Equivalent Circuit MESFET/HEMT Modelling Approaches · 2011. 3. 14. · Equivalent Circuit MESFET/HEMT Modelling Approaches Angel Mediavilla, Tomás Fernandez, J.A. García Antonio

Equivalent Circuit MESFET/HEMT Modelling Approaches

Angel Mediavilla, Tomás Fernandez, J.A. García

Antonio Tazón, F. Marante*

Dpto. Ingeniería de Comunicaciones

ETSII de Telecomunicación

Universidad de CANTABRIA

* Dpto. Telecomunicaciones – ISPJAE- La Habana

UNICAN

2

Modelización MESFET/HEMT

UNICANBRNO- march 2011

Presenter Contact Data

Angel Mediavilla

Dpto. Ingeniería de Comunicaciones

ETSII de Telecomunicación

Universidad de Cantabria

Av. Los Castros s/n

39005 – Santander – Cantabria – Spain

Phone: +34-942-201490 Fax: +34-942-201488

Mail: [email protected]

Web: http://www.unican.es

Was born in Santander, Spain, in 1955. He graduated in 1978 and received the Doctor of Physics (Electronic) degree with honours in 1983, both from the University of Cantabria, Santander, Spain.

From 1980 to 1983 he was Ingenieur Stagiere at THOMSON-CSF, France. He is currently professor at the Department of Communications Engineering at the University of Cantabria. He has a wide experience in the analysis and optimization of nonlinear microwave active devices in both hybrid and monolithic technologies. He is currently working in the area of nonlinear MESFET/HEMT and HBT device modelling with special application to the large signal computer design and intermodulation properties

A. MEDIAVILLA

3



Outline

Brief Introduction

- Physics of the device

- Physical meaning of the EECM

- Extraction techniques

- Analytical equations

- Temperature description

- Intermodulation Properties

- Conclusions

4



S G D

N+ GaAs

N Channel

Undopped Buffer

Semi Insulating GaAs

S G D

N+ GaAs

N AlGaAs

Undopped Buffer

Semi Insulating GaAs 2Deg AlGaAs

Active Region Ohmic Contact

MESFETMESFET HEMTHEMT

GaAsFETDevices

GaAsFETDevices

due to the 2Deg layer:- Superior mobility- Higher frequency- Lower noise figureIf GaN: higher Power density

MESFET / HEMT DevicesMESFET / HEMT Devices

5



S G D

N+ GaAs

N AlGaAs

Undoped GaAs Buffer

Semi Insulating GaAs 2Deg AlGaAs

HEMTHEMT

Simplified operation for HEMT DevicesSimplified operation for HEMT Devices

� A wide-bandgap material N AlGaAs lies on a undopednarrow-bandgap material GaAs.

� Thickness and Doping density of N AlGaAs chosen forabsence of free electrons under normal operation.

� Sharp dip in Ec occurs in the boundary: High carrierconcentration in this region (2Deg), and do not encounterdonnor atoms: high mobility

� Current flows through the electron gaz controlled by Vgs.As Vds increases, current saturates.

� As Vgs is more positive, sheet carrier density tends todecrease and current tends to saturateG

SchottkyGate

NAlGaAs

undopedGaAs

Ec

Ef

Ev2Deg

region

Band Diagram

6



Physical Meaning of the Equivalent Circuit ModelPhysical Meaning of the Equivalent Circuit Model

Rs

S G D

Rd

R g

Cgs

CgdRi

Cds

Ids,τ

Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

CdsIds,τ

Ri

Parasitic Inductances Lg, Ld, Ls:- due to metal contact pads- Lg, Ld between 5 to 20pH- Ls is lower: 1pH

Parasitic Resistances Rg, Rd, Rs:-Rd, Rs: ohmic contacts < 1 ohm-Rg: metalization resistance < 1 ohm

Intrinsic Resistance Ri:-Questionable physical meaning-Introduced to improve S11

Vds

Vgs

Ids(Vgs,Vds,τ)

7



Physical Meaning of the Equivalent Circuit ModelPhysical Meaning of the Equivalent Circuit Model

