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TCAD Simulation of CompoundSemiconductor Electronic Devices
May , 2006
Presenter NameOlin Hartin, Ph.D.
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Objective of Workshop
►This workshop will begin with a review of the fundamentals of TCAD
simulation and available tools. DC and small signal AC simulation of
devices will be discussed in detail. There will be a focus on
calibration and the meaning of that calibration. The fundamentals ofheterostructure simulation will be presented with examples.
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation
• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode
• Large signal
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Objective of TCAD simulation
►What can TCAD do• Provide a technical best prediction of DC, AC and transient performance
►Worst kind of TCAD problem• “I saw something funny in the data, run some simulations and tell me what’s
causing it”
►In TCAD simulation is a prediction based on physics and geometry• Predictions are limited to data supplied and physical mechanisms included
• When some of the key mechanisms are not well understood …• There are often clever ways to make predictions when some of the mechanisms
are unavailable or when key parameters are unknown, but not always
►When TCAD is used to solve a problem the most critical step is to
demonstrate the problem in TCAD• If you can’t simulate the problem, it may be difficult to use TCAD to find the
problem or simulate the solution
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Objective of TCAD simulation
The objective of TCAD is to leverage prediction to solve
problems that lead to better technologies• Since prediction is the objective then it is important to understand the
concept of prediction
Compact models are fit to a training data set, they can then predict the
performance of a device ~within the range of the training data set
TCAD is calibrated to a dataset, – Predictions are then based on a physical description of the gridded device and
physical mechanisms applied at those grid points
– We can presume that the TCAD solution can be used to do prediction outside the
range of the calibration data set, but
–The farther we get away from that calibration data the more risky the prediction – This is because there are approximations in the formulation and the calibration
eliminates the offset associated with these approximations locally
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation
• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode
• Large signal
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation
• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode•
Large signal
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Process simulation
►What do these tools do?• Process
As closely as is reasonable
fabricate the device in simulation – In Silicon simulation process is
the challenge, in compound
semiconductors the greater
challenge is typically in the
device simulation
Retain as many details aspossible
– That makes it possible for you
to use simulation to create spits
on those process steps
The tools are designed mostlyfor silicon simulation so there
are compromises
Example from Silvaco’s Athena
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Process simulation
There are two potential objectives ofprocess simulation
1. Investigate the process, and itsvariability using process simulation fordevelopment, (this is common in development
of Silicon devices, not so much in development ofcompound semiconductor devices)
2. Build a structure that accuratelydescribes a device for devicesimulation, this is more common incompound semiconductors, this can be
done in three ways1. A full process simulator (Athena or S-
Process)2. By importing some measured profiles
into a structure3. By using an edit program to draw the
device and then drop in measured or
conceptually determined profiles(Devedit, or S-Edit)
Example from Silvaco’s Athena
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Process simulation
►Process simulation emulates actual fabrication►There are commands to deposit layers, define doping, createimplantation profiles, mask off, and etch layers►Each of these steps has a thermal budget where defined diffusion
mechanisms are used►Movement of dopant species is described by these diffusion steps
►In Heterostructure simulations elements diffuse across material
boundaries creating new mixes of materials but this isn’t taken intoaccount in commercial simulators
• For example at AlGaAs InGaAs boundary there is diffusion of Al, In, Ga, As, these diffusions are typically small and the impact of a thin InAlGaAsinterface material between the AlGaAs InGaAs is not considered
►Crystalagraphic etching isn’t typically taken into account either
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation
• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode• Large signal
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Creating a grid
►Edit• The process grid is not well designed for device simulation so the device must be
re-gridded after process simulation specifically for device simulation
• Gridding is very important, and
there doesn’t seem to be analytical solution for compound semiconductors most grids require manual intervention
• What is important in gridding? Need enough grid points to
– Make the solution grid independent
– To accurately describe your device► Remember the device is only described in the simulator at the grid points
More grid points are not always good – The grid becomes stiffer
– The simulation gets a lot slower
You want the smallest number of grid points that is sufficient to describe the solution
Your grid will be mechanism dependent If there are surface traps - decrease the vertical grid spacing at the surface to describe
the trap depletion
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Gridding problems
►There isn’t a fool proof analytical gridding algorithm for compound
semiconductor devices that I am aware of • Manual grids are common
• You need a gridding philosophy for your device
• The grid spacing should be smaller at vertical and horizontal discontinuities
• Once a grid exists you may have problems getting convergence Run some tests with gridding options, this can be parameterized so that it can be
done in parallel on a compute farm
You may be able to run a simulation up to the point where convergence fails and
then save the output – Plots of the internal characteristics of the device at this point may reveal the issues
– There are ways to dump out the location of the largest update which helps in finding the
problem, and which equation is not converging
– Changes to the math, solver, or implementation of the physics may be tried► Solver, and math issues
► Highly doped semiconductors► Grid adaptation is incompatible with heterostructures (AGM) (chapter 30)
• Just remember, mistakes often show up as convergence problems
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Gridding case study
►Device: GaAs Gadolinium Gate Oxide FET
►Models, hydrodynamic, and density gradients
►Convergence is difficult in drain sweeps when there is very low
current• Solutions
Sweep the gate to turn on the channel before sweeping the drain
Decrease lateral grid spacing – slower solution
• Next step after getting good convergence Build a parallel study in which you increase the grid spacing in high grid
count regions
A courser grid isn’t as stiff, and generally converges better overall
Solution cutbacks occur when convergence fails
– These cutbacks take more time than a large grid would take – Very small minimum cutbacks (where convergence would fail) are seldom the
solution
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation
• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode• Large signal
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Heterostructure TCAD
►How do you describe a device in
some materials system in a
device simulator?
