EMSpice: Physics-Based Electromigration Check Using Coupled Electronic and Stress Simulation

GridNet

“…Recently, Sun et al [27] proposed a full-chip EM-induced IR drop analysis, which considers dynamic interplay between the hydrostatic stress and electronic current/voltage in a power grid network. This method solves the coupled time-varying partial di erential equations in time domain accurately and obtains the stress evolution in multi-segment interconnect trees.…”

“…In this section, we brie y review the coupled electronic and stress analysis method on the full-chip power grid EM check, EMspice [3,27], which represents the latest development for EM-induced IR drop analysis. This method is used for the baseline for the proposed IR-drop incremental prediction method.…”

“…Note that C, A matrices dependent on wire structures are time-independent in the coupled equation. Such coupled analysis on long target lifetime can be extremely time consuming for very large power grid networks [27]. As a result, it is indeed necessary to build a fast EM-induced IR drop estimation for incremental wire changes for IR drop ECO process.…”

“…In the past few years, research e orts focusing on so-called physicsbased EM analysis tool for power grid network analysis method have been explored [9,10,12,27]. However, all those methods need to solve the partial di erential equations (PDE) of hydrostatic stress in the multi-segment interconnect wires.…”

“…However, all those methods need to solve the partial di erential equations (PDE) of hydrostatic stress in the multi-segment interconnect wires. Due to the interplay between the stress and IR drops, a coupled time-varying EM and IR drop analysis is needed for accurate EM-induced time-varying IR drop analysis [27], which is very expensive (even without EM analysis) for full-chip PDN analysis.…”