Uncertainty Quantification of Electronic and Photonic ICs with Non-Gaussian Correlated Process Variations

TL;DR

This paper introduces a novel, efficient generalized polynomial chaos method to accurately quantify uncertainties in electronic and photonic integrated circuits with non-Gaussian correlated variations, significantly outperforming Monte Carlo simulations.

Contribution

It extends polynomial chaos to handle non-Gaussian correlations using smooth basis functions and scalable tensor methods for high-dimensional problems.

Findings

Outperforms Monte Carlo by 2500-3000 times in efficiency.

Accurately predicts multi-peak output density functions.

Validates approach on ICs with 19 to 57 correlated parameters.

Abstract

Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners. This paper propose a rigorous and efficient solution to address the challenge of non-Gaussian correlation. We first extend generalized polynomial chaos, and propose a class of smooth basis functions to efficiently handle non-Gaussian correlations. Then, we consider high-dimensional parameters, and develop a scalable tensor method to compute the proposed basis functions. Finally, we develop a sparse solver with adaptive sample selections to solve high-dimensional uncertainty quantification problems. We validate our theory and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. The results show that our approach outperforms Monte Carlo by $2500\times$ to $3000\times$ in terms of efficiency. Moreover, our method can accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which is hard to handle by existing methods. Based on the results in this paper, many novel uncertainty quantification algorithms can be developed and can be further applied to a broad range of engineering domains.