Monte Carlo calculation of the thermalization of atoms sputtered from the cathode of a sputtering discharge

Abstract

The Monte Carlo technique has been used to simulate the thermalization of sputtered atoms in the filling or background gas within a planar sputtering discharge. The model uses Thompson’s theoretical distribution of the energy of atoms sputtered from the cathode surface together with an approximation to the 6–12 Lennard–Jones potential to describe collisions between sputtered atoms and background gas atoms. The diffusion of the thermalized atoms is included explicitly in the Monte Carlo calculations. The velocity distribution of sputtered atoms between the cathode and substrate is calculated, from which their average kinetic energy is determined as a function of the product Pd, where P is the background gas pressure and d is the distance from the cathode. Because of the effect of the finite cathode-substrate separation on back diffusion, it was found that PD, where D is the cathode-to-substrate separation, is an important parameter in describing thermalization and, consequently, the average energy of sputtered atoms throughout the discharge. These calculations are compared with theoretical analyses of other workers and show good agreement with experimental results.