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In this paper, we propose a new spatial temperature aware transient EM induced stress analysis method. The new method consists of two new contributions: First, we propose a new TM-aware void saturation volume estimation method for fast immortality check in the post-voiding phase for the first time. We derive the analytic formula to estimate the void saturation in the presence of spatial temperature gradients due to Joule heating. Second, we developed a fast numerical solution for EM-induced stress analysis for multi-segment interconnect trees considering TM effect. The new method first transforms the coupled EM-TM partial differential equations into linear time-invariant ordinary differential equations (ODEs). Then extended Krylov subspace-based reduction technique is employed to reduce the size of the original system matrices so that they can be efficiently simulated in the time domain. The proposed method can perform the simulation process for both void nucleation and void growth phases under time-varying input currents and position-dependent temperatures. The numerical results show that, compared to the recently proposed semi-analytic EM-TM method, the proposed method can lead to about 28x speedup on average for the interconnect with up to 1000 branches for both void nucleation and growth phases with negligible errors. 

Electromigration (EM) is still the most important reliability concern for VLSI systems, especially at the nanometer regime. EM immortality check is an important step for full-chip EM signoff analysis. In this paper, we propose a new electromigration (EM) immortality check method for multi-segment interconnect considering the impacts of Joule heating induced temperature gradient. Temperature gradients from metal Joule heating, called thermal migration, can be a significant force for the metal atomic migrations, and these impacts get more significant as technology scales down. Compared to existing methods, the new method can consider the spatial temperature gradient due to Joule heating for multi-segment wires for the first time. We derive the analytic solution for the resulting steady-state EM-thermal migration stress distribution problem. Then we develop the new temperature-aware voltage-based EM immortality check method considering the multi-segment temperature migration effects, which carries all the benefits of the recently proposed voltage-based EM immortality method for multi-segment interconnects. Numerical results on an IBM power grid and self synthesized power delivery networks show that the proposed temperature-aware EM immortality check method is much more accurate than recently proposed state of the art EM immortality method.