Cross entropy minimization for efficient estimation of SRAM failure rate

As the semiconductor technology scales down to 45nm and below, process variations have a profound effect on SRAM cells and an urgent need is to develop fast statistical tools which can accurately estimate the extremely small failure probability of SRAM cells. In this paper, we adopt the Importance Sampling (IS) based information theory inspired Minimum Cross Entropy method, to propose a general technique to quickly evaluate the failure probability of SRAM cells. In particular, we first mathematically formulate the failure of SRAM cells such that the concept of `Cross Entropy Distance´ can be leveraged, and the distance between the ideal distribution for IS and the practical distribution for IS (which is used for generating samples), is well-defined. This cross entropy distance is now minimized resulting in a simple analytical solution to obtain the optimal practical distribution for IS, thereby expediting the convergence of estimation. The experimental results of a commercial 45nm SRAM cell demonstrate that for the same accuracy, the proposed method yields computational savings on the order of 17~50X over the existing state-of-the-art techniques.