Elements of Statistical SPICE Models

We discuss several elements of statistical SPICE models and present our solutions. We present (i) a solution of automatically detecting Monte Carlo vs. skewed simulations, (ii) a method of modeling an arbitrarily given asymmetric or symmetric distribution, (iii) a hierarchical structure of the skewing parameters of many process/device statistical distributions for skewed simulations, (iv) a technique of combining chip-mean and across-chip variations for a single model parameter, (v) a method of correctly combining a chipmean variation and an across-chip variation which is characterized as a percentage, and (vi) a method of enabling Monte Carlo simulations of across-chip variations at a skew corner of the chip-mean variations. These solutions establish a solid foundation for a good statistical SPICE model.