Yield and variability optimization of integrated circuits : principles and practical solutions

Vita.This dissertation deals with both theoretical and practical aspects of integrated circuits (IC's) statistical design. It stresses and explains that the essential difference between IC statistical design and discrete circuit statistical design lies in basic statistical features of two types of circuits. The main emphasis of the research is placed on principles and practical solutions for performance variability minimization rather than manufacturing yield enhancement alone. A variability gradient formula applicable to a general IC statistical model is first developed, which leads to understanding of the nature of IC variability minimization problem, forms a theoretical basis for the possibility of IC variability minimization, and clarifies the principles of variability minimization and performance tuning. A two-stage strategy, based on separate performance variability minimization and separate performance tuning, is proposed. Practical results show that the two-stage procedure leads to small variability, small "bias", and high yield. The use of Orthogonal Array based design of experiments is advocated for exploring the effects of circuit variables on circuit performances, which aims at eliminating noncritical circuit parameters in order to reduce problem dimension. Several design plans are considered for a variety of applications. The level 3 main effect Orthogonal Array design approach is used for statistical gradient estimation and applied together with the Stochastic Approximation method to yield optimization. Taguchi experiments are used to explore the interactions of designable circuit parameters and noise factors, leading to efficient estimation of gradient of variability, and gradient of the mean, in order to identify the parameters essential for variability minimization and performance tuning. The mathematical model corresponding to Taguchi experiments is also studied. The worst-case measure is considered as another measure of performance variability. It is of great importance for digital delay circuits. Mathematical interpretations are provided to bridge the gap between variability minimization and worst-case measure reduction, and make the underlying principles and methods for variability minimization equally applicable to the worst-case measure reduction. The research also goes one step further by using fuzzy set theory as a framework to handle statistical optimization with multiple circuit performances