►
You describe the conduction(valence) band in terms of the
electron affinity of each material
►This allows the simulator to
construct a model of conductionband discontinuities
►Poisson is then used to
determine the potential due tocharge
Free space
charge
potentialE
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Heterostructure TCAD
►These two solutions are added
together to give the vertical
potential profile► As we will see this is described
only at grid points
►
When there are quantum effectsquantization impacts the charge
profile and the resulting electric
potential solution
Ec
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Device Simulation
►Device• Ah, there’s the rub!• Device simulations
Material parameters Mechanisms
– Transport – Quantum – Recombination – Traps
Coupled equations are solved usinga Newton’s method approach
– The more effects included, the moreequations, the more memory and themore time required
Transport mechanisms, Poisson,Quantum – solve multiple eqns
DC
AC Temperature Mixed mode
Solve {
Poisson
Coupled {Poisson Electron}
Quasistationary (Goal { Name="gate" Voltage=2 }){ Coupled {Poisson Electron} }
}
Drift diffusion, or Hydrodynamic drive
Schroedinger solver, or Density Gradients
Fixed or Hydrogenic
Hydrodynamic – solution based on Boltsman
transport considering energy of carriers
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation
• Gridding• Device simulation Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode• Large signal
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Convergence control
►
RefErrControl►RhsFactor maximum change to allow the same Jacobian to be
used
►ErrRef(electron)=1e7
►ErrRef(hole)=1e7
►Keep good records, change one thing at a time, maintain the ability
to back up one step when you make it worse
• Impatience is your enemy
R
R
A
Digits R
A R
x x
x
x
x
x
x
ε
ε
ε
ε
ε ε
<+
∆=
<+
∆
∆
−10
1
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Transport Options
►“I just want to get a quick answer, use drift diffusion”• What difference does it take how long it takes to get the wrong answer?
►There are many opinions on drift versus hydrodynamic drive and
much of that comes from Silicon experience• In some software there are issues with the high field saturation model in
barrier materials when using drift diffusion in heterojunction devices
• Hydrodynamic drive provides a solution to Boltzman transport equation(BTE) using the relaxation time assumption
• Drift diffusion solves for the field at each point in a device and thendetermines current, impact ionization … from those fields, problem isthey are really determined based on electron energy not the local field
• Hydrodynamic drive/Energy balance approaches solve for electronenergy
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Velocity models
► Mobility models• You can specify a mobility, a mole fraction dependent mobility• You can also specify a doping dependent mobility
► Velocity models
• There are two choices for velocity models for compoundsemiconductors1. A saturation model that looks a whole lot like silicon
1. This is vsat_formula = 2
2. Energy dependent mobility model,
1. more complex, and harder to use► Relaxation times
• There are two choices1. A constant relaxation time
1. This and a constant saturation velocity may lead to an unrealistic transport
picture2. Energy dependent relaxation times
1. more complex, and harder to use
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Velocity model
►The high field velocity model for
GaAs is shown in the blue curve
►This model has negative
differential mobility (NDM)
► A saturated velocity model,
similar to that seen in Silicon is
shown in red
►Typically this saturated velocity
model is used instead of the
NDM model because of
complexity
0 5 10 15 200
5 .106
1 .107
1.5 .107
2 .107
2.5 .107
kV/cm
V e l
o c i t y ( c m / s e c )
a
GaAs
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Negative differential mobil ity - energy dependent relaxation time model
►Must include energy dependent
relaxation times
0 1000 2000 3000 4000 50000
0.5
1
1.5
2
Electron Temperature (K)
E D R T ( p s )
Increasing
AlGaAs mole
fraction
IncreasingInGaAs mole
fraction
0 1000 2000 3000 4000 50000
0.5
1
1.5
2
Electron Temperature (K)
R e l a x a t
i o n t i m e ( p s )
