Prediction of plasma properties from optical emission spectra via machine learning-based inversion of the collisional-radiative model for Ar plasmas

In low-pressure plasma processing such as those used in semiconductor manufacturing, it is desirable to monitor plasma properties such as the electron density (n_e) and the electron energy distribution function (EEDF) during the manufacturing processes as such information can be used for precise control of the process conditions. However, typical plasma processing tools used for manufacturing lack standard plasma diagnostics systems except for optical emission detection, so the direct assessment of such plasma properties is essentially impossible. Therefore, in this study, we aim to extract as much plasma information as possible from the optical emission data. As one of the simplest systems, we considered Ar plasmas and modeled their optical emission spectra using a collisional-radiative model (CRM) [1,2] to relate n_e and EEDF to the optical emission spectra (OES). We then used different machine learning techniques to create an inverse model of the CRM and attempted to predict the n_e and EEDF from the normalized OES data (without information on the absolute values of emission intensities) and gas pressure as data easily measurable in experiments.[3] For example, we applied a genetic algorithm to invert the CRM directly and evaluated the possible n_e and EEDF from experimentally measured OES data of capacitively-coupled plasmas (CCP) and compared the results with those obtained from the corresponding simulations.[2] It was found that the inversion of the CRM could not predict the n_e and EEDF with high accuracy because the forward mapping of CRM from the n_e and EEDF to the OES was not “sufficiently” injective (i.e., one-to-one). Therefore, we applied additional information such as numerical simulation data to improve the accuracy of the inverse mapping of CRM.