A failure rate based methodology for determining the maximum operating gate electric field, comprehending defect density and burn-in

We develop a new and accurate methodology for determining the maximum allowed operating gate electric field E/sub max/. It is based on achieving a failure rate requirement throughout the required product lifetime. The method is general, and rigorously comprehends the field dependence, an arbitrary defect density tail; and burn-in. We demonstrate the power of this technique with the first systematic study of the impact of defect density tail shape and field dependence on E/sub max/. The defect density tail slope s/sub d/ determines distinctly different behavior depending on whether s/sub d/<1 or s/sub d/>1. Of greatest significance, we show that in general it is not possible, a priori, to determine whether a desired operating field is safe or not. This uncertainty arises primarily because we cannot know the behavior of the defect density tail below some practical observable lower limit of the cumulative failure distribution function F. This uncertainty must be comprehended in the risk management associated with decisions to increase E/sub op/.