0 1000 2000 3000 4000 50000
0.5
1
1.5
2
Electron Temperature (K)
E D R T ( p s )
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Energy relaxation rate
►Energy relaxation rate• Assuming constant relaxation time
• GaAs Energy dependent relaxation
time (EDRT)
0 1000 2000 3000 4000 50000
20
40
60
80
Electron Temperature (K)
E n e r g y r e
l a x a t i o n r a t e ( x 1 e 1 0 )
τ
0ww R n −=
( ) AnngnSRH nen
Lnn RG E RkT nT T
k dt
dW −+⎟⎟
⎠
⎞⎜⎜⎝
⎛ +
−= λ
τ 23
23
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Energy vs Field
►GaAs, AlGaAs, and InGaAs
1 .103
1 .104
1 .105
1 .106
0.01
0.1
1
Electric Field (V/cm)
E n e r g y ( e V )
GaAs
AlGaAs
InGaAs
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Trap models
►Trap types• Traps are a big deal in compound semiconductors
They can be defined in a bulk or at an interface
• Fixed, Acceptor, Donor, neutral traps Fixed traps are constant amounts of charge, typically at an interface
– They reflect a circumstance in which the trap is always completely occupied – Note that these are static traps that change are dynamic, or transient because they change over timebased on changing bias conditions
Acceptor and eNeutral traps – Uncharged when unoccupied and carry a charge of one electron when occupied
Donor and hNeutral traps – Are uncharged when unoccupied and they carry the charge of one hole when fully occupied
►Traps can be defined with different distributions of charge, the mostcommon is Gaussian, but table input is also interesting
►N0 is the concentration, E0 is the center of the trap energy distribution,and Es is the sigma
( )2
20
2
0s E
E E
e N n
−−
=
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Density Gradient Model
►Density Gradient
►Where n is the charge density
►mn is the effective mass
►γ is a fit factor
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Quantization model
►In many structures quantized wells
are used
►This is particularly true of HEMT
structures where charge is placed
adjacent to the channel and themobility of the channel is maintained
►Due to quantization the charge in
the channel does not look like it
would under a semiclassical setting(shown in blue)
►Schroedinger Poisson can be use
to solve for this charge (shown in red)
►The density gradient model can be
used to give this same model
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode• Large signal
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Gate Leakage
structure at off-state breakdown
Peak Electric Field
• Typical electric field profileS D
G
Gate
Peak Electric Field
Gate
structure at on-state breakdown
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This slide shows the calibration between simulated and measured2 terminal breakdown current as a function of temperature from 25 to 150C
The mechanisms are impact ionization and thermionic field emission
Temperature Dependent Breakdown Calibration
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Tunneling and Impact Ionization
►This is an illustration of the proposed
gate to drain breakdown mechanism.
Here electrons tunnel in along the gate
due to high reverse fields. Tunneling is
anticipated to occur for fields near 1e6
V/cm[Robbins, 1988 #3].
►Impact ionization occurs in AlGaAs and
InGaAs material below resulting in holes
that escape to the gate, populate surface
states altering channel depletion and
degrading performance, and escape to
the substrate.
►Neither mechanism alone accounts for
the current observed in measured data
because the tunneling mechanism feedscarriers to the avalanche mechanism
EcE G a t e
φΜ
Ev
PHEMT Structure
II
Electron Tunneling
e
h
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0 1 .106
2 .106
3 .106
4 .106
5 .106
0.1
1
10
100
1 .103
1 .104
1 .105
1 .106
1 .107
1 .108
1/Electric Field (cm/V)
a l p h a
Impact Ionization Parameters
►Impact ionization generation
►GaAs
► AlGaAs in 10% molefraction
increments
►InGaAs 20% molefraction
GaAs
AlGaAs
InGaAs
I m p a c t i o
n i z a t i o n G e n e r a t i o n
1/Electric Field (cm/V)
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode• Large signal
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How does it work?
►
Solver runs a coupled solve of several equations describing the problem►Each additional equation adds to the size of the problem and the solution
time.
