Temperature-dependent dielectric function of intrinsic silicon: Analytic models and atom-surface potentials

The optical properties of monocrystalline, intrinsic silicon are of interest for technological applications as well as fundamental studies of atom-surface interactions. For an enhanced understanding, it is of great interest to explore analytic models which are able to fit the experimentally determined dielectric function $\epsilon(T_\Delta, \omega)$, over a wide range of frequencies and a wide range of the temperature parameter $T_\Delta = (T-T_0)/T_0$, where $T_0 = 293\,{\rm K}$ represents room temperature. Here, we find that a convenient functional form for the fitting of the dielectric function of silicon involves a Lorentz-Dirac curve with a complex, frequency-dependent amplitude parameter, which describes radiation reaction. We apply this functional form to the expression $[\epsilon(T_\Delta, \omega) -1]/[ \epsilon(T_\Delta, \omega)+2]$, inspired by the Clausius-Mossotti relation. With a very limited set of fitting parameters, we are able to represent, to excellent accuracy, experimental data in the (angular) frequency range $0 < \omega < 0.16 \, {\rm a.u.}$ and $0< T_\Delta < 2.83$, corresponding to the temperature range $293\,{\rm K} < T < 1123\, {\rm K}$. Using our approach, we evaluate the short-range $C_3$ and the long-range $C_4$ coefficients for the interaction of helium atoms with the silicon surface. In order to validate our results, we compare to a separate temperature-dependent direct fit of $\epsilon(T_\Delta, \omega)$ to the Lorentz-Dirac model.