Wafer quality monitoring using spatial Dirichlet process based mixed-effect profile modeling scheme

The objective of this work is to develop a profile-based statistical process control scheme for efficaciously monitoring wafer thickness profiles with non-normality in an industrial wafer slicing process. This is an important research area because the geometric quality of semiconductor wafers in a slicing process has a direct impact on the functional integrity of semiconductor parts and the efficiency of the production. Since non-normality in profiles indicates the existence of inter-cluster variations (i.e., the profiles cannot be represented by a single mean profile with normally-distributed random noise), it deteriorates the effectiveness of many traditional statistical process control methods with normality assumption. To realize the objective of this work, a mixed-effect profile monitoring (MEPM) scheme is proposed. The MEPM scheme adaptively groups profile data into clusters and models the inter-cluster variations, consequently, enabling a robust statistical process control scheme for detecting deviant profile data. Capturing the clustering information of the profile data leads to a deep understanding and an accurate modeling of the spatial data. It is a significant improvement over the current practice of monitoring the geometric product quality by summary quality features (such as total thickness variation) or by profiles neglecting inter-cluster variations. In this paper, the MEPM scheme is tested for detecting the out-of-control wafers from a wafer slicing process. Based on wafer thickness profiles, the MEPM scheme outperforms other benchmark methods and identifies the deviant wafers with low average type II error (missed detection rate) as 0.039. This profile monitoring scheme is extensible to geometrical quality assurance for products in other processes.