Ion energy distributions in radio frequency discharges sustained in gas mixtures obtained using a Monte Carlo-fluid hybrid model: endothermic processes and ion holes

The distributions of ion energies striking the substrate in radio frequency (RF) discharges are important with respect to the use of these devices for the etching of semiconductors and the fabrication of microelectronic devices. Previous works have demonstrated the importance of symmetric charge exchange and elastic collisions in the sheath in thermalizing the ion energy distributions (IEDS) and spreading their angular distribution. These processes have essentially gas kinetic rates since they have no activation energy. Ions can, however, be accelerated in the sheaths to energies above the threshold for non-thermal charge exchange collisions. These endothermic processes can result in a significant perturbation of the IEDs and ion mixing. In this work, we investigate the consequences of non-thermal charge exchange processes in parallel plate RF discharges using a Monte Carlo-fluid hybrid model. In this model particle simulations are used to resolve electron and ion energy distributions, while a fluid model is used to obtain species densities and electric fields. The reactor geometry is based on the GEC Reference Cell and we simulate both symmetric and asymmetric discharges. The gas mixtures we have investigated are pure argon, He/N₂, and He/CF₄/H₂. Ion energy distributions are presented which show depletion at energies greater than the threshold for endothermic processes. To account for particle-mesh interactions in the hybrid model a new technique called 'ion holes' is used in the particle simulation. Ion holes account for the dual loss of pseudoparticles resulting from, for example, ion-ion neutralization collisions, and remove trajectories from phase space resulting from the loss of a fluid ion.