Statistical Analysis of Integrated Circuits Using Decoupled Polynomial Chaos

Abstract

One of the major tasks in electronic circuit design is the ability to predict the performance of general circuits in the presence of uncertainty in key design parameters. In the mathematical literature, such a task is referred to as uncertainty quantification. Uncertainty about the key design parameters arises mainly from the difficulty of controlling the physical or geometrical features of the underlying design, especially at the nanometer level. With the constant trend to scale down the process feature size, uncertainty quantification becomes crucial in shortening the design time. To achieve the uncertainty quantification, this thesis presents a new approach based on the concept of generalized Polynomial Chaos (gPC) to perform variability analysis of general nonlinear circuits. The proposed approach is built upon a decoupling formulation of the Galerkin projection (GP) technique, where the large matrix is transformed into a block-diagonal whose diagonal blocks can be factorized independently. The proposed methodology provides a general framework for decoupling the GP formulation based on a general system of orthogonal polynomials. Moreover, it provides a new insight into the error level that is caused by the decoupling procedure, enabling an assessment of the performance of a wide variety of orthogonal polynomials. For example, it is shown that, for the same order, the Chebyshev polynomials outperforms other commonly used gPC polynomials.