Jerry L' Hudgins

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Semiconductor Modeling and Simulation

• Jerry L. Hudgins
• University of South Carolina

Enrico Santi University of South Carolina
Patrick R. Palmer University of Cambridge
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Technology Areas

• Device Characterization, Modeling, and Simulation
• Semiconductor Material Systems and
  Temperature-Dependent Physical Behavior to
  support modeling

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Model Levels

• 5 Levels of Models, 0 to 4.
• Modified from System Proposed by Budihardjo ,
  Lauritzen, Wong, Darling, and Mantooth.
• Focus on Development of Level-1, Level-2, and
  Level-3 Semiconductor Device Models.

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Level-0 Models

• No distinction of device type only ideal-like
  switch.
• No current flow in its off-state (forward or
  reverse blocking).
• No voltage drop in its on-state (forward
  conduction state).
• Maximum blocking voltage and conduction current
  limits can be set.
• No junction-temperature information.
• No power loss information.

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Level-4 Models

• All relevant physical behavior captured in this
  model.
• Model is 3- or 4-dimensional in space-time.
• Model is process dependent.
• Model maps charge flow, electric fields, and
  thermal gradients.
• No analytical description available so must use
  finite-element methods.

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Level-4 Model Examples
Heat flux and thermal gradients in a DBC module
Charge distribution in a NPT IGBT
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VTB Level-1 Models

• Forward conduction current as a function of
  forward voltage drop and temperature (this allows
  estimation of forward conduction losses).
• Off-state (forward blocking) leakage current
  included.
• Turn-on switching losses a function of blocking
  voltage and temperature.
• Turn-off switching losses a function of
  conduction current and temperature.

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VTB Level-1 Models

• No gating or triggering losses are calculated.
• Breakdown voltage limits are imposed (forward and
  reverse blocking).
• Maximum forward conduction-current limit is
  imposed.
• Maximum junction-temperature limit is imposed.
• Simple multi-section RC equivalent network
  included for junction temperature calculation.

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Example of Level-1 Model IGCT

• VDRM 4500 V (repetitive peak off-state voltage)
• ITAVM 1700 A (maximum average on-state current
  half sine wave)
• ITRMS 2700 A (maximum rms on-state current)

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Test Circuit

• The Level-1 Model of the IGCT tested under the
  following conditions
• High current
• Frequency 1000Hz

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Electrical and Thermal Waveforms
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VTB Level-2 Models

• 1-Dimensional in Space.
• Simplified Physical Description.
• Simple Thermal Effects on Carrier Motion
  Included.
• Uses Modified and Extended Lumped-Charge
  Technique first Developed by Ma, Lauritzen, et.al.

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Example of Level-2 Model

• IGCT

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VTB Level-3 Models

• All models are quasi-2D.
• All models solve the 1-D carrier diffusion
  equation at each point in space and time.

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Level-3 Model Attributes

• Based on Fourier Solution Initially Proposed by
  Leturcq and Further Expanded by Santi, Palmer,
  and Hudgins.
• All Level-3 models include temperature dependent
  effects, and are valid for junction temperatures
  from 150 to 150 oC.
• Bandgap Energy
• Density-of-States Effective Mass
• Carrier Mobilities
• Ionized Impurity Concentration
• Carrier Lifetimes

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IGBT Level-3 Model in SIMULINK
MOSFET conduction
IGBT
Base resistance
Miller capacitance
Carrier storage region
Depletion layer
Gate circuit
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IGBT Level-3 Models Developed

• IGBTs
• Non-Punch Through, NPT
• Planar-Gate Structure

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IGBT Models

• Punch-through (PT), planar- and trench-gate.
• High-Voltage and Field-Stop Designs

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Model Validation

• Experiment
• Atlas finite element simulation
• Physics-based model
• Atlas and the model allow us to look at the
  physics inside the device

