Premium
Harmonics Analysis of the Electron Component of rf Bulk Plasmas. I. Theoretical Base
Author(s) -
Voigt H.D.,
Wilhelm J.,
Winkler B.
Publication year - 1990
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.2150300507
Subject(s) - harmonics , distribution function , plasma , fourier transform , computational physics , fourier series , physics , fourier analysis , boltzmann equation , electron , momentum (technical analysis) , ordinary differential equation , collision frequency , balance equation , mechanics , materials science , differential equation , computer science , mathematical analysis , thermodynamics , quantum mechanics , mathematics , markov model , finance , voltage , machine learning , markov chain , economics
rf discharges are increasingly used in low pressure plasma processing, i.e. for etching, film deposition and sputtering. The modelling of such discharges is a very complex task, especially dependent on discharge conditions, however of large importance for the insight into the main physical processes and thus for their control to improve the final results. One main important aspect is the determination of the electron velocity distribution function and of relevant rate and transport coefficients. The paper contributes to the treatment of this problem. In the first part a systematic Fourier expansion of the kinetic equation and of the consistent particle, energy and momentum balance equation is described. Then, a mathematical analysis of the resulting ordinary differential equation system for the coefficients of the Fourier expansion is performed. Based upon this we succeeded to develop a numerical approach to calculate the physical relevant solution of this system. By this approach in addition to the harmonics of the distribution function that of relevant macroscopic quantities, as transport coefficients and collision frequencies, can be determined. In the second part of this paper this method will be applied to investigate the bulk plasma of a rf discharge in molecular hydrogen.