Gaussian process modeling for engineered surfaces with applications to Si wafer production

When producing engineered surfaces, the stochastic portion of the processing greatly affects the overall output quality. We propose a Gaussian process model that accounts for the impact of control variables on the stochastic elements of the produced surfaces. An optimization algorithm is outlined to find the maximum likelihood estimates of the model parameters. A case study involving the thickness surfaces of semiconductor wafers is examined that demonstrates the need for the proposed approach.