Application of statistical design and response surface methods to computer-aided VLSI device design II. Desirability functions and Taguchi methods

Methodology which incorporates the philosophy and methods of Taguchi is developed to address the issues of designing for manufacturability and sensitivity analysis. Specifically, the goal is to obtain responses (outputs) at or near required targets and to minimize output variability when the inputs are subject to manufacturing tolerances. The desirability functions, which generalize the notion of yield, are used to assess how close responses are to their targets. Manufacturing tolerances in the inputs are incorporated in the analysis by means of the expected loss of the desirability function which is estimated by a Taguchi outer array approach. The desirability expected loss is used to determine an optimum nominal input point to give responses close to target with small variability. The sensitivity of the various responses to the inputs is determined by an analytical method and an analysis of variance approach using a Taguchi outer array. The methods are applied to the optimization of a BIMOS NPN transistor