Failure analysis of MIM and MIS structures using spatial statistics

Within the wide variety of statistical techniques used to characterize the occurrence of failure events in metal-insulator-metal (MIM) and metal-insulator-semiconductor (MIS) structures, there is one that has received particular attention in recent years because of its relevance in oxide reliability analysis. Spatial statistics is a specialized branch of statistics aimed to summarize information about the spatial location of entities in 1, 2 and 3 dimensions. Since it has been shown that a device can still be operative after one or several breakdown events, it is of interest to investigate whether temporal and spatial correlations can occur among failure events. In this paper, the attention will be exclusively focused on the spatial aspect of the problem, with special emphasis on detecting departures from homogeneity. Two cases will be analyzed in which the failure events become visible on the top electrode as a 2D point pattern. These patterns can be assessed using a number of spatial statistical tools such as the intensity plot, the interevent distance histogram, the pair correlation function and residual analysis.