Quantitative modeling of secondary electron emission from slow-ion bombardment on semiconductors

When slow ions incident on a surface are neutralized, the excess potential energy is passed on to an electron inside the surface, leading to emission of secondary electrons. The microscopic description of this process, as well as the calculation of the secondary electron yield, is a challenging problem due to its complexity as well as its sensitivity to surface properties. One of the first quantitative descriptions was articulated in the 1950s by Hagstrum, who based his calculation on a parametrization of the density of states of the material. In this paper, we present a model for calculating the secondary electron yield, derived from Hagstrum's initial approach. We use first-principles density functional theory calculations to acquire the necessary input and introduce the concept of electron cascades to Hagstrum's model in order to improve the calculated spectra, as well as remove its reliance on fitting parameters. We apply our model to ${\mathrm{He}}^{+}$ and ${\mathrm{Ne}}^{+}$ ions incident on $\mathrm{Ge}\left(111\right)$ and $\mathrm{Si}\left(111\right)$ and obtain yield spectra that match closely to the experimental results of Hagstrum.