Electron energy partitioning after ionization

For the electron impact ionization one must decide how to split the remaining collision energy between incident and secondary electron. The most sophisticated numerical expression comes from Opal¹ et. al. who did some substantial measurements on this topic. However, using that expression in our PIC-MC code has seemingly no effect at all on any output results. Hence we checked systematically the two extreme case where the secondary electron is uneffected and the remaining collision energy is divided equally between incident and secondary electron, respectively.

Comparision of different partitioning schemes

One takes it all vs. equal share

As seen in the simulation results below there is no significant difference between the two extremes. Power dissipation, reaction rates and plasma density are pretty much the same whether we use "one takes it all" or the equal share. Thus, we decided to take the less computational expensive one which is the "one takes it all" scheme. Furthermore this is the one which has been proven sufficiently accurate accordant to the comprehensive studies of Yoshida² et. al.

Figure 1: Power dissipation for rf simulations in argon at different E/N conditions using the "one takes it all" and equal share scheme, respectively.

Figure 2: Electron density for magnetron discharge simulations at equal E/N conditions using the "one takes it all" and equal share scheme, respectively.

Footnotes

1. C.B. Opal: Measurements of Secondary-Electron Spectra Produced by Electron Impact Ionization of a Number of Simple Gases, J. of. Chem. Phys. Vol. 55 Nbr. 8, 1971 ↩

2. S. Yoshida, A. V. Phelps, L.C. Pitchford: Effects of electrons produced by ionization on calculated electron-energy distributions, Phys. Rev. Vol. 27 Nbr. 6, 1983 ↩