Gaussian Process Regression for Virtual Metrology-enabled Run-to-Run Control in Semiconductor Manufacturing

Abstract

Incorporating virtual metrology (VM) into run-to-run (R2R) control enables the benefits of R2R control to be maintained while avoiding the negative cost and cycle time impacts of actual metrology. Due to the potential for prediction errors from VM models, the prediction as well as the corresponding confidence information on the predictions should be properly considered in VM-enabled R2R control schemes in order to guarantee control performance. This paper proposes the use of Gaussian process regression (GPR) models in VM-enabled R2R control due to their ability to provide this information in an integrated fashion. The mean value of the GPR prediction is treated as the VM value and the variance of the GPR prediction is used as a measure of confidence to adjust the coefficient of an exponentially weighted-moving-average R2R controller. The effectiveness of the proposed GPR VM-enabled R2R control approach is demonstrated using a chemical mechanical polishing process case study. Results show that better control performance is achieved with the proposed methodology than with implementations that do not take prediction reliability into account.