Accurate Estimation of Signal Currents for Reliability Analysis Considering Advanced Waveform-Shape Effects

Abstract

In this work we propose an improved and efficient method for static estimation of average and root-mean-square currents used for electro migration (EM) reliability analysis. Significantly different from the state-of-the-art, the proposed method gives closed-form expressions for average and root mean-square currents in one complete cycle. The method, additionally, handles the asymmetric nature of the rise and fall current waveforms. We further present a detailed comparison of the proposed method with other conventional approaches and outline the inadequacies of using prevalent EM-severity metrics: either the net’s lumped capacitance or the net’s effective capacitance, along with the regular timing slew. As a correction, and, application of proposed method, we provide formulations for deriving the effective ‘EM’ slew, which can be used with conventional static approaches to accurately compute the currents. Additionally, unlike conventional understanding, for the first time, we note that not just the RMS current, but even the total charge transfer, and therefore the average current can also be dependent on the current waveform type and net’s electrical properties. We propose formulations to account for this behavior of average current. Finally, we share model validation results with respect to actual SPICE simulations from heavily loaded and/or high fan-out nets operating at high frequency from a production 40nm design. The method enables still higher performance of a design, which was otherwise optimized for an originally lower frequency target using conventional approaches.