Non-derivative design centering algorithm using trust region optimization and variance reduction

Abstract

Fluctuations in manufactured integrated circuit parameters may dramatically reduce the parametric yield. Yield maximization can be formulated as an unconstrained optimization problem in nominal parameter values, which is known as design centering. The high expense of yield evaluations, the absence of any gradient information, and the presence of some numerical noise obstruct the use of the traditional derivative-based optimization methods. In this article, a novel design centering algorithm is presented, which consists of a non-derivative unconstrained optimizer coupled with a variance reduction estimator. The used optimizer combines a trust region mechanism with quadratic interpolation and provides efficient use of yield evaluations. The stratified sampling technique is used to develop a lower variance yield estimator that reduces the number of circuit simulations required to reach a desired accuracy level. Numerical and practical circuit examples are used to demonstrate the efficiency of the proposed algorithm with respect to other methods in the same field.

Statistical design centering of RF cavity linear accelerator via non-derivative trust region optimization

“…The yield integral cannot be evaluated analytically, since it requires the evaluation of n dimensional integral over a 'nonexplicitly defined' region [11]. Instead, it can be estimated using any statistical approach.…”

A new hybrid method for optimal circuit design using semi-definite programming

“…The production yield cannot be evaluated analytically, since it requires the evaluation of ndimensional integral over a 'non-explicitly defined' region (Hassan et al 2006). However, it can be estimated using the Monte-Carlo method (Metropolis and Ulam 1949) for example.…”

“…In general, there are two approaches for yield optimization. The first approach is a statistical approach (Singhal and Pinel 1981, Hocevar et al 1984, Hassan et al 2006. In this approach, the yield function is optimized directly through estimating its values.…”

EM-based yield optimization exploiting trust-region optimization and space mapping technology

“…These approaches have fast convergence for convex and small dimensional problems. Statistical approaches, conversely, optimize the yield function in a straightforward way, regardless the size of the problem or its convexity . Hybrid methods, combining both approaches, may also be used for solving such problems.…”

“…To simulate these statistical fluctuations, circuit parameters are assumed to be random variables with a joint probability density function (PDF) p ( x , x 0 ), where is the vector of nominal parameter values. Therefore, the yield Y can be defined as the probability of satisfying the design specifications . …”