Uwe Höckele

Regression Methods for Virtual Metrology of Layer Thickness in Chemical Vapor Deposition

The quality of wafer production in semiconductor manufacturing cannot always be monitored by a costly physical measurement. Instead of measuring a quantity directly, it can be predicted by a regression method (virtual metrology). In this paper, a survey on regression methods is given to predict average silicon nitride cap layer thickness for the plasma-enhanced chemical vapor deposition dual-layer metal passivation stack process. Process and production equipment fault detection and classification data are used as predictor variables. Various variable sets are compared: one most predictive variable alone, the three most predictive variables, an expert selection, and full set. The following regression methods are compared: simple linear regression, multiple linear regression, partial least square regression, and ridge linear regression utilizing the partial least square estimate algorithm, and support vector regression (SVR). On a test set, SVR outperforms the other methods by a large margin, being more robust toward changes in the production conditions. The method performs better on high-dimensional multivariate input data than on the most predictive variables alone. Process expert knowledge used for a priori variable selection further enhances the performance slightly. The results confirm earlier findings that virtual metrology can benefit from the robustness of SVR, an adaptive generic method that performs well even if no process knowledge is applied. However, the integration of process expertise into the method improves the performance once more.

Regression methods for prediction of PECVD Silicon Nitride layer thickness

Different approaches for the prediction of average Silicon Nitride cap layer thickness for the Plasma Enhanced Chemical Vapor Deposition (PECVD) dual-layer metal passivation stack process are compared, based on metrology and production equipment Fault Detection and Classification (FDC) data. Various sets of FDC parameters are processed by different prediction algorithms. In particular, the use of high-dimensional multivariate input data in comparison to small parameter sets is assessed. As prediction methods, Simple Linear Regression, Multiple Linear Regression, Partial Least Square Regression, and Ridge Linear Regression utilizing the Partial Least Square Estimate algorithm are compared. Regression parameter optimization and model selection is performed and evaluated via cross validation and grid search, using the Root Mean Squared Error. Process expert knowledge used for a priori selection of FDC parameters further enhances the performance. Our results indicate that Virtual Metrology can benefit from the usage of regression methods exploiting collinearity combined with comprehensive process expert knowledge.