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
Modelización MESFET/HEMT
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: media@dicom.unican.es
A. MEDIAVILLA
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
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Modelización MESFET/HEMT
Outline
Brief Introduction
- Physics of the device
- Physical meaning of the EECM
- Extraction techniques
- Analytical equations
- Temperature description
- Intermodulation Properties
- Conclusions
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Modelización MESFET/HEMT
MESFET/ /HEMT
HEMTDevices
Devices
MESFET
GaAsFET
GaAsFET
Devices
Devices
MESFET
HEMT
Active Region
S
G
Ohmic Contact
D
S
N+ GaAs
N+ GaAs
N Channel
N AlGaAs
Undopped Buffer
Semi Insulating GaAs
D
G
Undopped Buffer
Semi Insulating GaAs
2Deg AlGaAs
due to the 2Deg layer:
- Superior mobility
- Higher frequency
- Lower noise figure
If GaN: higher Power density
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Modelización MESFET/HEMT
Simplifiedoperation
operationfor
forHEMT
HEMTDevices
Devices
Simplified
HEMT
S
D
G
N+ GaAs
A wide-bandgap material N AlGaAs lies on a undoped
narrow-bandgap material GaAs.
N AlGaAs
Undoped GaAs Buffer
Semi Insulating GaAs
Schottky
Gate
N
AlGaAs
2Deg AlGaAs
Thickness and Doping density of N AlGaAs chosen for
absence of free electrons under normal operation.
Sharp dip in Ec occurs in the boundary: High carrier
concentration in this region (2Deg), and do not encounter
donnor atoms: high mobility
undoped
GaAs
Current flows through the electron gaz controlled by Vgs.
As Vds increases, current saturates.
Ec
Ef
G
2Deg
region
Ev
As Vgs is more positive, sheet carrier density tends to
decrease and current tends to saturate
Band Diagram
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Modelización MESFET/HEMT
Parasitic Inductances Lg, Ld, Ls:
- due to metal contact pads
- Lg, Ld between 5 to 20pH
- Ls is lower: 1pH
PhysicalMeaning
Meaningof
ofthe
theEquivalent
EquivalentCircuit
CircuitModel
Model
Physical
Lg
Rg
Cgd
Cgs
Parasitic Resistances Rg, Rd, Rs:
-Rd, Rs: ohmic contacts < 1 ohm
-Rg: metalization resistance < 1 ohm
G
S
Rd
Ld
Vgs
Cds Vds
Ids,τ
Ri
Ids(Vgs,Vds,τ)
D
Rs
Rg
Ls
Cgs
Rs
Ri
Cgd
Rd
Ids,τ
Intrinsic Resistance Ri:
-Questionable physical meaning
-Introduced to improve S11
Cds
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Modelización MESFET/HEMT
Intrinsic Capacitances Cgs,Cgd,Cds:
- Cgs,Cgd: depletion charge
- Cds: geometrical capacitance D-S
- Cgs: 1pF/mm, Cgd&Cds 1/10 Cgs
PhysicalMeaning
Meaningof
ofthe
theEquivalent
EquivalentCircuit
CircuitModel
Model
Physical
Lg
Rg
Cgd
Cgs
Intrinsic Current Source Ids:
- reproduces I/V curves
- will reproduce the Gm and Gds values
G
S
Rd
Ld
Vgs
Cds Vds
Ids,τ
Ri
Ids[Vgs(t- τ),Vds]
D
Rs
Rg
Ls
Cgs
Rs
Cgd
Rd
Ri
Ids,τ
Cds
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Transconductande delay τ :
-Current does not respond instantaneously to
changes in Gate voltage.
