Temperature-dependent dielectric function of intrinsic silicon: Analytic models and atom-surface potentials (original) (raw)

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 ǫ(T∆, ω), over a wide range of frequencies and a wide range of the temperature parameter T∆ = (T − T0)/T0, where T0 = 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 [ǫ(T∆, ω) − 1]/[ǫ(T∆, ω) + 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 < ω < 0.16 a.u. and 0 < T∆ < 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 of ǫ(T∆, ω) to the Lorentz-Dirac model.