Achieving Uniformity in a Semiconductor Fabrication Process using Spatial Modeling

Abstract

Abstract Material is deposited onto the wafer surface during several steps of wafer fabrication. This material must be deposited evenly across the entire wafer surface, close to the targeted thickness, and with little wafer-to-wafer variability. But unequal variances across the wafer and under different process conditions, as well as nonstationary correlation across a wafer, make these goals difficult to achieve, because traditional methods for optimizing deposition processes assume homogeneity and independence. We avoid these assumptions and determine the best settings of process variables using physically motivated statistical models for the mean response, unequal variances, and nonstationary spatial correlation structure. Data from a rapid thermal chemical vapor deposition process is used to illustrate the approach. A simulation exercise demonstrates the advantages of fitting flexible variance models and using appropriate performance measures.