Virtual Metrology for Multistage Processes Using Variational Inference Gaussian Mixture Model and Extreme Learning Machine

Virtual metrology (VM) is crucial for improving process capability and production yield during semiconductor manufacturing processes. However, the performance of VM deteriorates owing to the variable operating regime and the nonlinear characteristics of the process. Herein, Variational inference Gaussian mixture model (VIGMM) and extreme learning machine (ELM) are combined to solve these issues. First, variational inference is conducted on a Gaussian mixture model to determine the number of Gaussian components automatically and the corresponding operating regimes are identified. Subsequently, an extreme learning machine is developed for each operating regime to investigate the nonlinear relationship between process inputs and outputs. Finally, VM is implemented using the corresponding local ELM, which is determined based on the responsibility of the Gaussian components. The feasibility and effectiveness of the proposed methods are validated based on a numerical case and the plasma sputtering process for fabricating thin-film transistor liquid-crystal displays. The proposed VIGMM-ELM can serve as a VM algorithm for manufacturing processes with multiple stages.