Reduction of EEDF Measurement Distortion in Regularized Solutions of the Druyvesteyn Relation

Abstract

Electron energy distribution function (EEDF) extraction from Langmuir probe data is an ill-posed problem due to the integral relationship between electron current and probe voltage. Both curve fitting of experimental data and reconstruction of the integral problem through methods, such as Tikhonov regularization, address this to some measure, with regularized solutions offering an advantage in overall EEDF accuracy over curve fitting. Although Tikhonov regularization provides a more accurate estimation of EEDF overall energy space, it typically also can distort the overall shape of the reconstructed distribution, particularly at high energies and energies below the distribution peak. This, combined with the relative ease of use that simple data smoothing algorithms provide, has limited the use of the more advanced reconstruction algorithms in EEDF analysis. In this paper, we will shed some light on these limitations and offer an alternative method to overcome these limitations.