►For a problem there are the number of grid points times the number of
equations to be solved
►LU decomposition of the Jacobian is typically done
( )
( )
nm
nGradients Density
mnkT T kn f nkT E nq J ic Hydrodynam
nq J Diffusion Drift
dt
dnqqR J Continuity
N N n pqPoisson
n
n
nnn
td
nncnn
nnn
net n
trap A D
6:
ln:
:
:
:
22
2
3
∇=Λ
∇+∇+∇+∇=
Φ−=
+=⋅∇
−−+−−=∇⋅∇
hγ µ
µ
ρ φ ε
)()()())((
1
1
1
nnF nn
nnnnF
xF x J x x xF x x x J
−+
+
−=−=−
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode• Large signal
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DC SolutionElectrode {{ Name="Source" Voltage=0 Resistor=417}{ Name="Drain" Voltage=0 Resistor=417}{ Name="Gate" Voltage=0 WorkFunction=5.2 Resistor=300 }{ Name="substrate" Voltage=0 schottky barrier=0.7 }
}File {
Grid = " input/ggofet_mdr"Doping = " input/ggofet_mdr"Current = "d_ox/plot"Output = "d_ox/log"Plot = "d_ThuFeb15122658200719/dat"
Parameter = "../../common_files/specific.par"}Plot {
EtrappedChargeEgapstatesrecombinationhtrappedchargehgapstatesrecombinationPotential Electricf ieldeDensity hDensity
eCurrent/Vector hCurrent/Vector TotalCurrent/Vector SRH Auger eMobility hMobilityeQuasiFermi hQuasiFermieGradQuasiFermi hGradQuasiFermieEparallel hEparalleleMobility hMobilityeVelocity hVelocity
DonorConcentration AcceptorcCncentrationDoping SpaceChargeConductionBand ValenceBandBandGap AffinityxMoleFractioneTemperature hTemperature
}
Note that electrodes are
defined with resistor values
that are scaled by theareafactor here it is 1000, so
the actual source resistance
implied Is 0.417
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DC SolutionMath {
CNormPrint
ExtrapolateDigits = 5
NotDamped=1000
Iterations=25
NewDiscretization
ConstRefPot
ElementEdgeCurrent
DerivativesRelErrcontrol
NUpperLimit=1e40
RhsFactor=1e20
CdensityMin=1e-10
ErrRef(electron)=1e8
ErrRef(hole) =1e8
DirectCurrent
}
Physics {
Fermi
eQuantumPotential
HeteroInterfaces
AreaFactor = 1000
Hydro(etemperature)
Recombination( SRH Auger )
}
►CNormPrint gives the maximum
size of the update and the nodethat it occurs at for each equation
solution
►Fermi specifies Fermi statistics
►eQuantumPotential is density
gradients (a quantum correction
particularly for describing thecharge in the channel)
► AreaFactor = 1000 is a 1 mm
device
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DC SolutionPhysics ( Material = "AlGaAs" ) {
MoleFraction(
XFraction=0.2)EffectiveIntrinsicDensity( Nobandgapnarrowing )Traps(
(Acceptor Conc=1e14 EnergyMid=0.62 fromCondBandeXsection=1e-14 hXsection=2e-13)(Donor Conc=1e15 EnergyMid=0.61 fromValBandeXsection=2e-18 hXsection=2e-18)
)
Mobility (
eHighFieldSaturation(CarrierTempDrive)hHighFieldSaturation(GradQuasiFermi)
)}
Physics ( Material = " InGaAs" ) {EffectiveIntrinsicDensity( Nobandgapnarrowing )MoleFraction(
XFraction=0.3)Mobility (
eHighFieldSaturation(CarrierTempDrive)hHighFieldSaturation(GradQuasiFermi)
)}
Physics ( MaterialInterface = "Oxide/GaAs" ) {Traps(conc=-1e9 fixedcharge)}
Describe the Physics
Here a mole fraction of 20% isgiven
InGaAs has a 30% mole
fraction but as it is strictlydefined using the software thiswould be 70% Indium (we haveour own internal materials filewhich has the oppositespecification)
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DC SolutionSolve {Coupled(Iterations=50) { Poisson }
Coupled(Iterations=50) { Poisson Electron Hole }
Coupled(Iterations=50) { Poisson eQuantumPotential }Coupled(Iterations=50) { Poisson Electron Hole eTemperature eQuantumPotential }
Quasistationary (
InitialStep=2e-2 Minstep=1e-8 MaxStep=0.20 Increment=1.4
Goal { Name="Gate" Voltage=2 }
) {
Coupled { Poisson Electron Hole eTemperature eQuantumPotential }currentplot ( time=(range=(0 1) intervals=40 ) )
}
Quasistationary (
InitialStep=5e-2 Minstep=1e-8 MaxStep=0.20 Increment=1.4
Goal { Name="Drain" Voltage=2.0 }
) {
Coupled { Poisson Electron Hole eTemperature eQuantumPotential }currentplot ( time=(range=(0 1) intervals=5 ) )
}
Quasistationary (
InitialStep=5e-2 Minstep=1e-8 MaxStep=0.20 Increment=1.4
Goal { Name="Drain" Voltage=2.0 }
) {
Coupled { Poisson Electron Hole eTemperature eQuantumPotential }currentplot ( time=(range=(0 1) intervals=5 ) )
}
}
To get initial solution use
coupled solutions with
additional equations
Current plot gives
solutions at predefined
points
Sweep the gate, then
the drain, then sweep the
gate back to get cut off
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode
• Large signal
Mi d M d Si l ti
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Mixed Mode Simulation
►Mixed mode allows the user todo circuit simulation with ideal
