Statistical Parameter Identification of Analog Integrated Circuit Reverse Models

We solve the manufacturing problem of identifying the model statistical parameters ensuring a satisfactory quality of analog circuits produced in a photolithographic process. We formalize it in a statistical framework as the problem of inverting the mapping from the population of the circuit production variables to the performances' population. Both variables and performances are random. From a sample of the joint population we want to identify the statistical features of the former producing a performance distribution that satisfies the design constraints with a good preassigned probability. The key idea of the solution method we propose consists of describing the above mapping in terms of a mixture of granular functions, where each is responsible for a fuzzy set within the input-output space, hence for a cluster therein. The way of synthesizing the whole space as a mixture of these clusters is learnt directly from the examples. As a result we have an analytical form both of the mapping approximating complex Spice models in terms of polynomials in the production variables, and of the distribution law of the induced performances that allows a relatively quick and easy management of the production variables' statistical parameters as a function of the probability with which we plan to satisfy the design constraint. We apply the method to case studies and real production data where our method outperforms current methods' running times and accuracies.