Evolution towards thermalization, and diffusion, of sputtered particle fluxes: Spatial profiles

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Abstract
Particles sputtered from solid targets in plasma deposition systems, under typical vacuum conditions, slow down in collisions with the gas phase. The spatial profiles of particle fluxes at given instantaneous energy are calculated with a simple model of a particle slowing down along straight-line trajectories, subject to a continuous energy-loss process. In particular, the profiles of flux thermalization are given. Model distributions in energy and direction of sputtered fluxes, with a reasonable physical basis, are used. The accumulation and diffusion of thermalized material in the gas phase is studied also, and the stationary spatial profiles are obtained. Diffusion particle currents back to the source, or towards the substrate, can then be estimated. Scaling laws are obtained that allow the analysis of any specific deposition conditions through the masses of the sputtering and sputtered particles, the binding energy of the target, and the working pressure. Because of the simplifying assumptions of the analytical model, predictions in the particular case of light targets sputtered in a comparatively heavier atmosphere should be only regarded on an orientative basis.