Computing parametric yield adaptively using local linear models

Abstract

A divide and conquer algorithm for computing the parametric yield of large analog circuits is presented. The algorithm targets applications whose performance spreads could be highly nonlinear functions of a large number of stochastic process disturbances, and therefore can not easily be modeled by traditional response surface methods. The work addresses difficulties with modeling by adaptively constructing the model piece by piece, namely, by efficiently and recursively partitioning the disturbance space into several regions, each of which is then modeled by a local linear model. Local linear models are used because they are less sensitive to dimension than polynomial models. Moreover, the resulting model can be made to be more accurate in some regions compared to others. The number of simulations required in statistical modeling can therefore be reduced since only critical regions, which define the boundary of the feasible region in the space of process disturbances, are modeled highly accurately. The resulting models are then used as cheap surrogates for circuit simulation in Monte Carlo estimation of the parametric yield. Examples indicate the efficiency and accuracy of this approach.