Interconnect Lifetime Prediction with Temporal and Spatial Temperature Gradients for Reliability-Aware Design and Runtime Management: Modeling and Applications

Thermal effects are becoming a limiting factor in high performance circuit design due to the strong temperature dependence of leakage power, circuit performance, IC package cost and reliability. While many interconnect reliability models assume a constant temperature, this paper analyzes the effects of temporal and spatial thermal gradients on interconnect lifetime in terms of electromigration. For temporal thermal variations, we present a physics-based dynamic model for estimating interconnect lifetime for any time-varying temperature/current profile, and this model returns reliability equivalent temperature and current density that can be used in traditional reliability analysis tools. For spatial temperature gradients, we give close bounds in terms of uniformly distributed temperatures to estimate the lifetime of interconnects subject to non-uniform temperature distribution. Our results are verified with numerical simulations and reveal that blindly using the maximum temperature leads to very inaccurate or too pessimistic lifetime estimation. In fact, our dynamic model reveals that when the temporal temperature variation is small, average temperature (instead of worst-case temperature) can be used to accurately predict interconnect lifetime. Therefore, our results not only increase the accuracy of reliability estimates, but they also enable designers to reclaim design margin in reliability-aware design. In addition, our dynamic reliability model is useful for improving the performance of temperature-aware dynamic runtime management by modeling reliability as a resource to be consumed at a stress-dependent rate. This report supersedes TR CS-2005-10.