Uncertainty quantification for integrated circuits: Stochastic spectral methods

Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the application of conventional stochastic Galerkin and stochastic collocation schemes to nonlinear circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.MIT Masdar Program (196F/002/707/102f/70/9374

An Efficient Method for Chip-Level Statistical Capacitance Extraction Considering Process Variations with Spatial Correlation

An efficient method is proposed to consider the process variations with spatial correlation, for chip-level capacitance extraction based on the window technique. In each window, an efficient technique of Hermite polynomial collocation (HPC) is presented to extract the statistical capacitance. The capacitance covariances between windows are then calculated to reflect the spatial correlation. The proposed method is practical for chip-level extraction task, and the experiments on full-path extraction exhibit its high accuracy and efficiency

Variational capacitance modeling using orthogonal polynomial method

ABSTRACT In this paper, we propose a novel statistical capacitance extraction method for interconnects considering process variations. The new method, called statCap, is based on the spectral stochastic method where orthogonal polynomials are used to represent the statistical processes in a deterministic way. We first show how the variational potential coefficient matrix is represented in a first-order form using Taylor expansion and orthogonal decomposition. Then an augmented potential coefficient matrix, which consists of the coefficients of the polynomials, is derived. After that, corresponding augmented system is solved to obtain the variational capacitance values in the orthogonal polynomial form. Experimental results show that our method is two orders of magnitude faster than the recently proposed statistical capacitance extraction method based on the spectral stochastic collocation approac

A stochastic collocation method combined with a reduced basis method to compute uncertainties in numerical dosimetry

International audienceIn this paper, a reduced basis method is introduced to deal with a stochastic problem in a numerical dosimetry application in which the field solutions are computed using an iterative solver. More precisely, the computations already performed are used to build an initial guess for the iterative solver. It is shown that this approach reduces significantly the computational cost with the same accuracy

A Stochastic Collocation Method Combined With a Reduced Basis Method to Compute Uncertainties in Numerical Dosimetry

International audienceA reduced basis method is introduced to deal with a stochastic problem in a numerical dosimetry application in which the field solutions are computed using an iterative solver. More precisely, the computations already performed are used to build an initial guess for the iterative solver. It is shown that this approach significantly reduces the computational cost

Robust simulation methodology for surface-roughness loss in interconnect and package modelings

In multigigahertz integrated-circuit design, the extra energy loss caused by conductor surface roughness in metallic interconnects and packagings is more evident than ever before and demands explicit consideration for accurate prediction of signal integrity and energy consumption. Existing techniques based on analytical approximation, despite simple formulations, suffer from restrictive valid ranges, namely, either small or large roughness/frequencies. In this paper, we propose a robust and efficient numerical-simulation methodology applicable to evaluating general surface roughness, described by parameterized stochastic processes, across a wide frequency band. Traditional computation-intensive electromagnetic simulation is avoided via a tailored scalar-wave modeling to capture the power loss due to surface roughness. The spectral stochastic collocation method is applied to construct the complete statistical model. Comparisons with full wave simulation as well as existing methods in their respective valid ranges then verify the effectiveness of the proposed approach. © 2009 IEEE.published_or_final_versio