Statistical model for the formation of excited atoms in the sputtering process

The formation of excited neutral atoms in the sputtering process has not previously been satisfactorily explained. It is shown that a reasonable description can be developed by the consideration of the inelastic energy transfer in the final collision associated with the sputtering of a surface atom. For low enough kinetic energies this inelastic energy transfer is proportional to the kinetic energy given to the sputtered atom. The result is an expression which reproduces in detail experimental measurements of the relative yields of sputtered excited atoms, and gives reasonable agreement with experiment regarding their kinetic energies and absolute yields. The expression equates the yield of the $i\mathrm{th}$ state to $2g_i\mathrm{UK}\Sigma {k=i}^{\infty }{G}_k^{-1\mathrm{}}({\epsilon }_k^{-1\mathrm{}}-{\epsilon }_{k+1\mathrm{}}^{-1\mathrm{}})$, where $g_i$ is the degeneracy, $U$ is the surface binding energy, $K$ is the proportionality constant relating the inelastic energy transfer to the kinetic energy, $G_i$ is the cumulative degeneracy (namely, $G_i=g_0+g_1+g_2+\cdots +g_i$), and ${\epsilon }_i$ is the excitation energy.