A New Sampling Technique for Monte Carlo-based Statistical Circuit Analysis

Variability is a fundamental issue which gets exponentially worse as CMOS technology shrinks. Therefore, characterization of statistical variations has become an important part of the design phase. Monte Carlo-based simulation method is a standard technique for statistical analysis and modeling of integrated circuits. However, crude Monte Carlo sampling based on pseudo-random selection of parameter variations suffers from low convergence rates and thus, providing high accuracy is computationally expensive. In this work, we present an extensive study on the performance of two widely used techniques, Latin Hypercube and Low Discrepancy sampling methods, and compare their speed-up and accuracy performance properties. It is shown that these methods can exhibit a better efficiency as compared to the pseudo-random sampling but only in limited applications. Therefore, we propose a new sampling scheme that exploits the benefits of both methods by combining them. Through a representative example, it is shown that the proposed sampling technique provides significant improvement in terms of computational efficiency and offers better properties as compared to each solely.