circuit elements and device
simulation elements
►This can be used for DC, AC,and for transient simulations
►Describe each device and give
them a name• Then in the system section
describe a circuit
• This may be simple or complex
Device FET1 {
Electrode {
{ name=“ source” voltage=0 Res=200 }{ name=“ drain” voltage=0 Res=200 }
{ name=“ gate” voltage=0 Res=200 }
{ name=“sub” voltage=0 Res=200 }
}
Physics {
…
}Plot {
…
}
Math {
…
}
File {
…
}
System {
FET1 DEV ( drain=dt gate=gt source=st
sub=st)
v v_g(gt 0) {type=“ dc” dc=0}
v v_d(dt 0) {type=“ dc” dc=0}v v_s(st 0) {type=“ dc” dc=0}
}
AC l ti
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AC solutionSolve {Coupled(Iterations=100) { Poisson }Coupled(Iterations=50) { Poisson Electron Hole }
Coupled(Iterations=50) { Poisson eQuantumPotential }Coupled(Iterations=50) { Poisson Electron Hole eTemperature eQuantumPotential }
Quasistationary (InitialStep=1e-2 Minstep=1e-7 MaxStep=0.2 Increment=1.4Goal { Parameter=v_g.dc Voltage= 2.0 }
) {Coupled { Poisson Electron Hole eTemperature eQuantumPotential }
}
Quasistationary (InitialStep=1e-2 Minstep=1e-7 MaxStep=0.2 Increment=1.4Goal { Parameter=v_d.dc Voltage= 2 }
) {Coupled { Poisson Electron Hole eTemperature eQuantumPotential }
}
Quasistationary (
InitialStep=1e-2 Minstep=1e-7 MaxStep=0.2 Increment=1.4Goal { Parameter=v_g.dc Voltage= 0 }
) {currentplot (time=(range=(0 1) intervals=40 ) )
ACCoupled ( StartFrequency=0.5e9 EndFrequency=20.0e9 NumberOfPoints=39 Linear
Node(gt dt) Exclude(v_d v_g) ACCompute (time=(range=(0 1) intervals=40 ))
){ Poisson Electron Hole eTemperature eQuantumPotential }}
}
O tli f W k h
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Calibration
►HBT/BJT
►Examples• Objectives of simulation• HBT
• GaAs MOSFET DC
– Calibration
AC – Small signal analysis
• Switch transient simulation under mixed mode• Large signal
Calibration
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CalibrationWhat does it mean?
First: Determine every parameter possible from measured data and from the literature►For the parameter values that cannot be determined determine the reasonablerange
• Calibration
Get only the parameters that cannot be directly determined from comparison of simulation tomeasured data Use only values for these parameters that are within the reasonable range for that value Objective of this procedure is to keep the device simulation physical Can be viewed as a fudge, or it can be viewed as a creative way of measuring that parameter
• How is calibration different from a model fitting Models may be nonphysical and are fit to a range of measured data
– As a result the model is only valid in the range of the measured data it was fit to
Physical device simulation uses a physical description of the device and mechanisms at grid points – A few parameters are set so that this fits a range of data – Simulation is predictive because of the basis in physics used beyond the range of the calibration data, this is
unlike a model – Calibration procedure should not violate the physical description
– It is important to us a good calibration procedure
Calibration to measured data
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Calibration to measured dataFET Procedure
1. Determine barrier height in the simulation by calibrating barrier height to fitmeasured gate current
2. Set mobilities and contact resistance from measurements, you really wantmeasured mobilities
3. Adjust total charge to get the threshold voltage seen in measurements4. Set surface trap density/mobility to get sheet resistance seen in measured
data1. You really want to use measured mobilities,2. if you do any adjustment to Rsh is in surface traps or sheet charge, you should have
the sheet charge right under the channel if the threshold is right
5. Adjust the saturation velocity to achieve the measured maximum current6. Add extrinsic inductance determined from small signal AC data
7. When you are done the resistances in each region of the device should addup to the on resistance, this is a useful check and allows you to look for
inconsistencies
Calibration to measured data
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Calibration to measured dataHBT Procedure
1. Compare gummels, your intrinsic diode parameters from
simulation should be good
2. Calibrate beta by emitter and collector resistance at highcurrent and recombination at low current …► Important parameter is bandgap narrowing
3. Adjust surface traps to take into account lateral regions
3. Consider impact of bulk traps
4. Differences between two dimensional assumptions and 3
