Electromigration in Nano-Interconnects: Determining Reliability Margins in Redundant Mesh Networks Using a Scalable Physical-Statistical Hybrid Paradigm

Abstract

This paper presents a hybrid modelling approach that combines physics-based electromigration modelling (PEM) and statistical methods to evaluate the electromigration (EM) limits of nano-interconnects in mesh networks. The approach, which is also compatible with standard Place and Route (P&R) tools and practises, takes into account the positive impact of network redundancy on EM current limits. The numerical simulations conducted in this study show that conventional methods underestimate the EM current limits of a power delivery network (PDN) unit-cell by 80% due to their lack of consideration for redundancy. Additionally, the time-to-failure (TTF) distributions of a PDN unit-cell obtained by the developed modelling framework adhered to a lognormal distribution, where the lognormal sigma, sigma logn, exhibits a 55% reduction compared to that of the single constituent interconnects. The study also found the negative voltage (i.e., ground or Vss) grid to be more susceptible to EM than the positive voltage, i.e.,