Functional Kernel-Based Modeling of Wavelet Compressed Optical Emission Spectral Data: Prediction of Plasma Etch Process

This study reports the use of a kernel-based process model, consisting of kernel partial least squares regression and kernel ridge regression, to model etch rate and uniformity in a plasma etch process. In order to characterize the plasma etch process, a 2^{4 - 1} fractional factorial design was implemented on the process parameters: CHF₃ flow rate, CF₄ flow rate, RF power, and pressure. In this modeling, both functional data and in situ optical emission spectroscopy (OES) data associated with the etch response were used to formulate the model. In an effort to effectively deal with the complexity of the data, wavelet transformation with vertical-energy-thresholding (VET) shrinkage procedures were used to reduce the dimensions of the functional data. In addition, a Bayesian information criterion (BIC) was used to select the best subset to improve the model predictions. The proposed kernel-based approaches were evaluated by comparing them to conventional neural networks (NNs)-based modeling and linear-based regression techniques. Comparisons revealed that the proposed approach exhibits an improved prediction over NNs and linear-based models. Implicated in the study is a detection of process fault patterns by combining the kernel-based modeling, wavelet transformation with VET, and BIC.