dimensional layout
Outline of Workshop
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode
• Large signal
Examples: Objectives of TCAD
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Examples: Objectives of TCAD
►Good device physics and a good understanding of device designare required to get a lot out of simulation
►These are some concepts that have been shown to be useful in the
past• Fets
Device doping is chosen by the tradeoff between current and breakdown
Focus on device designs that show different trends in this tradeoff
Remember FETs are impacted by surface effects, make sure you match thesheet resistance of the device in all regions
• HBTs Bulk parameters are more important
Fitting Gummels and beta curves typically involves some adjustment of
recombination parameters including band gap narrowing Surface effects are important near contacts
Outline of Workshop
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models
Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET• Switch transient simulation under mixed mode
• Large signal
Example HBT
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Example HBT
►HBT’s are described usingsimilar methods as in other
devices
►Vertical grid spacing is typically
decreased in junction regions• and lateral grid spacing is
typically decreased around
lateral device discontinuities
such as contacts and etches
Collector n-
Base p+Emitter n
Collector n+
collector
base
emitter
Outline of Workshop
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Outline of Workshop
►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding• Device simulation
Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET
DC – Calibration
AC – Small signal analysis
• Switch transient simulation under mixed mode• Large signal
Example GaAs MOSFET
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p
►The device as a GadoliniumGaAs Oxide layer under the gate,
it employs delta doping and a
InGaAs Channel
GaAs Oxide (κ=20)
2 nm undoped Al45GaAs
2 nm undoped GaAs
10 nm undoped In30GaAs
2 nm undoped GaAs
3 nm undoped Al30GaAs
65 nm undoped Al30GaAs
0.2 µm undoped GaAs
GaAs Substrate
Example GaAs MOSFET
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p
►Vertical grid must be small in theactive region from the surface past
the channel
►Gate voltage sweep convergence is
impacted by the vertical grid►Key points are the surface, channel,
delta doping, and barrier region
►Lateral gridding is needed at the
edge of lateral discontinuities in the
structure, such as the gate edges,
source and drain edges
►Recesses also create lateral
discontinuities
►Drain voltage sweep convergenceis impacted by the lateral grid
Planar
doping
Simulated and Meausred: Id/Vg Characteristics
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g
►The activation of charge isadjusted to about 0.65 (out of
1.0) to get the threshold seen in
the measured data
• Threshold of ~0.25 volts isachieved
►Log(Id)/Vg characteristic shows
the sub-threshold swing (s) of100 [mv/dec]
Drain Current vs Gate Voltage
0
50100
150
200
250
300
350
400
450
500
-0.50 0.00 0.50 1.00 1.50 2.00 2.50
Gate Voltage (V)
D r a i n
C u r r e n t ( m
A / m
m
)
ID (mA/mm)
gm (mS/mm)
sim Id/Vd
sim Gm
log Drain Current vs Drain Voltage
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
-0.50 0.00 0.50 1.00 1.50 2.00 2.50
Gate Voltage (V)
D r a
i n
C u r r e n t ( m
A / m
m
)
ID (mA/mm)
sim Id/Vd
Simulated vs Measured Id/Vd Characteristic
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►Set saturation velocity to1.3e7 cm/sec
• This is not completely
physical
►Set the effective contactresistance to achieve the
same on resistance
observed in the device
• This usually has to do withaccess resistance which is
not typically accurately
measured
• In this case the access
resistance used in thesimulation was ~.6 ohm mm
Drain Current vs Drain Voltage
-50
0
50
100
150
200
250
300
350400
450
0 0.5 1 1.5 2 2.5
Drain Voltage (V)
D r a i n
C u r r e n t ( m
A / m
m )
measured vg=2
simulated
Comparison to measured data
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►Comparison ofsome of the
device
characteristics to
measured data
►Differences in
Rc suggest• The meas Rc is
bad, or • The sim has
lower Rch mA2.6%449461Rsh
mA>2%435-421427Idss
47%
6%
0.9%
on
Error
0.417
106
2.25
0.25-0.27
Measured
0.617
100
2.23
0.254
Simulation
ohm mmRc
mv/decS
ohm mmRon
voltsVth
Unitspar
Check
Ron = 2*Rc + 0.85*2*Rsh + Lg*Rch ≈ 2.25 Ω
Outline of Workshop
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►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding
