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Monte Carlo Analysis
Statistical Variations
Statistical Variations
How statistical models are specified depends in general on the foundries. They define to place
the most appropriate distributions on parameters within their PDK model files.
Statistical models are generally written as functions of both process parameters and geometrical
parameters.
• Process parameters
These parameters determine the behavior of the instantiated devices, such as junction
depths, sheet resistances, dielectric thickness and doping levels.
• Geometric layout parameters
Device length and width, and more specific parameters related to the layout.
Specifying Statistical Variations
In statistical modeling, the variations in parameter P are formulated as either relative or
absolute. Some physical quantities such as mobility, sheet resistances, dielectric thicknesses and
doping concentrations have their variations directly in a relative sense:
In this case, the models use the percentage value δP = ΔP/P typ in the definition of parameters,
and P = P typ (1 + δP).
There are parameters for which this model does not apply. Geometrical variations will have
their variations in the absolute sense:
For example, the following statements define a gaussian distribution on the TOX parameter in a
relative sense:
.PARAM A_MM_TOX=0.4543U B_MM_TOX=0.1435
+ DEV_MM_TOX = ’A_MM_TOX/SQRT(WDRAWN*LDRAWN)+B_MM_TOX’
.PARAM TOX = TOX_TYP DEV/GAUSS={DEV_MM_TOX}%
The standard deviation of the Gaussian distribution is specified with the percent % character.
Eldo® User's Manual, 15.3 423