics. Four measuring parameterscan be applied to any size in theory.And it is convenient to be extended to computer aidedanalysis and design.

Large Signal Model

Later works have made many improvements to the previousmodels, such as 1990, Mccamant put forward TOM1 model,Statz model has been changed, and Ids are varied asoutside voltage. Considering the negative DC conductancecharacteristic, the proposed model can guarantee highprecision in the larger bias range.

In the business model, in 1993, Agilent established themodel EEHEMT1, which has a wide range of applications,but it is represented by a piecewise function. The inputoutput characteristics of different current output stages are indifferent modes.

Large Signal Model

In 1997, Dr. C.Wei of Alpha proposed a charge conservationmodel including the self heating effect and frequency migrationeffect. This model can predict the current voltage relations,charge –voltage relations and S parameters of differentfrequencies, more accurately.

Large Signal Model

15

Large Signal ModelTo sum up : the small signal equivalent circuit model of HEMT has been

developed relatively mature. How to establish a precisenonlinear model to improve the nonlinear performance of RF /microwave power circuits has always been a key and difficultpoint, especially the high order derivative is need to beguaranteed.

the input and output characteristics of HEMT are different underdifferent temperature environments. Self heating effect shouldbe considered.

the relatively complex extraction method is generally used, thedifference of the research mainly focus in the extraction of theembedded technology, the parasitic parameters, and thesimpleness of the extraction strategy.

Large Signal Model

Why Angelov model is chosen in this work? Accurate for HEMT

Simple although the extraction is a little bit complicated

High order continuous and derivative—— can be

used for harmonic analysis in the nonlinear

performance of RF / microwave circuits

Charge conservation is considered and the

convergence can be ensured.

16

Structure and band diagram of typical GaAs HEMT

Due to the wide band gap, the conduction band bends a lot in order to supplyenough electron, which leads to strong quantum effect.

Large Signal Model

17

Traditional small signal equivalent circuit model

Large Signal Model

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A schematic diagram of large signal equivalent model

Large Signal Model

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Angelov model——The Angelov model uses an exponentialfunction, and the relationship between the current and thevoltage is reflected by the hyperbolic tangent function. Thecurrent and capacitance of the Angelov model is as following

Proposed large signal equivalent circuit model

Large Signal Model

20

tanh( )

tanh( )6

(

10 )

g gd jg

bdg gd bdgd g jg

P V Vgd j

P V V P Vbdg

I I e

K e e

0 (1 tanh ) tanh( )(1 )d pk ds dsI I V V

(1 tanh )r s 21 2 3( ) ( ) ( )m gs pks gs pks gs pksP V V P V V P V V 2

1 1 1 2(1 / cosh ( ))m dsP P B B V

0 1 2(1 tanh )(1 tanh )gs gspi gsC C C

0 3 4(1 tanh )(1 tanh )gd gdpi gdC C C

1 10 11 gsP P V 2 20 21 dsP P V

3 30 31 dsP P V 4 40 41 gdP P V

tanh( )

tanh( )6

(

10 )

g gs jg

bdg gs bdgs g jg

P V Vgs j

P V V P Vbdg

I I e

K e e

Large Signal Model

21

OutlineMotivation

Large Signal Model


Model verification

Conclusion

22

Extract Rg, Rd, Rs, Lg, Ld, Ls• under cold FET condition (Ig=0, Id=0)• using the flat range for Rg, Rd, Rs at low frequency band• using the flat range for Lg, Ld, Ls at high frequency band

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS

Equivalent Circuit Model

1. Extract Rg, Rd, Rs• from cold FET

• at low frequency

2. Extract Lg, Ld, Ls• from cold FET

• at high frequency

Cold FET Extraction

G DRgLg Rd Ld

Rs LsS

Cold FET Equivalent Circuit Model

Cold FET


Extract Ij, Pg, Vjg• from Ig-Vgs• at forward Vgs• at zero Vds where Igs≈Igd ≈Ig/2

