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Monte Carlo Analysis
Specifying Statistical Variations
The parameters LEFF, WEFF, and AEFF contain respectively the effective length, width, and
area of the capacitor. Indirectly, the expression of AEFF depends on the statistical variations of
the geometry. This will vary the effective area AEFF, and therefore will affect the effective
capacitance value.
Process Parameters and Geometrical Variations
The process parameters are given for the oxide thickness TOX and the geometrical variations
DL and DW. The nominal value for the oxide thickness is 19nm. The typical values for the
variations for DL and DW are fixed to 0.
The local variations of the oxide thickness have an area dependency:
In the netlist this matches the expression:
.PARAM DEV_MM_TOX = ’A_MM_TOX/SQRT(WDRAWN*LDRAWN)+B_MM_TOX’
where the two factors, A_MM_TOX and B_MM_TOX are defined for the statistical
distribution of oxide thickness. They are defined as constant terms:
• A_MM_TOX=0.4543U
• B_MM_TOX=0.1435
This equation relates the variance of the process parameter TOX to the inverse square root of the
area. The local variation decreases as the device size increases. Note that by contrast, the global
process variations are independent of the effective length L and width W.
This equation is based on the mismatch model proposed by Pelgrom: M.J.M. Pelgrom et. al.,
Matching Properties of MOS Transistors, IEEE Journal of Solid-State Circuits, Vol. 24, No. 5,
1989, pp. 1433-1439.
Local Mismatch Variations
The modeling of local mismatch variations can be done using a MOS device L, W, M by
accessing the EVAL() function: E(X1.M1,L) or EVAL(*,W).
Related Topics
Specifying Statistical Parameters
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Eldo® User's Manual, 15.3