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.

arXiv comment18 pages, 9 figures, Version published in PRB

References in corpus (16)

• Atoms and Molecules in Cavities: From Weak to Strong Coupling in QED Chemistry
• Variational calculations of dispersion coefficients for interactions between H, He, and Li atoms
• Experimental Observation of Quantum Reflection in the High Energy Limit
• New asymptotic behaviour of the surface-atom force out of thermal equilibrium
• Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate
• Time-dependent density functional theory for many-electron systems interacting with cavity photons
• Casimir-Lifshitz force out of thermal equilibrium
• Light-Matter Response in Non-Relativistic Quantum Electrodynamics: Quantum Modifications of Maxwell's Equations
• Higher-order binding corrections to the Lamb shift of 2P states
• Casimir-Lifshitz force out of thermal equilibrium and asymptotic non-additivity
• Time-dependent Kohn-Sham approach to quantum electrodynamics
• Frequency-dependent dielectric function of semiconductors with application to physisorption
• A Shortcut to Self-Consistent Light-Matter Interaction and Realistic Spectra from First-Principles
• Birefringence Measurements on Crystalline Silicon
• Theory of noncontact friction for atom-surface interactions
• Relativistic dynamical polarizability of hydrogen-like atoms

Cited by in corpus (4)

• Revisiting the Divergent Multipole Expansion of Atom-Surface Interactions: Hydrogen and Positronium, alpha-Quartz, and Physisorption
• Retardation Effects in Atom-Wall Interactions
• Coupled Oscillators and Dielectric Function
• Temperature-Dependent Dielectric Function of Calcium Fluoride