Rs

S G D

Rd

R g

Cgs

Cgd

Ri

Cds

Ids,τ

Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

CdsIds,τ

Ri

Intrinsic Capacitances Cgs,Cgd,Cds:- Cgs,Cgd: depletion charge- Cds: geometrical capacitance D-S - Cgs: 1pF/mm, Cgd&Cds 1/10 Cgs

Intrinsic Current Source Ids:- reproduces I/V curves- will reproduce the Gm and Gds values

Transconductande delay ττττ :-Current does not respond instantaneously tochanges in Gate voltage.- Order of 1ps. Increases with Gate length

Vds

Vgs

Ids[Vgs(t- τ),Vds]

8



Dependence on the Bias Point (NL elemens)Dependence on the Bias Point (NL elemens)

Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

CdsIds,τ

Ri

Vds

Vgs

Ids[Vgs(t- τ),Vds]

Main Nonlinear Elements:

- Ids : Obviously I/V curves

- Cgs and Cgd depend on the bias becausethe depletion region changes with the bias

Secondary Nonlinear Elements:

- Parasitic resistors

- Cds geometrical capacitance

- Transconductance delay ττττ

9



Small Signal Equivalent Circuit for a given Bias PointSmall Signal Equivalent Circuit for a given Bias Point

Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

Cd

s

Gm

e-j

ωτ.V

gs

Ri

Vds

Vgs

Ids[Vgs(t- τ),Vds] � Gm e-jωτ .Vgs. + Gds.Vds

Given a Bias Point Vgso,Vdso

Gd

s

δδδδIdsGm = --------

δδδδVgs Vgso,Vdso

δδδδIdsGds = --------

δδδδVds Vgso,Vdso

Transconductance

Output Conductance

LINEAR EquivalentCircuit. Now Vgs andVds are AC values

10



350

300

100

0

200

250

150

50

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

Vds

Id (mA)

Vgs

-1.0

-0.6

-0.2

0

0.2

0.6

1.0350

300

100

0

200

250

150

50

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

Vds

Id (mA)

Vgs

-1.0

-0.6

-0.2

0

0.2

0.6

1.0

Example of I/V curves (DC)Example of I/V curves (DC)

Gds<0

Gds>0

Gm High

Gm low

Phenomena in DC:

- Gds<0 high current area(self-heating).

-Very different Slopes for Gds

- Gm varies having a max. atmedium curren range.

-Vgs Pinch-off voltage varieswith Vds.

- Soft Pinch-off evolution

Gm Low

All these behaviours must be tacken into account in order to write anequation for the Ids current source in DC.

11



101 102 103 104 105

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

Gd

s(m

S)

Frequency (Hz)

Gds Output Conductance Dispersion

101 102 103 104 105

40

35

30

25

20

15

10

5

0

Gm

(mS

)

Frequency (Hz)

Gm Transconductance Dispersion

Ids High

Ids Low

Gds = (δ δ δ δ Ids / δ δ δ δ Vds)|Vgo,Vdo Gm = (δ δ δ δ Ids / δ δ δ δ Vgs)|Vgo,Vdo

DC

area

RF

area

Transition

area

VERY IMPORTANT NOT IMPORTANT

From AC meas. orfrom S meas.

Cutoff

Behaviour of Gm and Gds in RF OperationBehaviour of Gm and Gds in RF Operation

12



Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

Cd

s

Gm

e-j

ωτ.V

gs

Ri

Vds

Vgs

Gd

s

LINEAR EquivalentCircuit.

Compensation for Gds in RF OperationCompensation for Gds in RF Operation

Clf

Rlf

- Above cutoff, the DC output resistance Gdsparallels with the additional Rlf.

- The Clf capacitor is in the microfaradrange because cutoff is in the KHz range.

-This correction is the same at anybias point (first approach)

-This correction can be used in Large Signalequivalent circuit


13



DE

VIC

E M

EA

SU

RE

ME

NT

S

14



S Measurement SetupS Measurement Setup

Pay attention to theaccess resistancesinside the N.A.

15



How to extract the values of the SS equivalent circuitHow to extract the values of the SS equivalent circuit

Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

Cd

s

Gm

e-j

ωτ.V

gs

Ri

Vds

Vgs

Gd

s

LINEAR EquivalentCircuit.

Intrinsicpart

Totaldevice

S params


Totaldevice

Z or Y params

Intrinsicpart

Y params

Circuit Transf.

