Field solver technologies for variation-aware interconnect parasitic extraction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 207-213).Advances in integrated circuit manufacturing technologies have enabled high density onchip integration by constantly scaling down the device and interconnect feature size. As a consequence of the ongoing technology scaling (from 45nm to 32nm, 22nm and beyond), geometrical variabilities induced by the uncertainties in the manufacturing processes are becoming more significant. Indeed, the dimensions and shapes of the manufactured devices and interconnect structures may vary by up to 40% from their design intent. The effect of such variabilities on the electrical characteristics of both devices and interconnects must be accurately evaluated and accounted for during the design phase. In the last few years, there have been several attempts to develop variation-aware extraction algorithms, i.e. algorithms that evaluate the effect of geometrical variabilities on the electrical characteristics of devices and interconnects. However, most algorithms remain computationally very expensive. In this thesis the focus is on variation-aware interconnect parasitic extraction. In the first part of the thesis several discretization-based variation-aware solver techniques are developed. The first technique is a stochastic model reduction algorithm (SMOR) The SMOR guarantees that the statistical moments computed from the reduced model are the same as those of the full model. The SMOR works best for problems in which the desired electrical property is contained in an easily defined subspace.(cont.) The second technique is the combined Neumann Hermite expansion (CNHE). The CNHE combines the advantages of both the standard Neumann expansion and the standard stochastic Galerkin method to produce a very efficient extraction algorithm. The CNHE works best in problems for which the desired electrical property (e.g. impedance) is accurately expanded in terms of a low order multivariate Hermite expansion. The third technique is the stochastic dominant singular vectors method (SDSV). The SDSV uses stochastic optimization in order to sequentially determine an optimal reduced subspace, in which the solution can be accurately represented. The SDSV works best for large dimensional problems, since its complexity is almost independent of the size of the parameter space. In the second part of the thesis, several novel discretization-free variation aware extraction techniques for both resistance and capacitance extraction are developed. First we present a variation-aware floating random walk (FRW) to extract the capacitance/resistance in the presence of non-topological (edge-defined) variations. The complexity of such algorithm is almost independent of the number of varying parameters. Then we introduce the Hierarchical FRW to extract the capacitance/resistance of a very large number of topologically different structures, which are all constructed from the same set of building blocks. The complexity of such algorithm is almost independent of the total number of structures. All the proposed techniques are applied to a variety of examples, showing orders of magnitude reduction in the computational time compared to the standard approaches. In addition, we solve very large dimensional examples that are intractable when using standard approaches.by Tarek Ali El-Moselhy.Ph.D

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System

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

Reducing power and increasing accuracy of on-body sensing in motion capture application.

Motion capture coupled with on-body sensing and biofeedback are key enabling technologies for assisted motor rehabilitation. However, wearability, power efficiency and measurement repeatability remain the principle challenges that need to be addressed before widespread adoption of such systems becomes possible. The weight and the size of the on-body sensing system needs to be kept small, and the system should not interfere with the user's movements or actions, but in general they are bulky due to their power consumption requirements. Furthermore, on-body sensors are very sensitive to positioning, which causes increased variability in the motion data. Isolating the characteristic patterns that represent the most important motion data affected by random positioning errors, while also reducing the power consumption, is the authors' main concern. An automated computational approach is considered to address the two problems. The use of functional principal component analysis is investigated for signal separation, whilst accounting for variability in the sensor position. To generate motion data, movements of human subjects and a robot arm are captured. As joint angles are considered in the analysis, the results are independent from the technology used to measure motion. The proposed post-processing technique can compensate for uncertainties due to sensor positional changes, whilst allowing greater energy efficiency of the sensors, thus enabling improved flexibility and usability of on-body sensing