Determination of the electron energy distribution function in weakly ionized plasma by means of a Langmuir probe and numerical methods

Abstract

Numerical methods are used to determine the Electron Energy Distribution Function (EEDF) from I(V) probe characteristics, which are measured using a cylindrical Langmuir probe in the case of weakly ionized plasmas. This task becomes difficult when measurement is complicated by the presence of an external magnetic field or in high pressure plasma because of collision between electrons and heavy particles within the sheath formed around the probe tip. In this case, the electron current must be calculated using the Swift law instead of the Langmuir law. The numerical methods consist of determining the derivative functions of the I(V) probe characteristics in the case of a noisy signal and correcting the EEDF taking into account the electron diffusion coefficient within the sheath formed around the probe collector. Algorithms are given to detail the methods step by step, which can be used to write homemade codes. The methods are tested in the case of different plasma reactors described in the literature, such as microwave plasma and rf (radio-frequency) and dc (direct current) plasma reactors working at different pressures with or without magnetic field. The results show the effect of pressure or magnetic field on the I(V) probe characteristics because of the change in the electron diffusion coefficient.