eldo_user

Monte Carlo Analysis
Importance Sampling Monte Carlo Examples
Importance Sampling Monte Carlo Examples
The sample netlists monte_carlo_sram_bitcell.cir and monte_carlo_vco_lc_tank.cir can be
used to demonstrate the advantages of the IMSC method over the standard Monte Carlo
method.
SRAM Bit Cell Circuit
Netlist file: monte_carlo_sram_bitcell.cir
The sample circuit is a classic six-transistor SRAM bit cell designed in CMOS 45nm. A subset
of the device model parameters has variability information, in the form of a DEV/GAUSS
specification. The total number of statistical parameters is 36 (6 per device). Although the
IMSC method is insensitive to the number of statistical parameters, it is always preferable to
keep this number “reasonable”.
The cell is configured for measuring the write delay, and the purpose of the Monte Carlo
simulation is to estimate the probability of the write delay exceeding a certain threshold. This
threshold could be used to define a “fail” behavior for yield estimation. Formally, the problem is
to estimate π = Pr{Y > y} and the associated confidence interval on (the empirical estimator
of π), where y is the threshold.
The following .EXTRACT MC … MCROB() statement is given in the netlist:
.EXTRACT MC LABEL=prob_plus_6 MCPROB(write_delay_qx, GE, 53.12)
This statement illustrates how to use the .EXTRACT and MCPROB commands to specify this
kind of probability estimation problem: refer to (usually) another .EXTRACT or .MEAS
statement, specify a right tail (upper threshold) or a left tail (lower threshold), then specify the
threshold. The following results are obtained:
Lower Pr. Value Upper CV(%) #Runs Speedup
Tail / Complementary
-----------------------------------------------------------------------------
8.89e-06 9.65e-06/1.00e+00 1.04e-05 7.87 8060 8.0e+03
This kind of low probability estimation is very difficult (if not impossible) using the standard
Monte Carlo method because a very large number of runs is required to obtain a decent
accuracy (in terms of the confidence interval on the probability). In this example, the ISMC
method estimates a probability of 9.6×10 −6 to within +/-7.8% (with a 95% confidence level) in
roughly 8,000 runs, whereas the standard Monte Carlo method would require roughly
64,000,000 runs (see Table 11-1).
The estimation of the speedup of the ISMC method over the standard Monte Carlo method
comes from the binomial law. The random variable:
528
Eldo® User's Manual, 15.3