Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects
主 题: Stochastic Collocation Method for Variation-Aware Capacitance Extraction of Interconnects
报告人: 朱恒亮 博士(复旦大学)
时 间: 2010-12-29 上午10:00-11:00
地 点: 理科一号楼1303
Parasitic extraction of interconnects, which is one of the key techniques for ULSI (Ultra Large Scale Integration) circuit design, aims to model the interconnects by a RLC (Resistance, Inductance and Capacitance) equivalent circuit. Methods for parasitic extraction are generally based on the PEEC formulation proposed by Ruehli in 1974, and can be further categorized as capacitance extraction methods based on EQS (Electric-Quasi-Static) assumption, inductance extraction methods based on MQS (Magnetic-Quasi-Static) assumption and impedance extraction methods based on EMQS (Electric-Magnetic-Quasi-Static) assumption. From mathematical viewpoint, all of these methods are numerical IE (Integral Equation) approaches for solving Maxwell equations. Charges, distributed on the surface of conductors, and currents, distributed inside the conductors, are generally used as the unknowns of the equation. As the ULSI technology reaches 65nm and beyond, the shape of interconnects is no longer deterministic and becomes stochastic. Integral Equation problems become Stochastic Integral Equation problems for parasitic extraction as random fields are applied to model these geometric variations. For solving such Stochastic Integral Equation problems, Stochastic Collocation Method is applied. In this talk, we will use examples of capacitance extraction to demonstrate the Stochastic Collocation Method from several aspects, including how to simplify the random filed model of stochastic variations by finding the dominating random dimensions of the problem, how to model the capacitance parameters of interconnects by general Polynomial Chaos expansion, and how to avoid the exponential increase in computation complexity w.r.t. the dimensionality by introducing the Sparse Grids. Numerical results will also be provided to illustrate the efficiency and accuracy of Stochastic Collocation Method.
