Optical diagnostics for the highly populated tail of an electron energy distribution function in very-high-frequency capacitively coupled plasma using spin- and dipole-forbidden lines

Abstract

A novel method is proposed to determine an electron energy distribution function (EEDF) that includes the highly populated tail originated by energetic beam-like electrons (>20 eV), which often occur in narrow gap, very-high-frequency capacitively coupled plasma (VHF-CCP). This method combines conventional Langmuir probe analysis to represent the EEDF in the low-energy regime and the line-ratio method taken from the optical emission spectrum to represent the highly populated tail of the EEDF. Here the emission lines are chosen with consideration of the excitation rates, which are a function of the shape of the cross-section of the spin- and dipole-forbidden states of an argon atom and the EEDF at corresponding energy. In this method, the analytical EEDF model is chosen for the composition of the Maxwellian for low-energy (bulk) electrons, and Schulze’s time-averaged form of the shifted Maxwellian (Schulze et al 2008 J. Phys. D: Appl. Phys. 41 042003) is chosen for the highly populated tail of the EEDF. The variables of the time-averaged form of the shifted Maxwellian, the fraction and mean energy of the beam-like electrons, are determined using an emission model of line-intensity ratios, which describes the line-intensities as a function of the EEDF. This method is advantageous for the diagnostics of a time-averaged EEDF with a highly populated tail, especially where this is due to beam-like electrons that originate from stochastic heating, compared to a two-temperature EEDF.