- Order of 1ps. Increases with Gate length
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Modelización MESFET/HEMT
Dependenceon
onthe
theBias
BiasPoint
Point(NL
(NLelemens)
elemens)
Dependence
Main Nonlinear Elements:
Lg
Rg
Cgs
Cgd
Rd
Ld
Vgs
Cds Vds
Ids,τ
- Ids : Obviously I/V curves
- Cgs and Cgd depend on the bias because
the depletion region changes with the bias
Ri
Ids[Vgs(t- τ),Vds]
Rs
Secondary Nonlinear Elements:
- Parasitic resistors
Ls
- Cds geometrical capacitance
- Transconductance delay τ
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Modelización MESFET/HEMT
SmallSignal
SignalEquivalent
EquivalentCircuit
Circuitfor
foraagiven
givenBias
BiasPoint
Point
Small
Given a Bias Point Vgso,Vdso
Ri
Vgs
Rd
LINEAR Equivalent
Circuit. Now Vgs and
Vds are AC values
Cds
Cgs
Cgd
Gds
Rg
Gm e-jωτ .Vgs
Lg
Ld
Vds
Transconductance
Rs
Ls
Ids[Vgs(t- τ),Vds] Gm e-jωτ .Vgs. + Gds.Vds
δIds
Gm = -------δVgs Vgso,Vdso
Output Conductance
δIds
Gds = -------δVds Vgso,Vdso
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Exampleof
ofI/V
I/Vcurves
curves(DC)
(DC)
Example
Gm low
Gds<0
Id (mA)
350
1.0
0.6
300
Phenomena in DC:
0.2
250
0
200
Vgs
Gm High
-0.2
-Very different Slopes for Gds
Gds>0
150
100
-0.6
Gm Low
50
-1.0
0
Vds
0
0.5
1.0
1.5
2.0
2.5
- Gds<0 high current area
(self-heating).
3.0
3.5
- Gm varies having a max. at
medium curren range.
-Vgs Pinch-off voltage varies
with Vds.
4.0
- Soft Pinch-off evolution
All these behaviours must be tacken into account in order to write an
equation for the Ids current source in DC.
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Modelización MESFET/HEMT
Behaviourof
ofGm
Gmand
andGds
Gdsin
inRF
RFOperation
Operation
Behaviour
From AC meas. or
from S meas.
Gds Output Conductance Dispersion
2.4
35
2.2
30
2.0
1.8
Cutoff
1.6
Gm Transconductance Dispersion
40
Gm (mS)
Gds (mS)
2.6
20
15
1.4
10
1.2
5
1.0
Ids High
25
Ids Low
0
101
102
103
104
105
101
102
103
Frequency (Hz)
DC
area
Transition
area
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Frequency (Hz)
RF
area
Gds = (δ
δ Ids / δ Vds)|Vgo,Vdo
VERY IMPORTANT
104
Gm = (δ
δ Ids / δ Vgs)|Vgo,Vdo
NOT IMPORTANT
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Compensationfor
forGds
Gdsin
inRF
RFOperation
Operation
Compensation
Given a Bias Point Vgso,Vdso
Ld
Clf
Rd
Vds
Rlf
Ri
Vgs
Cds
Cgs
Gds
Rg
Gm e-jωτ .Vgs
Lg
LINEAR Equivalent
Cgd Circuit.
Rs
Ls
- Above cutoff, the DC output resistance Gds
parallels with the additional Rlf.
- The Clf capacitor is in the microfarad
range because cutoff is in the KHz range.
-This correction is the same at any
bias point (first approach)
-This correction can be used in Large Signal
equivalent circuit
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DEVICE MEASUREMENTS
Modelización MESFET/HEMT
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Modelización MESFET/HEMT
MeasurementSetup
Setup
SS Measurement
Pay attention to the
access resistances
inside the N.A.
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Modelización MESFET/HEMT
Howto
toextract
extractthe
thevalues
valuesof
ofthe
theSS
SSequivalent
equivalentcircuit
circuit
How
Given a Bias Point Vgso,Vdso
Cgd
Intrinsic
part
Vgs
Ri
Ld
S params
Cds
Cgs
Rd
Gds
Rg
Gm e-jωτ .Vgs
Lg
Vds
Total
device
Circuit Transf.
Rs
LINEAR Equivalent
Circuit.
Z or Y params
Total
device
Ls
De-embedding
Y params
Intrinsic
part
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Modelización MESFET/HEMT
Howto
toextract
extractthe
thevalues
valuesof
ofthe
theSS
SSequivalent
equivalentcircuit
circuit
How
From Intrinsic Y params.
