Wafer-Level Characteristic Variation Modeling Considering Systematic Discontinuous Effects

Abstract

Statistical wafer-level characteristic variation modeling offers an attractive method for reducing the measurement cost in large-scale integrated (LSI) circuit testing while maintaining test quality. In this method, the performance of unmeasured LSI circuits fabricated on a wafer is statistically predicted based on a few measured LSI circuits. Conventional statistical methods model spatially smooth variations in the wafers. However, actual wafers can exhibit discontinuous variations that are systematically caused by the manufacturing environment, such as shot dependence. In this paper, we propose a modeling method that considers discontinuous variations in wafer characteristics by applying the knowledge of manufacturing engineers to a model estimated using Gaussian process regression. In the proposed method, the process variation is decomposed into systematic discontinuous and global components to improve estimation accuracy. An evaluation performed using an industrial production test dataset indicates that the proposed method effectively reduces the estimation error for an entire wafer by over 36% compared with conventional methods.