Abstract

No abstract

Increased variability of process parameters and recent progress in statistical static timing analysis make extraction of statistical characteristics of process variation and spatial correlation an important yet challenging problem in modern chip designs. Unfortunately, existing approaches either focus on extraction of only a deterministic component of spatial variation or do not consider actual difficulties in computing a valid spatial correlation function and matrix, simply ignoring the fact that not every function and matrix can be used to describe the spatial correlation. Based upon the mathematical theory of random fields and convex analysis, in this paper, we develop (1) a robust technique to extract a valid spatial correlation function by solving a constrained nonlinear optimization problem; and (2) a robust technique to extract a valid spatial correlation matrix by employing a modified alternative projection algorithm. Our novel techniques guarantee to extract a valid spatial correlation function and matrix that are closest to measurement data, even if those measurements are affected by unavoidable random noises. Experiment results based upon a Monte-Carlo model confirm the accuracy and robustness of our techniques, and show that we are able to recover the correlation function and matrix with very high accuracy even in the presence of significant random noises.

Chips manufactured in 90 nm technology have shown large parametric variations, and a worsening trend is predicted. These parametric variations make circuit optimization difficult since different paths are frequency-limiting in different parts of the multi-dimensional process space. Therefore, it is desirable to have a new diagnostic metric for robust circuit optimization. This paper presents a novel algorithm to compute the criticality probability of every edge in the timing graph of a design with linear complexity in the circuit size. Using industrial benchmarks, we verify the correctness of our criticality computation via Monte Carlo simulation. We also show that for large industrial designs with 442,000 gates, our algorithm computes all edge criticalities in less than 160 seconds.