De-embedding

16



How to extract the values of the SS equivalent circuitHow to extract the values of the SS equivalent circuit

[ ]C

Ygd =

− Im 12

ω

[ ] [ ] [ ]( )[ ] [ ]( )

CY Y Y

Y Ygs =

+⋅ +

+

Im Im Re

Im Im

11 12 12

2

11 12

21

ω

[ ][ ]( ) [ ] [ ]( )

RY

Y Y Yi =

+ +

Re

Re Im Im

11

11

2

11 12

2

( ) [ ]( ) [ ]( )G C R Y Y Cm gs i gd= + ⋅ ⋅ ⋅ + + ⋅12 2 2

21

2

21

2ω ωRe Im

[ ] [ ][ ] [ ]

τω

ω ω

ω ω= ⋅

− ⋅ ⋅ ⋅ − ⋅

− ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅

1 21 21

21 212

arctg - Im Re

Re Im

Y R C Y C

Y R C Y R C C

i gs gd

i gs i gs gd

[ ]C

Y Cds

gd=

− ⋅Im 22 ω

ω

[ ]G Yds = Re 22

Capacitors

Internal Resistor

Current Source

From Intrinsic Y params.

17



Vgs=-0.5

Vgs=0.5

Vgs=10.8

0.6

0.4

0.2

00 2 4 6 8

Cgs (pF)

Vds (Volt)

Vgs=-1

0.3

0.24

0.18

0.12

00 2 4 6 8

Cgd (pF)

Vds (Volt)

Vgs=1

Vgs=0.5

Vgs=-0.5

Vgs=-1

0.06

Multibias Extraction (Capacitors)Multibias Extraction (Capacitors)

CdsTauRi

CdsTauRi

CONSTANTSIn a first step

18



-2-1.5

-1-0.5

00.5 1.5

2

2.5

3

0

20

40

60

Vgs [V]

Vds [V]

Gm

[m

S]

HEMT: DO2AH. Gm vs. Vgs & Vds.

-2-1.5

-1-0.5

00.5 1.5

2

2.5

3

0

1

2

3

4

Vgs [V]

Vds [V]G

ds [m

S]

HEMT: DO2AH. Gds vs. Vgs & Vds.Gm Gds

Multibias Extraction (Gm & Gds)Multibias Extraction (Gm & Gds)

Gain Compression

Pinchoffregion

19



Device Breakdown: DC and PulsedDevice Breakdown: DC and Pulsed

IgId

VgsVds

Ibreak - Occurs when the GD junction is highlynegatively biased (Ibreak=-Ig)

-DC breakdown < Pulsed breakdown

- Important in Power Applications

Vgs = -3

-2.5

-2

Vds

Id

10 to 20 volt

GaN devicesvery high

DC Breakdown

Pulsed Breakdown

20



Extended HEMT Nonlinear ModelExtended HEMT Nonlinear Model

Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

Cd

s

Ids,τ

Ri

Vds

Vgs

Ids[Vgs(t- τ),Vds]

Igs

Igd

Rgd

Clf

Rlf

G-D Breakdown

Gatecurrent

High frequency

- Normally: G-D breakdown and

Gate current are modelled by

using simple diode equations.

- Rgd: high freq. fitting to S.

21



-2-1.5

-1-0.5

00.5 1.5

2

2.5

3

0

20

40

60

Vgs [V]

Vds [V]

Gm

[m

S]

HEMT: DO2AH. Gm vs. Vgs & Vds.

Equations for the HEMT Nonlinear Model (Angelov)Equations for the HEMT Nonlinear Model (Angelov)

Ids(Vgs,Vds) = Ipk.[1+tanh(ΦΦΦΦ)].(1+λλλλ.Vds).tanh(αααα.Vds)

ΦΦΦΦ = P1m.(Vgs-Vpk) + P2(Vgs-Vpk)2 + P3(Vgs-Vpk)3 + ...

