Effect of a free surface in ion backscattering and sputtering

The transport equation for the slowing down of an energetic particle in matter is solved in a P1 approximation, both for a half space and for an infinite medium. Nuclear stopping with a power-law dependence on energy is assumed. The existence of the target surface affects the range distribution near the surface and the asymptotic energy spectrum of backscattered particles. In a half space, the range distribution decreases to zero at the surface and the backscattered particle spectrum is flatter than in the infinite medium. For the case of recoil generation, the analogous results for the deposited-energy distribution and the spectrum of sputtered recoils are derived. Explicit results are given for the case of hard-sphere cross sections with a power-law dependence on energy