• Device simulation Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD
DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET
DC – Calibration
AC – Small signal analysis
• Switch transient simulation under mixed mode• Large signal
AC characteristics
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►The “intrinsic” device in the inner box is
simulated using TCAD but this is notexactly what is built in the laboratory
►The external box contains the
extrinsics seen there
►In order to assess the AC
characteristics the extrinsic parasiticsmust be considered/added
►The output of simulator is conductance
and acceptance at the ports, which can
be converted to y, z or s
►To add extrinsics convert TCAD resultsto z parameters and add
►Then convert back to y or s parameters
R_ g L_ g ω⋅ 1i⋅+ R_ s L_ s ω⋅ 1i⋅+( )+
R_ s L_ s ω⋅ 1i⋅+( )
R_ s L_ s ω⋅ 1i⋅+( )
R_ d L_ d ω⋅ 1i⋅+ R_ s L_ s ω⋅ 1i⋅+( )+⎡
⎣
⎤
⎦
Extrinsic Device
Intrinsic Device
S parameters►S parameters that result both
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►S parameters that result, both
intrinsic and extrinsic sparameters are shown
0
30
60
90
120
150
180
210
240
270
300
330
GridZ
0
30
60
90
120
150
180
210
240
270
300
330
0.04
0.02
0 0
30
60
90
120
150
180
210
240
270
300
330
15
10
5
0
S22
S11
S12 S21
G+iA Z
Z+Ze Sextrinsic
Sintrinisic
Small Signal Gain
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Add gate resistance
Gate inductance
Load inductance
Impact of these parasitics
is, Fmax is decreased from
from ~200 to 20 GHz
Source inductance …
0.1 1 10 1000
5
10
15
20
25
30
Frequency (GHz)
M
a x i m u m P r a c t i c a l G a i n
( d B )
0
2 3.5
Maximum
StableGain
Maximum Available
Gain
TCAD
S21/S12
You must have a good handle on parasitics to get the right answer
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►Impact of SourceInductance is to significantly
reduce the corner frequency
which results in lower gain at
high frequency
In some cases the source
inductance is not well known
but can be set to achieve thegain observed
0.1 1 10 1005
10
15
20
25
30
Frequency (GHz)
M a x i m u m P r a c t i c a l G a i n ( d B )
0 pH30 pH
Ls
You must have a good handle on parasitics to get the right answer
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►This is the impact of the gateresistance,
►TCAD simulations typically
don’t include the gate resistance
►Increases in gate resistancealso impact the gain curve and
the location of the corner
frequency
0.1 1 10 1000
5
10
15
20
25
30
Frequency (GHz)
M a x i m u m P r a c t i c a l G a i n
( d B )
Rg
0.5
2.5
Outline of Workshop
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►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding
• Device simulation Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET
DC – Calibration
AC – Small signal analysis
• Switch transient simulation under mixedmode
• Large signal
PHEMT Switch Evaluation of Harmonics
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►SPDT Switch implementedwith PHEMT multi gate
switches
PHEMT TCAD Calibration
to Measured Data
DC I/V
S param
Single Pole Double Throw Switch Simulation
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System {*----------------------------------------------------------------------*
HEMT phemt (Source=s Drain=d Gate1=g1 Gate2=g2Gate3=g3 )
Plot "switch" (time() v(s) v(d) v(n2) i(s d) i(s n2) )
Vsource_pset vs ( vs 0 ) { sine =(0 1.25892541179417 1e9 0 0) }Resistor_pset Rin ( vs s ) { resistance = 50 }
Resistor_pset RD ( s d ) { resistance = 16000 }Vsource_pset vc ( vc 0 ) { dc = 0 }
Resistor_pset Ron (s n2) { resistance = 2.35 }Resistor_pset RL_ (n2 0) { resistance = 50 }Resistor_pset RL (d 0) { resistance = 50 }
Resistor_pset RG1 (g1 vc) { resistance = 16000 }Resistor_pset RG2 (g2 vc) { resistance = 16000 }
Resistor_pset RG3 (g3 vc) { resistance = 16000 }** Switch circuit*----------------------------------------------------------------------*}
More complex mixed mode simulations can be done including ones with
multiple active devices and ideal passive components, here a single pole double
throw circuit is described
Switch SimulationSolve {
*----------------------------------------------------------------------*
On device
looks likeOff device
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----------------------------------------------------------------------
*--Computing initial guess:
NewCurrentFile=off
circuit
Coupled( Iterations=100 ){ Poisson Contact Circuit }
Coupled { Poisson Contact Circuit Electron Hole eTemperature }
Quasistationary (
