Modeling of physical etching based on the two-dimensional velocity distributions of ions and fast neutrals using the Boltzmann equation

A numerical model based on the Boltzmann equation is proposed to simulate the physical etching by energetic particles in the sheath region of the discharge. The local profiles of the two-dimensional velocity distributions of ions and fast neutrals in the gas phase are calculated in a radially uniform discharge, under a set of collision cross sections, for external parameters: sheath voltage and width, ion current density, and pressure. A case study is performed in a dc abnormal glow discharge in Ar having a masked Al electrode. The time evolution of the etching profile is simulated as a result of the physical interaction between the surface and energetic particles from the gas phase. This enables the estimation of the etch rate and anisotropy for ions and fast neutrals. A great advantage of the present numerical procedure is that it is free from stochastic fluctuations and the lengthy central processing unit time found in particle simulations.