Monte Carlo simulations of sputter atom transport in low-pressure sputtering: The effects of interaction potential, sputter distribution, and system geometry

A comparative study of the various model assumptions in Monte Carlo simulations of low-pressure sputter-atom transport is presented. The few-collision conditions and actual "racetrack" magnetron geometry, typical of low-pressure magnetron sputtering, are emphasized. For the gas phase scattering problem, a comparison is made between hard sphere, Lennard-Jones 6-12, and Abrahamson Thomas-Fermi-Dirac [Phys. Rev. 178, 76 (1969)] interatomic potentials. The hard sphere potential results in both a significantly lower energy distribution and a more diffuse angular distribution for the depositing flux, as compared with the more realistic "softer" potentials. Because energy-dependent cross sections are obtained when using the 6-12 and Abrahamson potentials, an "energy filtering" effect is observed, i.e., high-energy particles arrive at the substrate preferentially to those at low energy. It is concluded that the hard sphere model will lead to serious errors in both the energy and angular distributions of the arrival flux, and that the 6-12 and Abrahamson potentials yield results that are similar to each other. For the nascent sputter distribution, fractal TRIM (transport of ions in matter) simulations are compared to the analytic Thompson distribution. While both distributions give nearly identical results for the angle-integrated fluxes, the fractal TRIM distribution shows a strong angular dependence of the energy distribution. The implications of this effect for finite geometry systems are discussed.