An improved virtual metrology method in chemical vapor deposition systems via multitask gaussian processes and adaptive active learning

Chemical vapor deposition (CVD) has been widely applied to create thin films in semiconductor manufacturing. Virtual metrology (VM) can assist the quality prediction in CVD based on control variables and preceding metrology results. However, the multitask learning problem and limited labeled data from available real metrology are challenges for VM modeling. Accordingly, this paper presents the improved method to combine multitask Gaussian process (MTGP) and adaptive active learning (AAL) for the VM modeling in CVD systems. Initially, a multitask Gaussian processes-based virtual metrology (MTGPVM) model is built based on the intrinsic coregionalization model (ICM). Subsequently, active learning methods based on different sampling criteria are improved to address the limited training data issue. Furthermore, an adaptive algorithm is promoted to update the VM model according to the temporary performance of active learning. Finally, the evaluation of the proposed methods was carried out using the practical dataset in a factory. The proposed MTGPVM achieved prediction performance with 1.44-1.79% mean-absolute-percentage error (MAPE) in thickness and 0.39-0.49% MAPE in refractive index. The proposed AAL algorithm can enhance the learning accuracy of the MTGPVM model with a small sample size.