Trace rare gases optical emission spectroscopy: Nonintrusive method for measuring electron temperatures in low-pressure, low-temperature plasmas

Abstract

Trace rare gases optical emission spectroscopy (TRG-OES) is a new, nonintrusive method for determining electron temperatures ${(T}_e)$ and, under some conditions, estimating electron densities ${(n}_e)$ in low-temperature, low-pressure plasmas. The method is based on a comparison of atomic emission intensities from trace amounts of rare gases (an equimixture of He, Ne, Ar, Kr, and Xe) added to the plasma, with intensities calculated from a model. For Maxwellian electron energy distribution functions (EEDFs), $T_e$ is determined from the best fit of theory to the experimental measurements. For non-Maxwellian EEDFs, $T_e$ derived from the best fit describes the high-energy tail of the EEDF. This method was reported previously, and was further developed and successfully applied to several laboratory and commercial plasma reactors. It has also been used in investigations of correlations between high-$T_e$ and plasma-induced damage to thin gate oxide layers. In this paper, we provide a refined mechanism for the method and include a detailed description of the generation of emission from the Paschen $2p$ manifold of rare gases both from the ground state and through metastable states, a theoretical model to calculate the number density of metastables ${(n}_m)$ of the rare gases, a practical procedure to compute $T_e$ from the ratios of experimental-to-theoretical intensity ratios, a way to determine the electron density ${(n}_e),$ a discussion of the range of sensitivity of TRG-OES to the EEDF, and an estimate of the accuracy of $T_e.$ The values of $T_e$ obtained by TRG-OES in a transformer-coupled plasma reactor are compared with those obtained with a Langmuir probe for a wide range of pressures and powers. The differences in $T_e$ from the two methods are explained in terms of the EEDF dependence on pressure.