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, σlogn, 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., Vdd grid. In the examined grid unit-cell design, both the number of interconnect sites prone to voiding and also the magnitude of the peak tensile stress within the nano-interconnects were found to be two times as high in the Vss case compared to Vdd. The lognormal sigma of TFF for the grid unit-cells, σlogn−tile, show a marked reduction compared to the lognormal sigma of the constituent single interconnects, σlogn, with a 50% and 66% decrease compared to single interconnects, for downstream (Vss) and upstream (Vdd), respectively. In addition, σlogn−tile was three times higher for downstream (Vss) compared to upstream (Vdd), whilst, in contrast, this difference was only 2-fold at the single interconnect level. TTF50% was predicted to be 4.13-fold higher at the grid unit-cell level for the upstream compared to downstream operation, which was also more pronounced than in the single interconnect level where the difference was only 2-fold. This research provides valuable insights into the EM ageing of nano-interconnects in mesh networks and could pragmatically enhance the accuracy of EM compliance evaluation methods.