InitialStep=1e-2 Increment=1.2 Minstep=1e-8 MaxStep=0.1Goal{ parameter=vc.dc Value=-3 } )
{
Coupled { Poisson Contact Circuit Electron Hole eTemperature }
}
NewCurrentFile=off_
Transient (
InitialTime=0 FinalTime=2e-9
InitialStep=3.90625e-12 MaxStep=3.90625e-12 MinStep=1e-17
Increment=1.2
)
{
Coupled { Poisson Contact Circuit Electron Hole eTemperature }
CurrentPlot (
Time = ( Range=( 0.0 2e-9 ) intervals=512 ))
}
plot
}
In this case we are doing a single pole
double throw simulation with a switch
composed of two devices
a resistor Looks is modeled
Transient Simulations
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►This is the resulting devicesimulation showing the
transient solution of the off
state device
Outline of Workshop
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►Vendor review►Objective of simulation►General simulation flow
• Process simulation• Gridding
• Device simulation Heterostructure simulation Convergence Transport options Trap models Stress Quantum correction Material properties Special topics
– Gate leakage
Solutions in TCAD DC Simulation syntax Mixed mode
►Calibration
►Examples• Objectives of simulation• HBT• GaAs MOSFET
DC – Calibration
AC – Small signal analysis
• Switch transient simulation under mixed mode• Large signal
Large Signal
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► There are three ways to do large signal simulations using TCAD1. Use mixed mode to simulate transient response of RF circuits
Simulations are long and difficult, not well integrated with designer problems
2. Use integrated harmonic balance algorithm
Not operable for practical problems, long simulations, not well integrated withdesigns
3. Extract a model based on TCADLimits to what the model is capable, well integrated with designer
0
10
20
-30 -20 -10 0 10 20
Pin (dBm)
G a i n ( d B )
15 15.616.2 16.817.4 18
Low Power Gain (dB
1 5. 84 1 6.7 6
Gain
0
25
50
75
-30 -20 -10 0 10 20
Pin (dBm)
P A E ( % )
58 59.2 60.4 61.6 62.8 64
PAE (%)
60.3 62.3
PAE
-10
0
10
20
-30 -20 -10 0 10 20
Pin (dBm)
P o u t ( d B m )
22 22.2 22.4 22.6 22.8 23
Pout (dBm)
22.26 22.54
a
Pout
In Review
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►Heterostructure process and device simulation can be done usingbasic methods. Key mechanisms necessary for FETs and Bipolars
are available in commercial vendor packages. Methods exist that
make it possible to integrate known material data and calibration to
measured data. These methods enable TCAD simulations for DC,small signal AC, and large signal prediction.
References
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Hartin, O., et al. (2001). Compound Semiconductor Physical Device Simulation for Technology Development atMotorola. GaAs IC Symposium 23rd Annual Technical Digest:163-165Li, P. H., et al. (2002). “An updated temperature-dependent breakdown coupling model including both impact ionizationand tunneling mechanisms for AlGaAs/InGaAs HEMTs.” IEEE Transactions on Electron Devices 49(9): 1675-1678.Quay, R. (2001). Analysis and Simulation of High Electron Mobility Transistors. Electrical Engineering. Freiburg,Technischen Universität Wien Fakultät für Elektrotechnik und Informationstechnik.Klimeck, G., R. Lake, et al. (1996). Nemo: A General Purpose Quantum Device Simulator. Texas Instruments
Research Colloquium, Dallas, TX.Sentaraus Manual version Y-2006.06Silvaco Atlas Manual 5th Edition, 1997Kalna, K., et al. (2007). “Monte Carlo Simulations of High-Performance Implant Free In0.3Ga0.7As Nano-MOSFETsfor Low-Power CMOS Applications.” IEEE Transactions on Nanotechnology 6(1).Rajagopalan, et al. (2007). “1-ìm Enhancement Mode GaAs N-Channel MOSFETs With Transconductance Exceeding250 mS/mm.” IEEE ELECTRON DEVICE LETTERS 28(2).
Adachi, S., Ed. (1993). Properties of Aluminum Gallium Arsenide. EMIS Data Reviews Series. London, INSPEC, theInstitution of Electrical Engineers. Adachi, S. (1994). GaAs and Related Materials: Bulk Semiconducting and Superlattice properties. London, WorldScientific.Vendelin, G. D., A. M. Pavio, et al. (1990). Microwave Circuit Design. New York.Lundstrom, M. (1990). Fundamentals of Carrier Transport. Reading, Ma., Addison Wesley Publishing Co.Vogl, P. (1983). “A Semi-Empirical Tight-Binding Theory of the Electronic Structure of Semiconductors.” Journal of thePhysical Chemistry of Solids 44(5): 365-378.
Wolfe, C. M., J. Nick Holonyak, et al. (1989). Physical Properties of Semiconductors. Engelwood Cliffs, New Jersey,Prentice hall.Blakey, P. A., Ed. (2001). Technology Computer Aided Design. The RF Microwave Handbook. London, CRC Press.
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