A Big-Data Approach to Handle Many Process Variations: Tensor Recovery and Applications

TL;DR

This paper introduces a tensor recovery-based high-dimensional uncertainty quantification method that significantly reduces computational complexity in modeling process variations in nano-scale integrated circuits, MEMS, and photonic devices.

Contribution

It presents a novel tensor recovery algorithm with sparse and low-rank constraints to efficiently handle over 50 random parameters, overcoming the curse of dimensionality.

Findings

Reduces simulation samples from billions to hundreds.

Successfully applied to ICs, MEMS, and photonic devices with many parameters.

Outperforms traditional stochastic collocation methods in high-dimensional settings.

Abstract

Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique to quantify the uncertainties caused by process variations. Despite their superior efficiency over Monte Carlo for many design cases, these algorithms suffer from the curse of dimensionality; i.e., their computational cost grows very fast as the number of random parameters increases. In order to solve this challenging problem, this paper presents a high-dimensional uncertainty quantification algorithm from a big-data perspective. Specifically, we show that the huge number of (e.g., $1.5 \times 10^{27}$) simulation samples in standard stochastic collocation can be reduced to a very small one (e.g., $500$) by exploiting some hidden structures of a high-dimensional data array. This idea is formulated as a tensor recovery problem with sparse and low-rank constraints; and it is solved with an alternating minimization approach. Numerical results show that our approach can simulate efficiently some ICs, as well as MEMS and photonic problems with over 50 independent random parameters, whereas the traditional algorithm can only handle several random parameters.