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Atlas Simulation vs Experiment
VGE
IC
VCE
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Level-3 Model vs Experiment
VGE
IC
VCE
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Charge Profile Atlas
3.0?s
3.5?s
4.3?s
2.8?s
2.0?s
8.0?s
2.7?s
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Charge Profile Model
3.5?s
4.3?s
3.0?s
2.8?s
2.0?s
2.7?s
8.0?s
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Examples of NPT-IGBT Simulations
NPT-IGBT at 100 oC. Comparison between the
experimental result (dark blue-current
pink-voltage) and simulation (yellow- current
light blue- voltage) during turn-off.
NPT-IGBT at -125 oC. Comparison between the
experimental result (dark blue-current
pink-voltage) and simulation (yellow- current
light blue- voltage) during turn-off.
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Examples of PT-IGBT Simulations
PT-IGBT at room temperature. Comparison between
the experimental result (dark blue-current
pink-voltage) and simulation (yellow- current
light blue- voltage) during turn-off.
PT-IGBT at 100 oC. Comparison between the
experimental result (dark blue-current
pink-voltage) and simulation (yellow- current
light blue- voltage) during turn-off.
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Model Validation Turn On Losses
Energy J
Temperature C
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Model Validation Turn Off Losses
Energy J
Temperature C
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Diode Level-3 Models
Diodes B and A at room temperature. Comparison
between the experimental result (dark
blue-voltage pink-current) and simulation
(yellow-voltage light blue-current) during
turn-off.
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Two-Step Parameter Extraction Procedure

• Step 1 practical parameter extraction Only one
  clamped inductive switching experiment needed
• Step 2 automated optimization procedure

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Step 1 IGBT Parameters
Only one inductive switching experiment
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Step 2 Parameter Optimization
Automated procedure
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Semiconductor Properties and Material Systems
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Fundamental Semiconductor Physics for Cryogenic
Operation
for T 170 K for T gt 170 K
Included Accurate Description of Bandgap Energy
as a Function ofTemperature.
Temperature dependence of the bandgap energy in
silicon.
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Fundamental Semiconductor Physics for Cryogenic
Operation
Improved Effective MassRelationships (Hole).
Electron
__ Equation (3) - - Equation, Ref. 16
Data, Ref. 13
__ Equation (4) - - Equation, Ref. 16
Data, Ref. 13
Hole
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Cryogenic Operation
Developed New Description forIonized Donors for
Tlt77 K.
Developed New Description for Electron and Hole
Mobilities for Tlt77 K.
Electron Mobility (cm2/Vs)
Ionized donor concentration as a function of
temperature. The background doping density is
assumed to be 1014 cm-3 and phosphorous as the
dopant species.
Electron mobility as a function of temperature
for T lt 300 K.
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Cryogenic Operation
Improved Lifetime ExpressionIncludes SRH and
Auger Recombination.
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Semiconductor Materials

• Compared Thermal Conductivity, CTE, Mobility, and
  Bandgap

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Critical Field as a Function of Energy Bandgap
Direct Gap Ec 1.73?105 (EG)2.5
Indirect Gap Ec 2.38?105 (EG)2
Equation (SzeGibbons)
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Semiconductors with Good Thermo-Mechanical
Properties
Semiconductors with CTE between 4 and 6 ppm/K. C
and BN included because of high thermal
conductivity.
Semiconductors with thermal conductivity above
100 W/mK.
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Thermo-Mechanical Best

• The reduced list of semiconductors to achieve
  high thermal conductivity as well as match the
  CTE of common package substrate materials
  becomes GaN, AlN, GaP, SiC (6H), SiC (4H)
• C (Diamond) and BN (Cubic) are included as the
  very high thermal conductivity implies very small
  temperature rise so the relatively low CTE may
  not be so important for these materials.

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Electron Mobility vs. Bandgap Energy

• Semiconductors with electron mobilities above 700
  cm2/Vs and with a bandgap energy above 1 eV
  are InP, GaAs, InN, GaN, AlN, Si, SiC (3C), SiC
  (4H), and C.

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Thermo-Mechanical-Electrical Selection

• The semiconductors with the best electrical and
  thermo-mechanical characteristics are now reduced
  to C, GaN, AlN, and SiC (4H).

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GaN Devices

• Breakthrough in GaN Transistor Development
• High Density 2D Electron Gas at AlGaN/GaN
  Interface as high as 2 x 1013 cm-2
• The screening of defects and impurities by the 2D
  gas causes the effective electron mobility to
  increase to 1500-2000 cm2/Vs

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GaN Hetero-Junction Field-Effect Transistors
(Simin, Khan)

• MOSHFET

• HFET

GaN 2 mm, Si-doped (1018-1019 cm-3) Al0.2Ga0.8N
30 nm S-D spacing of 2-16 mm, L0.1-1 mm,
W50-100 mm
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I-V Characteristics of MOSHFET
VDS 8.1 V _at_VGS6 V, JD15 A/mm2, and 300 K
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Summary Here Today, Gone Tomorrow
I wouldnt worry about those little fuzzy guys.
Si
Si
C
GaN
Si
SiC
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Electrical Equivalent Model