Optical emission spectroscopy-based estimation of plasma parameters with ensemble Kalman filtering

Low-temperature plasmas (LTPs) are extensively used in industrial processes to modify surface properties for various applications, including semiconductor etching and thin film deposition. Optical emission spectroscopy (OES) is a valuable non-intrusive diagnostic tool for these plasmas, due to the abundance of optical transitions resulting from the numerous excited states present in LTPs. However, the interpretation of the OES data can be challenging as the electron energy distribution functions (EEDFs) may be non-Maxwellian and optical emissions occur only at specific wavelengths. This work introduces a novel computational approach that merges a zero-dimensional, global, collisional radiative (CR) model with time-dependent experimental OES data. This integrated framework allows for the simultaneous estimation of multiple plasma parameters, including those that are challenging to measure directly. In particular, we utilize the ensemble Kalman filtering approach in an argon plasma across a range of conditions to obtain accurate estimates of parameters such as electron temperature, electron density, and the electron energy distribution function exclusively from experimentally observed optical transition data. In addition, our Bayesian approach quantifies the uncertainty in parameter estimates, highlighting those parameters most sensitive to experimental noise and potentially requiring refined modeling.