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 model parameters to the population of the performances. Both parameters and performances are random. From a sample of the latter population we want to identify the statistical features of the former that produce a performance distribution complying with production samples. The key artifact 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 of the mapping that approximates complex Spice models in terms of polynomials in the model parameters, and an implicit expression of the distribution law of the induced performances that allows a relatively quick and easy management of the model distribution statistical parameters. This flows into a semiautomatic procedure managing an adaptive composition of different granular modules to cope with the circuit peculiarities. We check the method both on real world manufacturing problems and on ad hoc benchmarks.