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MOSFET Simulation Models
Dr. David W. Graham
West Virginia University
Lane Department of Computer Science and Electrical Engineering
© 2010 David W. Graham
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Rigorous Modeling
• Requires 3D modeling equations
• Finite-element analysis (coupled PDEs for
thousands of small elements)
• Great for designing devices
• Unusable for circuit design
– Simulations take far too long
–  Need a faster simulation model for circuit
design
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“Compact Models”
• Simplification of the finite-element analysis
approach
• Include only what needs to be included
– This is a tough job in developing simulation models
– Models have to be simple enough to simulate fast, but
complex enough to permit design
– Tradeoff between simulation speed and model
accuracy/complexity
• We use “compact models” in SPICE
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Types of Compact Models
1. Table Models
2. Empirical Models
3. Physical Models
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Table Models
• Look-up-table approach
• Contains currents (+ maybe small-signal parameters) for
a given bias condition
• Fast simulation
– No need to solve complicated equations
– May use interpolation
• Easy to develop
– Simply characterize your device
• Provides current value regardless of the mechanism
causing it
– Not concerned with the physics
• Cannot be used to predict changes if parameters change
– e.g. if W or L change, a completely new table is required
• Rarely used for sophisticated design
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Empirical Models
• Relies on curve fitting
• Can use any equation that adequately fits the
data
• Parameters have no physical meaning
– e.g. coefficient to the curve-fit polynomial
• Fairly easy to characterize devices and extract
the curve-fit parameters
• Purely empirical models are rarely used
– Typically they help other types of models to model
real devices
– Some device characteristics are very hard to model
analytically
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Physical Models
• Based on device physics
• Parameters have a physical meaning
– e.g. flat-band voltage, substrate doping, etc.
• Hard to develop
• Typically result in the best simulation results
• Can be used to predict the performance for
changing parameters
• May require significant overhead for changing
process technology
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Common Compact Models for IC Simulations
1. BSIM Model
2. EKV Model
3. PSP Model
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BSIM Model (e.g. BSIM3v3)
• From UC Berkeley
• Most widely used model in industry (currently)
• Performance
– Very good for strong inversion
– Okay for weak inversion (improving)
– Poor performance in moderate inversion
• Mixture of empirical and physical models
• Typically >100 parameters
• Parameters available from foundry
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EKV Model (e.g. EKV 2.6 Model)
• Developed by 3 Swiss engineers
– Enz, Krummenacher, and Vittoz
• Originally developed to be a better hand-calculation
model for low-power circuit design
• Used primarily in low-power circuit-design, but its
influence is growing
• Performance
– Works well in strong inversion
– Works very well in weak inversion
– Decent in moderate inversion
• Physical model
– Only 18 parameters
– Each parameter has physical significance
– Therefore, parameter extraction is a simpler process
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PSP Model
• Developed jointly by Penn St. (now ASU) and
Philips Research
• Slated to become the “next industry standard”
– Decided by the Compact Modeling Council
– Not widely used yet, but will soon be
• Based on “charge-sheet modeling”
– i.e. it is based upon looking at the surface potential
• Physical Model
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Smoothing Function
• Modeling moderate inversion is hard
• Given strong-inversion and weak-inversion
models, how do we go between the two?
– i.e. How can best approximate moderate-inversion
operation?
•  Use a smoothing function that incorporates
both weak and strong inversion
– Only one side (e.g. weak inv.) is “revealed” under a
given set of biasing conditions
– EKV model is particularly suited to this approach
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EKV Model (Simplified)
Smoothing Function
 V V V
 V V V




K
  log 2 1  e 2U
I
2UT2 log 2 1  e 2U


2




g
T
s
g
T
x

2
2 
log 1  e 


when x<0
T
d




Interpolates smoothly between exponential and
quadratic relationship
I f  I 0e
Vg  1 Vb Vs  U T
where I 0 
when x>0
T
2U T2 Coxe V
T0
UT

K
2
Vg  1   Vb  VT  Vs 
If 
2
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Statistical Modeling
• Designs must be robust to process
variations (e.g. mismatch, variations in
doping, variations in Vdd, etc.)
• Many degrees of freedom and parameters
that can be varied
• Monte Carlo simulation is a popular choice
for statistical modeling
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Monte Carlo Simulation
• Define a given set of possible ranges for
parameters
– e.g. substrate doping, VT, Vdd
• Randomly pick a subset of the values
within the range
• Perform simulations
• Is design within tolerance?
– If YES – Done
– If NO – Modify design
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Corner Simulations (PVT Corners)
• Special case of Monte Carlo simulations
• Looking for the best and worst case
scenarios of varying parameters
• Vary 3 specific parameters
– Process
– Supply Voltage
– Temperature
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Process Variation
• Deviations in the fabrication process
• Examples include
–
–
–
–
–
Doping concentrations
Oxide thickness
Diffusion depths
W and L sizes
(Usually described as “fast” or “slow” transistors)
• Caused by non uniform conditions during
fabrication
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Supply Voltage Variation
• If Vdd changes, it could significantly alter
the performance of a circuit
– i.e. change current, gm, etc.
• Vdd could also vary by location on an IC
• Could significantly affect “overhead” and
power consumption
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Temperature Variation
• Temperature can change due to
– Environment
– Heat caused by other parts of the IC (i.e.
temperature gradients caused by self heating)
• As Temperature increases
– Mobility ↓
– VT↓
– UT↑
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