3. Extract Ij, Pg, Vjg• from Ig – Vgs

• at forward Vgs

4. Extract Kbdg, Pbdg,Vbdgs, Vbdgd

• from Ig – Vgs

• at reverse Vgs

5. Extract Ipk0, Vpks, P1• from Id – Vgs

7. Extract λ• from Id – Vds

8. Optimize B1, B2, αr, αs

• from Id – Vds

I – V Extraction

6. Optimize P2, P3• from Id – Vds

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS


tanh( )g gs jgP V Vgs jI I e

tanh( ) tanh( )6( 10 )g gs jg bdg gs bdgs g jgP V V P V V P Vgs j bdgI I e K e e

Vgs>0

linear range

ln lngs g gs g jg jI P V P V I

saturation range

, ,j g jgI P V

, , / gPj gs sat forI I e


Extract Kbdg, Pbdg, Vbdgs, Vbdgd• from Ig-Vgs• at reverse Vgs• introduce 0≤k≤1• assume Igs=kIg, Ids=(1-k)Ig• scan k to achieve the smallest error


• at forward Vgs


• from Ig – Vgs

• at reverse Vgs




• from Id – Vds

I – V Extraction


tanh( ) tanh( )6( 10 )g gs jg bdg gs bdgs g jgP V V P V V P Vgs j bdgI I e K e e

Vgs<0

linear range

6

ln | | | |

ln(10 )gs bdg gs bdg bdgs

bdg j

I P V P V

K I

saturation range

6, , | | /10 bdgP

bdg gs sat re jK I I e

, ,bdg bdg bdgsK P V

tanh(| | )6| | 10 bdg gs bdgsP V Vgs bdg jI K I e

gdI

bdgdV

in the same way

as left

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS



Extract Ipk0, Vpks, P1• from Id-Vgs• Ipk0, Vpks, P1 are found to be

Id, Vgs, gm/Id for maximum gm


• at forward Vgs


• from Ig – Vgs

• at reverse Vgs




• from Id – Vds

I – V Extraction


IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS


0 (1 tanh ) tanh( )(1 )d pk ds dsI I V V

0 (1 tanh )d pkI I

1

22

33

( )

( )

( )

m gs pks

gs pks

gs pks

P V V

P V V

P V V

1( )gs pksP V V

21 0 1

22 2

2 1 02

2

(1 tanh ) (1 tanh )

2 tanh (1 tanh )

0 tanh 0

dm pk d

gs

dm pk

gs

m

Ig PI PIV

Ig P IV

g


Optimize P2, P3• with targets of Id, gm, gm2, gm3

versus Vgs

Extract λ• from Id-Vds• λ is the slope at the saturation range

Optimize B1, B2, αr, αs• with targets of Id, Id’ versus Vds


• at forward Vgs


• from Ig – Vgs

• at reverse Vgs




• from Id – Vds

I – V Extraction


IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS



Extract Cgspi, Cgs0• from Cgs – Vgs

at zero Vdsand Cgs – Vdsat zero Vgs

• at a fixed frequency

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS

Equivalent Circuit Model9. Extract Cgspi, Cgs0

• from Cgs – Vgs at zero Vds

and Cgs – Vds at zero Vgs


10. Extract Cgdpi, Cgd0• from Cgd – Vgs at zero Vds

and Cgd – Vds at zero Vgs


11. Extract Cds• from Cds – Vgs

• at zero Vds and low Vgs


12. Extract P10, P11• from Cgs – Vgs

• at zero Vds


13. Extract P40, P41• from Cgd – Vgs

• at zero Vds


14. Extract P20, P21• from Cgs – Vds

• at zero Vgs


15. Extract P30, P31• from Cgd – Vds

• at zero Vgs


C – V Extraction

16. Optimize Rgs, Rgd• from Rgs,eq and Rgd,eq

– frequency

0 1 2

0 10 11 20

0

(at zero )

(1 tanh )(1 tanh )

(1 tanh( ))(1 tanh )

( , 2 )

gs gspi gs

gspi gs gs

gspi gspi s

ds

g

C C C

C C P P V P

C C

V

C

0 0min{min ( ) | , min ( ) | }ds gsgspi gs gs V gs ds VC C V C V

0 0 0max ( ) | min ( ) |ds dsgs gs gs V gs gs VC C V C V

1 10 11 gsP P V 2 20 21

20(at zero )s

ds

dVP P V

P


Extract Cgdpi, Cgd0• from Cgd – Vgs

at zero Vdsand Cgd – Vdsat zero Vgs

• at a fixedfrequency

0 3 4

0 30 40 41

0

(at zero )

