광학 임계 치수의 베이지안 추론을 위한 대체 모형 기반 Metropolis-Hastings 알고리즘 적용

In semiconductor manufacturing, it is important to rapidly estimate the values of the line widths or height, called the critical dimension (CD), of a nanoscale structure. In this paper, we consider the optical CD measurement that is designed to figure out CD values by comparing a given measured spectrum with calculated spectra from a simulation model. The main problem of this study is to identify the posterior distributions of the CD values using Bayesian inference with high computational efficiency in the optical CD measurement. The delayed acceptance Metropolis-Hastings algorithm (DAMH) uses a surrogate model in the proposal distribution to avoid unnecessary computations within the Metropolis-Hastings algorithm. We introduced a single-layered Bayesian neural network as a surrogate model and then implemented the DAMH algorithm with the model to identify the posterior distributions of the CD values of the 2-dimensional high-aspect-ratio structure in semiconductor manufacturing. We applied the DAMH algorithm and a basic Metropolis–Hastings algorithm to the case study and obtained numerical results showing that the DAMH algorithm significantly improves computational efficiency while maintaining the same level of accuracy as a basic Metropolis-Hastings algorithm.