Application of Gaussian processes with variable shrinkage method and just-in-time modeling in the semiconductor industry

In semiconductor manufacturing, as some of the variables in processes cannot be easily measured during or after the production, virtual metrology (VM) is employed to predict metrology outputs using ancillary process variables. However, because of changeable processes and high-dimensional inputs, VM can be expensive or difficult to implement. In this work, just-in-time (JIT) modeling is used to cope with changes in process characteristics and to automatically update the statistical model. In addition, owing to the non-uniform data distribution, Gaussian process regression (GPR) as a probabilistic approach is a typical method to enhance the robustness of the system in the probability density space. With high-dimensional input variables in deposition processes, a variable shrinkage and selection method for GPR is proposed. It is superior to the conventional methods. The features of the proposed method are shown by way of illustrative examples and the proposed method is compared to conventional work based on real semiconductor process data.