Non-Maxwellian electron energy distribution function in a pulsed plasma modeled with dual effective temperatures

Abstract

A non-Maxwellian electron energy distribution function (EEDF) has been modeled within a pulsed rf inductively coupled plasma source with the aid of experimental emission spectra and Ar metastable measurements obtained by laser diode absorption. The lower energy portion of the EEDF up to the first excited state energy of 11.5 eV for argon was accurately measured with a Langmuir probe and satisfactorily modeled with a generalized two-parameter expression. Above 11.5 eV, though, inelastic collisions caused the EEDF to deviate from the lower energy generalized expression and soon after, the energy limit of accuracy of the Langmuir probe was approached. In this work, a unique EEDF model was applied for electron energies above 11.5 eV that accounts for spectral effects due to both direct excitation from the Ar ground state and step-wise excitation from the metastable state. Previously tabulated optical cross sections were used with experimental data to simulate the optical emission spectra using a theoretical non-Maxwellian EEDF with dual effective electron temperatures; one for energies below 11.5 eV and one for above. The parameters of the high energy portion of the EEDF were adjusted to produce a least squares fit to up to 10 emission peaks in the 415–428 nm range. The fits provided practical agreement with experimental spectra using the dual effective temperature EEDF. Comparisons were made for the model fitting 10 emission peaks compared to a method of analyzing only the relative intensities of 2 closely spaced emission lines: the 420.1 nm to 419.8 nm line ratio.