Problems of Yield Gradient Estimation for Truncated Probability Density Functions

In this paper theoretical possibilities of statistical yield gradient estimation are discussed for those cases where circuit element probability density functions are truncated or nondifferantible, with a uniform distribution being a special case. With the yield gradient information available, the efficient derivative methods of yield optimization can be used. General derivative formulas are developed and their intuitive and geometric interpretations are given. Relationship between the yield derivatives and the marginal density functions of "pass" (or "fail") points is shown. Two possible algorithms for yield derivative estimation are discussed. The theory developed is also used to provide insight into some other methods of yield optimization.