P1m = P1 / [1+B1/cosh2(B2.Vds)]

Vpk = Vpko + (Vpks-Vpko).tanh(α.Vds)

as Vpk and P1m dpends on Vds:

Vpk and Ipk : values at peak Gm

Vgs dependence Saturation Slope Initial increase slope

αααα = αr + αs.[1+tanh(Φ)]

as α depends on Vgs,Vds:

Current is continuously derivable

22



350

300

100

0

200

250

150

50

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

Vds

Id (mA)

Vgs

-1.0

-0.6

-0.2

0

0.2

0.6

1.0350

300

100

0

200

250

150

50

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

Vds

Id (mA)

Vgs

-1.0

-0.6

-0.2

0

0.2

0.6

1.0

ΦΦΦΦ

λλλλ

αααα

λλλλ : Saturation Slope

αααα : Initial Slope

ΦΦΦΦ : Gate modulation

Vpk(Vds) & P1m(Vds)controls the pinchoffdependence with Vds

Simplified meaning of the different parametersSimplified meaning of the different parameters

The Hiperbolic Tangent assures thecontinuity and coherence of the highOrder derivatives

The Hiperbolic Tangent assures theSoft Pinchoff evolution

23



Equations for the HEMT Nonlinear Model (Angelov)Equations for the HEMT Nonlinear Model (Angelov)

Reactive Current:

∂Qg ∂Vgs ∂Qg ∂VgdIg = -------- . -------- + -------- . --------

∂Vgs ∂t ∂Vgd ∂t

Cgs(Vgs,Vds) = Cgs1 + Cgs2 = ∂∂∂∂Qg/∂∂∂∂Vgs

Cgs1(Vgs,Vds) = Adiv.Cgso.[1+tanh(P20+P21.Vds)].[1+tanh(P10+P11.Vgs)]

Cgs2(Vgs,Vds) = (1-Adiv).Cgso.[1+tanh(P20+P21.Vds)].[1+tanh(P110+P111.Vgs)]

Cgd(Vgs,Vds) = ∂∂∂∂Qg/∂∂∂∂Vgd = Cgdo.[1+tanh(P30+P31.Vds)].[1+tanh(P40+P41.Vgd)]

Qg : total charge in the channel

Adiv ≅ 1

Charge is continuously derivable

24



Ids

Vds

Q(Vgs0,Vds0) Vgs

DC

Pulsed

Ids

Vds

Q’(Vgs0,Vds0) Vgs

DC

Pulsed

For each bias point we have a Pulsed I/V plane

Frequency Dispersion EffectsFrequency Dispersion Effects

25



IdsDC

Clf(µµµµF)

Rlf

Clf(µµµµF)

Rlf(VgsDC,VdsDC)

Possible Solutions

IdsDC

Clf(µµµµF)

Ipu(Vgs,Vds)

IdsDC

Clf(µµµµF)

Ipu(VgsDC,VdsDC,Vgsi,Vdsi)

SingleBias

MultiBias

Pulsed I/VSingle-Bias

Pulsed I/VMulti-Bias

IdsDC

IdsDC


26



Lg Ld

Ls

Rg Rd

Rs

Cgs

Cgd

Cd

s

Ids,τ

Ri

Vds

Vgs

Ids[Vgs(t- τ),Vds]

Igs

Igd

Rgd

Clf

G-D Breakdown

Gatecurrent

High frequency

Ilf

Ilf(VgsDC,VdsDC,Vgs,Vds)


27



LAYOUT

HEMT DEVICE

1 to 21 GHz (-1,3)

ValidationValidation

0

0.5

1

1.5

22.5

34

56

78

Vds ( V )

-3

-2.5

-2

-1.5

-1

-0.5

0

Vgs ( V )

0

2

4

6

8

10Etot (%)

0

2

4

6

8

10Etot (%)

Multibias Scattering

-2

-1.5

-1

-0.5

0

0.5

1

28



Sa

tura

tio

nS

lop

eλλ λλ

Cd

s(p

F)

Linear Scaling

Nonlinear Scaling

Linear Scaling Rules (W)

Non-Linear Scaling Rules (W)


29




Pulsed I/V validation for a givenBias Point

GEC-MARCONI F-20 Bathtub 10*140 micronsGaAs MESFET

MEASURED

MODELED

Pin-Pout validation for a givenBias Point

Documents

Equivalent Circuit MESFET/HEMT Modelling Approaches · 2011. 3. 14. · Equivalent Circuit MESFET/HEMT Modelling Approaches Angel Mediavilla, Tomás Fernandez, J.A. García Antonio