Depth distributions of implanted atoms under the influence of surface erosion and diffusion

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Abstract
Shallow range distributions are altered significantly by diffusion and surface erosion. It will be shown here that the simultaneous processes of implantation, diffusion, and surface erosion can be described by a second order differential equation which is mathematically tractable and yields general results in terms of analytical functions. The resulting depth distributions depend on one parameter only which is a combination of the mean particle range, the diffusion coefficient, and the velocity of surface erosion (e.g. sputtering). The theory is applied to practical cases, e.g. implantation of plasma particles in the wall of fusion reactors, or solar wind ions in the surface of meteorite materials.