On the Construction of Distribution-Free Prediction Intervals for an Image Regression Problem in Semiconductor Manufacturing

Abstract

The high-volume manufacturing of the next generation of semiconductor devices requires advances in measurement signal analysis. Many in the semiconductor manufacturing community have reservations about the adoption of deep learning; they instead prefer other model-based approaches for some image regression problems, and according to the 2021 IEEE International Roadmap for Devices and Systems (IRDS) report on Metrology a SEMI standardization committee may endorse this philosophy. The semiconductor manufacturing community does, however, communicate a need for state-of-the-art statistical analyses to reduce measurement uncertainty. Prediction intervals which characterize the reliability of the predictive performance of regression models can impact decisions, build trust in machine learning, and be applied to other regression models. However, we are not aware of effective and sufficiently simple distribution-free approaches that offer valid coverage for important classes of image data, so we consider the distribution-free conformal prediction and conformalized quantile regression framework. The image regression problem that is the focus of this paper pertains to line edge roughness (LER) estimation from noisy scanning electron microscopy images. LER affects semiconductor device performance and reliability as well as the yield of the manufacturing process; the 2021 IRDS emphasizes the crucial importance of LER by devoting a white paper to it in addition to mentioning or discussing it in the reports of multiple international focus teams. It is not immediately apparent how to effectively use normalized conformal prediction and quantile regression for LER estimation. The modeling techniques we apply appear to be novel for finding distribution-free prediction intervals for image data and will be presented at the 2022 SEMI Advanced Semiconductor Manufacturing Conference.