The theoretical treatment of ion sputtering at energies above about 50 kev is simplified by the fact that the emergent particles originate at depths in the material which are small compared to the range of the incident particles. The displacement rate is nearly constant over this region and this enables one to obtain relatively simple solutions of the diffusion problem for emission.

The emission problem is reduced to an effective one-velocity diffusion calculation by an artifice. The volume displacement rate is increased by the factor $\overline{\nu }$, where $\overline{\nu }$ is the average number of secondaries, and the macroscopic absorption and scattering cross sections are adjusted to make the average number of collisions of each particle equal to the actual average over the secondaries. The resultant sputtering ratio, $\mathfrak{R}$, varies with incident energy $E$, incident angle $\psi$, and mass ratio $\mu =\frac{M_1}{M_2}$ (where $M_1=\mathrm{mass}\mathrm{of}\mathrm{incident}\mathrm{particle}$, $M_2=\mathrm{mass}\mathrm{of}\mathrm{target}\mathrm{particle}$), as $\mathfrak{R}\propto \mu \left(\frac{\ln E}{E}\right)sec\psi$.

• Received 23 December 1957

DOI:https://doi.org/10.1103/PhysRev.111.383