Collision Processes

Collisions

rfEDIPIC is built to handle the following collision types:

1. Electron-neutral elastic
2. Electron-neutral excitation (2 types)
3. Electron-neutral ionization
4. Ion-neutral elastic
5. Ion-neutral charge exchange

There are two additional types of interactions which are unused in RF processing plasma applications and will not be covered here:

6. Electron-turbulence "collisions"
7. Ion-turbulence "collisions"

Cross Sections

rfEDIPIC determines collision frequency through two methods:

1. Tabulated total cross sections. In this method, cross sections should be inputted by files with names:

   • Electron-neutral collisions
     • ssc_crsect_en_elast.dat - Elastic collisions
     • ssc_crsect_en_excit.dat - Excitation (model 1) collisions
     • ssc_crsect_en_excit_2.dat - Excitation (model 2) collisions
     • ssc_crsect_en_ioniz.dat - Ionization collisions
   • Ion-neutral collisions:
     • ssc_crsect_in_elast.dat - Elastic collisions
     • ssc_crsect_in_elast.dat - Charge exchange collisions

   The contents of each cross section file are formatted the same, where the first row is the number of cross sections to be read, N, and the ensuing N rows are a list of energies [eV] and cross sections [m^2]. Any comments after the first N + 1 rows of the file will be ignored. See an example below:

   Click to expand the example ssc_crsect_en_ioniz.dat input file

      201
      2.459000e+1   0.000000e+0
      2.460000e+1   0.000000e+0
      2.460000e+1   1.234870e-26
      2.462214e+1   4.339590e-24
      2.465852e+1   8.831680e-24
      2.469617e+1   1.348160e-23
      ... (191 more lines)
      8.945506e+2   1.488170e-21
      9.251581e+2   1.454840e-21
      9.568413e+2   1.423160e-21
      9.896379e+2   1.390360e-21
   -----------------------------------------------
   Ionization cross-section of electrons in Helium
   column # 1 - energy, [eV]
   column # 2 - cross-section, [m^2]
   line # 1 - number of cross-section values to read [ formatted for READ(*, '(2x,i4)') ]
   
   Sources:
   Taken from Biagi-v7.1 database, www.lxcat.net, retrieved on September 25, 2023.
   Cross sections extracted from PROGRAM MAGBOLTZ, VERSION 7.1 JUNE 2004
   

2. Built in total cross sections. If cross sections are not provided for ion-neutral collisions, a built in model will be used.

   • For ion-neutral elastic collisions, the default model uses a constant collision frequency of 10 MHz.
   • For ion-neutral charge exchange collisions, the default model uses an analytic formula for the cross section from 10.1134/S1063780X09090098. For constant $a$ (~0.05 for helium and argon), charge exchange cross section $\sigma_\mathrm{1 eV}$ at 1 eV, and relative energy $\epsilon$ this formula is

$$ \sigma_\mathrm{ce}(\epsilon) = \sigma_\mathrm{1 eV} * (1 - a * \log (\epsilon))^2. $$

Electron-Neutral Collision Processing

EDIPIC handles three types of electron-neutral collisions: elastic, ionizing, and excitation. In doing so,

Elastic

Ionizing

Excitation

Ion-Neutral Collision Processing

EDIPIC handles two types of ion-neutral collisions: elastic and charge exchange. That is, following the model of Phelps (1994) the total momentum transfer

Elastic

Charge Exchange