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 e(TA, w), over a wide range of frequencies and a wide range of the temperature parameter T-Delta = (T - T0)/T0, where T-0 = 293 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, w)- 1]/[epsilon(T-Delta, w) + 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 < w < 0.16 a.u. and 0 < T-Delta < 2.83, corresponding to the temperature range 293 K < T < 1123 K. Using our approach, we evaluate the short-range C3 and the long-range C4 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 o epsilon(T-Delta, w) to the Lorentz-Dirac model.