Uncertainty quantification of machine learning models: on conformal prediction

Background: Machine learning is predicted to have an increasingly important role in semiconductor metrology. Prediction intervals that describe the reliability of the predictive performance of machine learning models are important to guide decision making and to improve trust in deep learning and other forms of machine learning and artificial intelligence. Image processing is an important application of artificial intelligence. Low-dose images from the scanning electron microscope (SEM) are often used for roughness measurements such as line edge roughness (LER) because of relatively small acquisition times and resist shrinkage, but such images are corrupted by noise, blur, edge effects, and other instrument errors. LER affects semiconductor device performance and the yield of the manufacturing process. Aim: We consider prediction intervals for the deep convolutional neural network EDGENet, which was trained on a large dataset of simulated SEM images and directly estimates the edge positions from a SEM rough line image containing an unknown level of Poisson noise. Approach: Conformal prediction is a relatively recent, increasingly popular, rigorously proven, and simple methodology to address this need for both classification and regression problems, and it does not use distributional assumptions such as Gaussianity or the Bayesian framework; one new variant combines it with another technique to generate prediction intervals known as quantile regression. Results: We illustrate the strengths and limitations of different conformal prediction procedures for the EDGENet approach to LER estimation. Combining these approaches into ensemble schemes and incorporating domain knowledge produces more informative prediction intervals. Conclusions: Deep learning models can help in the estimation of LER, but their acceptance has been hindered by a lack of trust in these techniques. Prediction intervals that provide coverage guarantees are an approach to alleviate this problem and may catalyze the transition within semiconductor manufacturing to a wider acceptance and implementation of machine learning.