Material dependent modeling of secondary electron emission coefficients and its effects on PIC/MCC simulation results of capacitive RF plasmas

Abstract

The ion-induced secondary electron emission coefficient (γ) is a vital parameter in the modeling of low temperature RF plasmas. Often, the value of γ drastically affects the electron power absorption dynamics, the plasma parameters and the quality of the separate control of ion flux and mean ion energy at the electrodes. Experimental results for γ under plasma exposure are difficult to obtain. Therefore, γ is either assumed to be a constant chosen with some uncertainty, or is approximated as a quantity that is a function of the ion energy and cleanliness of the electrode surface. It is hypothesized that these assumptions are not valid for all materials and plasma conditions. In this work, Hagstrum’s theory on Auger emission is suggested as a robust, ab initio model for accurately predicting γ for metal surfaces with a wide range of surface conditions and for a variety of ion species. To demonstrate the effect of the choice of γ on modeling results, we carry out particle-in-cell/Monte Carlo collision simulations of 13.56 MHz, single-frequency argon and helium capacitive discharges. Simulations are run assuming that: (i) γ is a constant, (ii) γ is an energy and surface condition dependent quantity that is independent of the electrode material, and (iii) γ is obtained from the ab initio model for different clean metals. The energy distribution of the emitted electrons resulting from Hagstrum’s theory is also implemented as a uniform, metal dependent distribution with physically accurate energy domain. It is found that this is important for some metals in both helium and argon. Lastly, it is observed that, depending on the assumed surface conditions, the plasma properties change dramatically. Based on these results we conclude that a realistic, material dependent implementation of γ is required to obtain realistic simulation results and that Hagstrum’s model suits this purpose.