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

Abstract

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 $T_0=293\mathrm{K}$ 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 $0<\omega <0.16a.u.$ and $0<T_{\Delta }<2.83$, corresponding to the temperature range $293\mathrm{K}<T<1123\mathrm{K}$. 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.

18 pages, 9 figures, Version published in PRB

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