Cgd =
− Im[Y12 ]
Cds =
ω
Im[Y22 ] − ω ⋅ Cgd
ω
Capacitors
2

Re[Y12 ])
Im[Y11 ] + Im[Y12 ] 
(

Cgs =
⋅ 1 +
2
ω
 (Im[Y11 ] + Im[Y12 ]) 
Ri =
Re[Y11 ]
2
( Re[Y11 ]) + (Im[Y11 ] + Im[Y12 ])
Gm =
(1 + ω
2
)
2
Internal Resistor
2
(
2
⋅ Cgs
⋅ Ri2 ⋅ ( Re[Y21 ]) + Im[Y21 ] + ω ⋅ Cgd
)
2
Gds = Re[Y22 ]
Current Source


- Im[Y21 ] − ω ⋅ Ri ⋅ Cgs ⋅ Re[Y21 ] − ω ⋅ Cgd


τ = ⋅ arctg 
2

ω
 Re[Y21 ] − ω ⋅ Ri ⋅ Cgs ⋅ Im[Y21 ] − ω ⋅ Ri ⋅ Cgs ⋅ Cgd 
1
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MultibiasExtraction
Extraction(Capacitors)
(Capacitors)
Multibias
Cgs (pF)
0.8
Cgd (pF)
0.3
Vgs=1
Cds
Cds
Tau
Tau
Ri
Ri
Vgs=1
0.24
Vgs=0.5
0.6
Vgs=0.5
0.18
Vgs=-0.5
0.4
Vgs=-0.5
0.12
Vgs=-1
Vgs=-1
0.2
CONSTANTS
0.06
In a first step
0
0
0
2
4
6
8
Vds (Volt)
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0
2
4
6
8
Vds (Volt)
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Modelización MESFET/HEMT
MultibiasExtraction
Extraction(Gm
(Gm&&Gds)
Gds)
Multibias
Gm
Gds
HEMT: DO2AH. Gm vs. Vgs & Vds.
HEMT: DO2AH. Gds vs. Vgs & Vds.
Gain Compression
Pinchoff
region
4
40
3
20
2.5
0
-2
-1
-0.5
0
Vgs [V]
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0.5 1.5
3
3
2
1
0
-2
2
-1.5
Gds [mS]
Gm [mS]
60
2.5
2
-1.5
-1
-0.5
0
Vds [V]
0.5 1.5
Vds [V]
Vgs [V]
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Modelización MESFET/HEMT
DeviceBreakdown:
Breakdown: DC
DC and
andPulsed
Pulsed
Device
Ibreak
Id
Ig
- Occurs when the GD junction is highly
negatively biased (Ibreak=-Ig)
-DC breakdown < Pulsed breakdown
Vds
Vgs
- Important in Power Applications
DC Breakdown
-2.5
Id
-2
Pulsed Breakdown
Vgs = -3
GaN devices
very high
Vds
10 to 20 volt
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Modelización MESFET/HEMT
ExtendedHEMT
HEMTNonlinear
NonlinearModel
Model
Extended
G-D Breakdown
Igd
High frequency
Cgd
Cgs
Igs
Ld
Vgs
Ids,τ
Ri
Vds
Rlf
Gate
current
Rd
Rgd
Clf
Rg
Cds
Lg
Ids[Vgs(t- τ),Vds]
Rs
Ls
- Normally: G-D breakdown and
Gate current are modelled by
using simple diode equations.
- Rgd: high freq. fitting to S.
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Modelización MESFET/HEMT
Equationsfor
forthe
theHEMT
HEMTNonlinear
NonlinearModel
Model (Angelov)
(Angelov)
Equations
Ids(Vgs,Vds) = Ipk.[1+tanh(Φ
Φ)].(1+λ
λ.Vds).tanh(α
α.Vds)
Vgs dependence
Saturation Slope
Initial increase slope
Vpk and Ipk : values at peak Gm
HEMT: DO2AH. Gm vs. Vgs & Vds.
