Statistical Performance Modeling and Optimization

Abstract

As IC technologies scale to finer feature sizes, it becomes increasingly difficult to control the relative process variations. The increasing fluctuations in manufacturing processes have introduced unavoidable and significant uncertainty in circuit performance; hence ensuring manufacturability has been identified as one of the top priorities of today's IC design problems. In this paper, we review various statistical methodologies that have been recently developed to model, analyze, and optimize performance variations at both transistor level and system level. The following topics will be discussed in detail: sources of process variations, variation characterization and modeling, Monte Carlo analysis, response surface modeling, statistical timing and leakage analysis, probability distribution extraction, parametric yield estimation and robust IC optimization. These techniques provide the necessary CAD infrastructure that facilitates the bold move from deterministic, corner-based IC design toward statistical and probabilistic design.

Enhanced-Precision LHSMC of Electrical Circuit Considering Low Discrepancy

“…Process variations can be classified into the following categories, depending on their physical range on a die or wafer [8]:…”

Indirect performance sensing for on-chip analog self-healing via Bayesian model fusion

“…First, the Gaussian distribution pdf(α NEW,k ) is peaked at its mean value α NEW,k = α OLD,k , implying that the old coefficient α OLD,k and the new coefficient α NEW,k are likely to be similar. In other words, since the Gaussian distribution pdf(α NEW,k ) exponentially decays with (α NEW,k − α OLD,k ) 2 , it is unlikely to observe a new coefficient α NEW,k that is extremely different from the old coefficient α OLD,k . Second, the standard deviation of the prior distribution pdf(α NEW,k ) is proportional to |α OLD,k |.…”

Timing Analysis Techniques Review for sub-30 nm Circuit Designs

“…This is often tackled by performing Monte Carlo (MC) SPICE simulations, requiring significant computing and time resources. MC simulations attempt to estimate the probability distribution of the performance of circuits via three steps [1]:…”

“…To improve the manufacturability and yield of designs, various analyses and simulation techniques are used at each design level. However, there are still many problems that need to be solved [1]. For example, transistor-level simulations using a SPICE-like engine can be used to analyze circuit blocks such as standard library cells, analog memory blocks, and interconnect wires.…”