A virtual metrology method with prediction uncertainty based on Gaussian process for chemical mechanical planarization

Abstract

The prediction of the average material removal rate (MRR) in chemical mechanical planarization (CMP) process has been recognized to be a critical factor of virtual metrology (VM) modeling for advanced process control (APC). This paper proposes a Gaussian process regression (GPR)-based model to dynamically predict MRR in CMP process. The proposed method uses K-nearest neighbor (KNN) to search for reference MRR samples in the historical dataset. Furthermore, a GPR model is trained to fuse the information from reference samples. Finally, the proposed method employs multi-task Gaussian process (MTGP) to predict the final MRR and quantify the prediction uncertainty based on the historical and the reference MRR. Compared with other methods in the recent literature, the proposed method, named KNN-MTGP model, yields better prediction accuracy than ensemble models, and comparable accuracy with deep neural networks (NN). Besides, KNN-MTGP model is capable to demonstrate the behavior of the past MRR changing with time and provide quantified prediction uncertainties. In this paper, the feasibility and advantages of KNN-MTGP model are evaluated based on the dataset of 2016 prognostic and health management (PHM) data challenge.