Uncertainty Quantification in Line Edge Roughness Estimation Using Conformal Prediction

Abstract

With its increasing pervasiveness across multiple industries, machine learning is expected to occupy greater significance in the semiconductor manufacturing industry. To foster trust and facilitate the adoption of machine-learning models, it is necessary to employ prediction intervals which summarize the performance and consistency of their predictions. Conformal prediction is a recent, and mathematically proven technique to approach prediction intervals for classification and regression problems. Unlike traditional approaches, conformal prediction does not require distributional assumptions such as Gaussianity. Furthermore, it can be combined with other techniques to yield a variety of interval predictions algorithms. We aim to illustrate the applications and performance of some of these methods on line edge roughness (LER) estimation. Experimental studies have shown that LER degrades the performance of semiconductor devices. While scanning electron microscope (SEM) is the method of choice for measuring LER, it is fraught with added uncertainty such as instrumental noise, edge effects, and Poisson noise. This work focuses on developing prediction intervals for LER estimates derived from EDGENet, which is a deep convolutional neural network trained on a large dataset of simulated SEM images. EDGENet was originally developed by our research group and directly outputs predictions of true edge positions from a corrupted SEM image.