Data-Driven Yield Estimation and Maximization Using Bayesian Optimization Under Uncertainty

In this paper, we propose a novel method which utilizes samples of measured product quality characteristics to efficiently estimate the probabilities of those quality characteristics being within the desired specifications and, consequently, the process yield. Specifically, when dealing with 1D Gaussian distributions, we formally prove that the proposed yield estimator asymptotically gives a lower Mean Squared Error compared to the best unbiased estimator. In order to enable maximization of yield, this novel estimator is incorporated into the framework of Bayesian Optimization which iteratively seeks controllable tool parameters under which the outgoing product yield is maximized. The newly proposed yield maximization method is demonstrated in an application involving high-fidelity simulations of a reactive ion etch chamber, a tool component commonly used in semiconductor manufacturing. The aim of these simulations was to rapidly and reliably determine tool parameters that maximize the probability of delivering desired plasma density characteristics under stochastic variations in chamber conditions. The novel yield estimation and optimization methods show superiority when the number of experimental observations is limited and the distributions of outgoing product characteristics can be approximated well by a Gaussian distribution.