Numerical queue solution of thermal noise-induced soft errors in subthreshold CMOS devices

Power consumption requirements drive CMOS scaling to ever lower supply voltages, reducing the stability margin with respect to thermal noise and raising the probability for thermally-induced soft errors. Given the long time scale of noise-induced soft errors, conventional Monte Carlo simulations cannot be used to predict error rates and alternative approaches are needed. In this paper, the analysis of thermal fluctuations in a CMOS flip-flop is performed using a 2D queue that maps the available configurations for the flip-flop in terms of electron populations on the two inverters, with the two stable logic states at the opposite corners of the 2D matrix. Trial simulations for model systems show that the thermally-induced logic transitions involve only a limited number of states immediately above and below the main diagonal of the full 2D queue. We present a numerical solution based on variable precision arithmetic for a truncated 2D queue consisting of a variable number of near-diagonal states. It is shown that increasing the width of the near-diagonal queue, an accurate solution for the error rate is asymptotically obtained without the need to consider the full 2D queue. Our approach is used to calculate the mean time to failure of flip-flops built in a 45-nm fully-depleted silicon-on-insulator (FD-SOI) technology modeled in the subthreshold regime, including parasitics. As a predictive tool, the framework can be used to investigate the thermal stability of devices built in future technologies and as a measure of device reliability in VLSI design.