Harmonics Analysis of the Electron Component of rf Bulk Plasmas. I. Theoretical Base

Abstract

Abstractrf 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. I n the first part a systern;itic 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 t o 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.

Time ‐ Dependent Multi ‐ Term Treatment of Plasma Electrons Acted upon by RF Electric Fields

“…Equations (11) and (14) represent a limit of the Fourier expansion treatment of the equation system (3ibc) in strict time-dependent two-term approximation, i.e. for 1 = 2, described in [34,35]. If the frequency vmd is formally assumed to be independent of the electron energy, equation (14) agrees with the well-known steady-state equation for the isotropic distribution which is obtained in the so-called effective field approximation [13, 151.…”