Reference-based Virtual Metrology method with uncertainty evaluation for Material Removal Rate prediction based on Gaussian Process Regression

The prediction of average Material Removal Rate (MRR) in Chemical Mechanical Planarization (CMP) process is regarded as a crucial research objective of Virtual Metrology (VM) for semiconductor manufacturing. In this paper, a novel VM model is proposed to predict MRR in CMP process based on the integration of Gaussian Process Regression (GPR) with a reference-based strategy. The proposed method estimates the similarity of the changing trends of the sensor traces using Maximum Mean Discrepancy (MMD) as a metric to extract reliable references for further prediction. The temporal information is also combined in the strategy by filtering the data samples by timestamps. Afterwards, GPR is used to fuse the reference data samples to predict the metrology with a confidence interval. Compared with the benchmarks in the recent literature, the proposed method, referred as MMD-GPR model, gives better prediction performance than ensemble learning methods and equivalent accuracy compared with Deep Neural Networks (DNN) but with a more efficient framework.