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

Incorporating virtual metrology (VM) into run-to-run(R2R) control enables the benefits of R2R control to be maintainedwhile avoiding the negative cost and cycle time impactsof actual metrology. Due to the potential for prediction errorsfrom VM models, the prediction as well as the correspondingconfidence information on the predictions should be properlyconsidered in VM-enabled R2R control schemes in order toguarantee control performance. This paper proposes the use ofGaussian process regression (GPR) models in VM-enabled R2Rcontrol due to their ability to provide this information in anintegrated fashion. The mean value of the GPR prediction istreated as the VM value and the variance of the GPR predictionis used as a measure of confidence to adjust the coefficient ofan exponentially-weighted-moving-average (EWMA) R2R controller.The effectiveness of the proposed GPR VM-enabled R2Rcontrol approach is demonstrated using a chemical mechanicalpolishing process case study. Results show that better controlperformance is achieved with the proposed methodology thanwith implementations that do not take prediction reliability intoaccount.