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

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