Correlation analysis of particle clusters on integrated circuit wafers

Defect clustering results in correlations between the numbers of defects or faults that occur on integrated circuit chips located adjacent to one another on semiconductor wafers. Until now, it has been believed that correlations of this type were not accounted for in existing yield models. It is shown in this paper that such correlations are present in yield models based on mixed or compound Poisson statistics. A quadrat analysis of particle distributions on semiconductor wafers is used to compare data and theory. The results show that the theoretical correlation coefficients are in agreement with the experimental ones. It was also determined from the particle data how these correlation coefficients vary as the distance between quadrats is increased. This variation provides a convenient method for determining the cluster dimensions.