State estimation in high-mix semiconductor manufacturing

Abstract

The traditional way of state estimation in semiconductor manufacturing, known as “threaded” state estimation, segregates the process data into different bins and uses the ones that match the current event of the specific context information (such as tools, layers, products) to update the process state. The limitation of threaded state estimation is that a narrowly defined process stream can result in too many different threads and insufficient data for each thread. This limitation becomes more severe in high-mix manufacturing, where there can be many products and many tools. Hence there is great interest in estimation methods that utilize all available data in the analysis. In this work, the characteristics inherent in state estimation of high-mix semiconductor manufacturing processes are analyzed, and a general framework is introduced for the non-threaded state estimation methods, i.e., state estimation without segregating the process data into different bins. The framework is based on the best linear unbiased estimate (BLUE) of a simplified stationary singular Gauss–Markov process, and non-threaded state estimation methods based on the Kalman filter, least squares and recursive least squares (RLS) are analyzed using the general framework. Simulation examples are presented to illustrate the equivalence between different algorithms. As real processes are rarely stationary, modifications to the Kalman filter and RLS are discussed. We show that in non-threaded state estimation, how to regulate the estimate covariance plays a significant role in estimation performance. To handle nonstationary disturbances that often occur in semiconductor processes, Bayesian-enhanced adaptive versions of the Kalman filter and RLS are proposed. Both simulated and industrial nonstationary processes are used to demonstrate the effectiveness of the proposed adaptive methods.