Statistics associated with spatial fault simulation used for evaluating integrated circuit yield enhancement

Clustered faults that affect the manufacture of integrated circuits are modeled by a simulation approach in which the fault formation is a function of time. In one such approach, the probability of generating a fault in a given subarea of an integrated circuit at any given time is assumed to depend on the number of faults already in that area and on the number of faults in the nearest-neighbor adjacent subareas. Although such procedures had been used heuristically, technical considerations show that this stochastic approach actually is analytically justifiable. It is found that the resulting distribution functions, the joint probability distribution function, the distribution function of the sum of dependent random variables, and the correlation between these variables are identical to results obtained with a large-area cluster model using compound Poisson statistics. This offers a unique insight into a statistical isomorphism that has been a puzzling issue