Φ = P1m.(Vgs-Vpk) + P2(Vgs-Vpk)2 + P3(Vgs-Vpk)3 + ...
as α depends on Vgs,Vds:
as Vpk and P1m dpends on Vds:
P1m = P1 / [1+B1/cosh2(B2.Vds)]
Gm [mS]
Vpk = Vpko + (Vpks-Vpko).tanh(α.Vds)
60
40
3
α = αr + αs.[1+tanh(Φ)]
20
2.5
0
-2
2
-1.5
-1
-0.5
0
0.5 1.5
Vds [V]
Vgs [V]
Current is continuously derivable
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Modelización MESFET/HEMT
Simplifiedmeaning
meaningof
ofthe
thedifferent
differentparameters
parameters
Simplified
Id (mA)
350
1.0
0.6
300
0.2
λ
250
-0.2
Φ
150
α : Initial Slope
0
Vgs
200
λ : Saturation Slope
α
100
-0.6
Φ : Gate modulation
Vpk(Vds) & P1m(Vds)
controls the pinchoff
dependence with Vds
50
-1.0
0
Vds
0
0.5
1.0
1.5
2.0
2.5
3.0
The Hiperbolic Tangent assures the
continuity and coherence of the high
Order derivatives
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3.5
4.0
The Hiperbolic Tangent assures the
Soft Pinchoff evolution
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Modelización MESFET/HEMT
Equationsfor
forthe
theHEMT
HEMTNonlinear
NonlinearModel
Model (Angelov)
(Angelov)
Equations
Reactive Current:
∂Qg
∂Vgs
∂Qg
∂Vgd
Ig = -------- . -------- + -------- . -------∂Vgs
∂t
∂Vgd
∂t
Qg : total charge in the channel
Cgs(Vgs,Vds) = Cgs1 + Cgs2 = ∂Qg/∂
∂Vgs
Adiv ≅ 1
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)]
Charge is continuously derivable
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Modelización MESFET/HEMT
FrequencyDispersion
DispersionEffects
Effects
Frequency
Ids
Ids
Pulsed
Pulsed
DC
Q(Vgs0,Vds0)
DC
Q’(Vgs0,Vds0)
Vgs
Vds
Vgs
Vds
For each bias point we have a Pulsed I/V plane
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Modelización MESFET/HEMT
FrequencyDispersion
DispersionEffects
Effects
Frequency
Possible Solutions
Single
Bias
Clf(µ
µF)
Multi
Bias
IdsDC
IdsDC
Rlf
Pulsed I/V
Single-Bias
IdsDC
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Clf(µ
µF)
Clf(µ
µF)
IdsDC
Ipu(Vgs,Vds)
Rlf(VgsDC,VdsDC)
Pulsed I/V
Multi-Bias
Clf(µ
µF)
IdsDC
Ipu(VgsDC,VdsDC,Vgsi,Vdsi)
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Modelización MESFET/HEMT
FrequencyDispersion
DispersionEffects
Effects
Frequency
G-D Breakdown
Igd
High frequency
Cgd
Cgs
Igs
Gate
current
Rd
Rgd
Ld
Clf
Rg
Vgs
Ids,τ
Cds
Lg
Vds
Ri
Ilf
Ids[Vgs(t- τ),Vds]
Rs
Ilf(VgsDC,VdsDC,Vgs,Vds)
Ls
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Modelización MESFET/HEMT
Validation
Validation
Multibias Scattering
10
Etot (%) 10
8
8
6
6
4
4
2
2
HEMT DEVICE
0
-2
-3
-1.5
-2.5
4
-1
-2
2
1.5
-1
0
Vds ( V )
1
-0.5
0.5
0.5
01
LAYOUT
6
0
1 to 21 GHz (-1,3)
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0
8
3
2.5
-0.5
-1.5
Vgs ( V )
5
7
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Etot (%)
Modelización MESFET/HEMT
Validation
Validation
Cds (pF)
Linear Scaling Rules (W)
Nonlinear Scaling
Linear Scaling
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Saturation Slope λ
Non-Linear Scaling Rules (W)
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Validation
Validation
Pin-Pout validation for a given
Bias Point
GEC-MARCONI F-20 Bathtub 10*140 microns
GaAs MESFET
Pulsed I/V validation for a given
Bias Point
MEASURED
MODELED
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