Monte Carlo analysis is a procedure to assess manufacturing yields by repeating simulation runs with varying applied random variations to component parameters.
Sensitivity analysis repeats runs while perturbing a single parameter for each step. This allows the sensitivity to that parameter of any number of measurements to be evaluated. This makes it possible to identify components and parameters that may require a tight tolerance to maintain a particular specification, or in some cases identify instabilities in the design.
Worst-case analysis attempts to find the combination of component and parameter variances which will lead to the worst possible result. It assigns each component or parameter with a value that is either at the positive extreme or the negative extreme. The decision as to which to use is obtained from the results of a prior sensitivity analysis using the sign of each sensitivity value.
Both Monte Carlo and worst-case may be used to assess production yield and reliability. For many applications, Monte Carlo produces the most realistic results but rarely locates the extremes that are theoretically possible even if statistically unlikely.
It should be noted that worst-case analysis is not guaranteed to locate the worst possible result. The algorithm assumes that the relationship between component or parameter variation and the measured result is linear. This is almost never the case in practice.
The implementation of these analysis modes in SIMetrix has been designed to be quick to set up for simple cases while still providing the required flexibility for more advanced requirements as might be required for integrated circuit design.
SIMetrix offers a high-degree of flexibility for tolerance specification. It is possible, for example, for different model parameters to be dependent on a single random variable. This makes it possible to model the fact that a number of model parameters might be dependent on a single physical characteristic, for example, the base width of a bipolar transistor. Of course, lot tolerances are also implemented accounting for the matching of devices in integrated circuits and other multiple components built onto a common substrate. However, in many products, lot tolerances can only be applied to the same type of device. In SIMetrix it is possible to model parametric relationships between different types of device which occur in integrated circuits but which are rarely taken into account.
As well as conventional multiple step Monte Carlo, sensitivity and worst-case analyses, single step sweeps may also be performed. These are available for the four swept modes, .AC, .DC, .NOISE and .TF. For example, a Monte Carlo analysis of the DC offset voltage of an amplifier can be performed using a single run of .DC using a special sweep mode. This is dramatically faster than the alternative of repeated .OP runs. This type of analysis can also be used to analyse the gain of an amplifier at a single frequency using .AC or .TF or even the noise, again at a single frequency, using .NOISE.
For sensitivity analysis, each point of an AC,DC, Noise or TF analysis would be a single perturbation case. This swept mode may be used, for example to find the sensitivity of an amplifier at a specified single frequency in a single run. For large circuits which have thousands of parameters, this can make sensitivity analysis practical when otherwise it might not be.
Note that the sensitivity analysis described in this chapter is not the same as the .SENS DC sensitivity analysis. .SENS perturbs every parameter in the circuit and uses an approximate matrix based algorithm to determine DC sensitivity only.
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