eldo_user

Monte Carlo Analysis
Monte Carlo Basic Features
* Example of Monte Carlo analysis with a swept parameter.
* Extract the leakage current of a BSIM4 device. The manufacturing
* process introduces statistical variation in the threshold voltage.
.MODEL N NMOS LEVEL=60 VTH0=250m DEV/GAUSS=5%
M1 D G 0 0 N W=1u L=65n
VD D 0 2
VG G 0 PVG
.DC
.EXTRACT DC LABEL=ID ID(M1)
* Specify Monte Carlo analysis and request statistical outputs.
.MC 1000 NBINS=60 DATAFLOW=1 PRINT_TEST_AP=1 PRINT_MOMENTS=1
* Sweep the voltage applied to the gate from 2V to 0V.
.PARAM PVG=2
.STEP PARAM PVG LIST 2 1 0.4 0.35 0.3 0.1 0
.END
In this example, Eldo will perform 7 separate Monte Carlo analyses and generate files
example_1.mcm, example_2.mcm, …, example_7.mcm containing statistical information about
the output measure ID (the leakage current of M1) for PVG=2, PVG=1, …, PVG=0
respectively. In particular, each .mcm file contains an estimate of the skewness of the
distribution of ID:
PVG Output File Skewness of ID
2 example_1.mcm 6.26×10 -2
1 example_2.mcm 5.86×10 -2
0.4 example_3.mcm 2.98×10 -2
0.35 example_4.mcm 3.31×10 -1
0.3 example_5.mcm 7.30×10 -1
0.1 example_6.mcm 1.40
0 example_7.mcm 1.42
The distribution of ID is almost normal for PVG=2 to PVG=0.4, but as PVG approaches 0 the
distribution of ID becomes log-normal.
In addition to affecting the input and output sample distributions, the values of circuit
parameters and the circuit’s configuration can affect the convergence rate of the Monte Carlo
algorithm. This means that the quality of the statistical results may vary as the circuit varies. In
the above example, the coefficient of variation for ID (at 95%) ranges from 0.408% to 2.756%
as PVG is swept from 2 to 0. By increasing the number of runs per Monte Carlo analysis to
10000, this range can be improved to 0.013%–0.888%. However, the disadvantage of uniformly
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Eldo® User's Manual, 15.3