Adaptive mass alteration to model ion–ion recombination in a Particle-in-Cell simulation of silane radio-frequency discharges

In discharges in electronegative gases, negative ions are generated by (dissociative) attachment and lost by recombination with positive ions. Straightforward modeling of the recombination in a Particle-in-Cell simulation by removing a positive and negative super-particle gives rise to large numerical fluctuations. These fluctuations lead to non-physical electric fields and heating of the electrons. In this paper, a method is proposed that enables the simulation of the recombination of positive and negative ions in an accurate way, even at low densities. The recombination in a cell is done by changing the mass of the super-particles in this cell. Thus it is possible to recombine any desired amount of real particles even if it is less than one super-particle. Moreover, the number of super-particles in each cell is kept nearly constant by adding super-particles (if a cell contains too few particles) or by removing a super-particle while increasing the mass for each of the rest (if a cell contains too many). It is shown that this simulation of ion recombination results in a lower level of non-physical fluctuations. The lower level of computational noise is shown to result in a lower ionization rate and lower ion fluxes compared to PIC/MCC simulations without adaptive mass alteration.