Time-dependent clustering model versus combination-based approach for BEOL/MOL and FEOL non-uniform dielectric breakdown: Similarities and disparities

Similarities and disparities between time-dependent clustering model and combination-based approach are thoroughly investigated. It is shown that two approaches can provide similar description of non-uniform dielectric breakdown provided that a dielectric system can be rigorously characterized by two random variables and input parameters verified from independent experiments as in the case of FEOL gate dielectrics. On the other hand, the notion of a single thickness for complicated dielectric systems with multiple random variables as in BEOL and MOL applications is shown to be questionable. As a result, a two-random variable combination-based approach is not necessarily correct to model non-uniform dielectric breakdown without rigorous justification. In contrast, time-dependent clustering model is based on the fundamental preservation of area scaling properties of failure percentiles and failure times, rendering a fundamentally new methodology to characterize non-uniform dielectric breakdown as technology variability issues continue to rise for modern technology nodes.