(1 tanh )(1 tanh )

(1 tanh )(1 tanh( ))

( , 2 )

gd gdpi gd

gdpi gd gs

gdpi gdpi d

ds

g

C C C

C C P P P V

C C

V

C

0 0min{min ( ) | , min ( ) | }ds gsgdpi gd gs V gd ds VC C V C V

0 0 0max ( ) | min ( ) |ds dsgs gd gs V gd gs VC C V C V

4 40 41

40 41(at zero )d

gd

gss

P P V

P VV P

3 30 31

30(at zero )s

ds

dVP P V

P

9. Extract Cgspi, Cgs0• from Cgs – Vgs at zero Vds










• at zero Vds



• at zero Vds



• at zero Vgs



• at zero Vgs


C – V Extraction


– frequency

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS



Extract Cds

• from Cds-Vgs• at zero Vds• at a fixed frequency• using the flat range

for Cds at small Vgs

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS












• at zero Vds



• at zero Vds



• at zero Vgs



• at zero Vgs


C – V Extraction


– frequency


Extract P10, P11• from Cgs-Vgs• at zero Vds• at a fixed frequency• linear regression:

Extract P20, P21• from Cgs-Vds• at zero Vgs• at a fixed frequency• linear regression:

IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS












• at zero Vds



• at zero Vds



• at zero Vgs



• at zero Vgs


C – V Extraction


– frequency

10 11 10tanh (( ) / 1)gs gspi gs gsC C C P V P

121 20

0 10

tanh 1(1 tanh )gs gspi

dsgs

C CP V P

C P


IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS












• at zero Vds



• at zero Vds



• at zero Vgs



• at zero Vgs


C – V Extraction


– frequency

Extract P40, P41• from Cgd-Vgs• at zero Vds• at a fixed frequency• linear regression:

Extract P30, P31• from Cgd-Vds• at zero Vgs• at a fixed frequency• linear regression:

10 41 40tanh (( ) / 1)gd gdpi gd gsC C C P V P

131 30

0 40 41

tanh 1(1 tanh( ))

gd gdpids

gd ds

C CP V P

C P P V


IgdG D

RgLg Rd LdRgd

Rgs

Cgd

Cgs

Igs Id Cds

Rs LsS












• at zero Vds



• at zero Vds



• at zero Vgs



• at zero Vgs


C – V Extraction


– frequency

Optimize Rgs, Rgd

• with targets:

versus frequency

1, 11 12Re(( ) )gs eqR Y Y

1, 12Re(( ) )gd eqR Y


OutlineMotivation

Large Signal Model


Model verification

Conclusion

34

HEMTs of six different sizes (finger number × finger width = 2×20μm, 4×20μm,6×20μm, 8×20μm, 4×15μm, 4×25μm) are fabricated in 70nm GaAs technology andmeasured in extensive ways to evaluate the proposed model along with its parameterextraction. S-parameters are measured up to 67GHz. Large signal performancesincluding power gain and power added efficiency (PAE) are also evaluated bymeasurements at 30GHz.

Model verification

35

Measured and modeled RF small signal characteristics

Model verification

36

Model verification

37

Measured and modeled RF large signal characteristics: (a) output power, (b) powergain, (c) PAE versus input power at 30GHz

Model verification

38

OutlineMotivation

Large Signal Model


Model verification

Conclusion

39

Conclusion

An Angelov large signal model and its parameterextraction strategy for GaAs HEMT are established.The model is composed of a unified equivalent circuitmodel and a set of analytical formulas.All the key parameters are taken directly frommeasurements step by step.The above work is validated by extensivemeasurements with good accuracy and cancontributes to GaAs HEMT millimeter-wave circuit andsystem design.Heat effect modeling is our next emphasis.

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Thanks for your attention!

an angelov large signal model and its parameter …...curticemodel: in 1980, walter r. curtice first...

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