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A phenomenological-based virtual metrology (VM) technique is developed for predicting the silicon nitride film thickness in multi-layer plasma-enhanced chemical vapor deposition (PECVD). Particularly, the analysis of optical emission spectroscopy based on the excitation kinetics in nitrogen plasma is used to develop novel variables, named plasma-information (PI) variables. One variable, PIWall, is determined by analyzing the light transmittances of the nitrogen emissions at the contaminated window, representing the drift of reactor-wall condition. The other variable, PIVolume, is determined by analyzing vibrational distribution of N2( \textC^3 \Pi \text u , $\nu =0-4$ ) states, representing the drift of plasma density and temperature. These PI variables are applied as part of input variables of VM to improve the prediction accuracy. The partial least squares regression is adopted as the statistical method and the contribution of PI variables on the VM are evaluated through the variable influence evaluation on projection. It demonstrates the necessity of PI variables in VM for PECVD and the reactor-wall condition is a major cause of drift in PECVD. [ABSTRACT FROM AUTHOR]