An efficient method for analyzing on-chip thermal reliability considering process variations

Abstract

This work provides an efficient statistical electrothermal simulator for analyzing on-chip thermal reliability under process variations. Using the collocation-based statistical modeling technique, first, the statistical interpolation polynomial for on-chip temperature distribution can be obtained by performing deterministic electrothermal simulation very few times and by utilizing polynomial interpolation. After that, the proposed simulator not only provides the mean and standard deviation profiles of on-chip temperature distribution, but also innovates the concept of thermal yield profile to statistically characterize the on-chip temperature distribution more precisely, and builds an efficient technique for estimating this figure of merit. Moreover, a mixed-mesh strategy is presented to further enhance the efficiency of the developed statistical electrothermal simulator. Experimental results demonstrate that (1) the developed statistical electrothermal simulator can obtain accurate approximations with orders of magnitude speedup over the Monte Carlo method; (2) comparing with a well-known cumulative distribution function estimation method, APEX [Li et al. 2004], the developed statistical electrothermal simulator can achieve 215× speedup with better accuracy; (3) the developed mixed-mesh strategy can achieve an order of magnitude faster over our baseline algorithm and still maintain an acceptable accuracy level.