High-Dimensional Uncertainty Quantification of Electronic and Photonic IC With Non-Gaussian Correlated Process Variations

Abstract

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters are mutually independent or Gaussian correlated, which is rarely true in real applications. For instance, in chip manufacturing, many process variations are actually correlated. Recently, some techniques have been developed to handle non-Gaussian correlated random parameters, but they are timeconsuming for high-dimensional problems. We present a new framework to solve uncertainty quantification problems with many non-Gaussian correlated uncertainties. Firstly, we propose a set of smooth basis functions to well capture the impact of non-Gaussian correlated process variations. We develop a tensor approach to compute these basis functions in a highdimension setting. Secondly, we investigate the theoretical aspect and practical implementation of a sparse solver to compute the coefficients of all basis functions. We provide some theoretical analysis for the exact recovery condition and error bound of this sparse solver in the context of uncertainty quantification. We present three adaptive sampling approaches to improve the performance of the sparse solver. Finally, we validate our methods by synthetic and practical electronic/photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. Our approach outperforms Monte Carlo by thousands of times in terms of efficiency. It can also accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which are hard to capture by existing methods.Index Terms-High dimensionality, uncertainty quantification, electronic and photonic IC, non-Gaussian correlation, process variations, tensor, sparse solver, adaptive sampling.

Chance-Constrained and Yield-Aware Optimization of Photonic ICs With Non-Gaussian Correlated Process Variations

“…If the parameters ξ are non-Gaussian correlated, the computation is more difficult. In such cases, Ψ α (ξ) can be constructed by the Gram-Schmidt approach in [28], [29] or the Cholesky factorization in [45], [46]. The main difficulty lies in computing high order moments of ξ, which can be well resolved by the functional tensor train approach proposed in [46].…”

A Perturbative Stochastic Galerkin Method for the Uncertainty Quantification of Linear Circuits

“…where φ kj is a polynomial of degree k j . For non-standard distributions, including dependent or correlated ones, suitable orthonormal polynomials can be numerically constructed using a Gram-Schmidt orthogonalization [24] or Cholesky decomposition [25]. In (3), k is a positive integer that maps to a vectorial multi-index element k = (k 1 , .…”

Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

“…to the distribution of the uncertain parameters [1], thus enabling a precise uncertainty quantification in terms of statistical moments and distribution functions. The PCE framework became widely popular also in the field of electrical engineering [2], e.g., to investigate the impact of process variations in large-scale integration circuits [3]- [17]. The available techniques can be subdivided into two classes: intrusive ones [3]- [8], chiefly…”