Characteristics of a plasma information variable in phenomenology-based, statistically-tuned virtual metrology to predict silicon dioxide etching depth

A phenomenology-based virtual metrology (VM) for monitoring SiO2 etching depth was proposed by Park (2015). It achieved high prediction accuracy by introducing newly developed plasma information (PI) variables as designated inputs, called PI-VM. The PI variables represent the state of the plasma, the sheath, and the target during the process. We investigate how a PI variable can help to improve prediction accuracy of VM and how it plays a special role in the statistical selection. We choose only PIEEDF among the three PI variables to focus on the investigation. The PIEEDF is determined from the ratio of line-intensities of optical emission spectroscopy. We apply Pearson's correlation filter (PCF), principal component analysis (PCA), and stepwise variable selection (SVS) as statistical selection methods on the variables set including PIEEDF or not. Multilinear regression is used to model the VM. This study reveals that PIEEDF variable is a good variable in terms of independence from other input variables and explanatory power for an output variable. Especially, VM using SVS method applied to variable sets including PIEEDF achieves the highest accuracy, comparable to Park's PI-VM. This study shows that PIEEDF variable is particularly useful for monitoring of the fine variations in semiconductor manufacturing process and it also extends the utilization of OES sensor data.