Plasma etch process virtual metrology using aggregative linear regression

To enhance product quality semiconductor manufacturing industries are increasing the amount of metrology information collected during manufacturing processes. This increase in information has provided companies with many opportunities for enhanced process monitoring and control. However, the increase in information also posses challenges as it is quite common now to collect many more measurements than samples from a process leading to ill-conditioned datasets. Ill-conditioned datasets are very common in semiconductor manufacturing industries where infrequent sampling is the norm. It is therefore critical to be able to quantify virtual metrology models developed from such data sets. This paper presents an aggregative linear regression methodology for modeling that allows the generation of confidence intervals on the predicted outputs. The aggregation enhances the robustness of the linear models in terms of process variation and model sensitivity towards prediction. Also, to deal with the large number of candidate process variables, variable selection methods are employed to reduce the dimensionality and computational efforts associated with building virtual metrology models. In the paper three methods for variable selection are evaluated in conjunction with aggregative linear regression (ALR). The proposed methodology is tested on a benchmark semiconductor plasma etch process dataset and the results are compared with state-of-art multiple linear regression (MLR) and Gaussian Process Regression (GPR) VM models.