Behavior of the Electronic Dielectric Constant in Covalent and Ionic Materials

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Abstract
Refractive-index dispersion data below the interband absorption edge in more than 100 widely different solids and liquids are analyzed using a single-effective-oscillator fit of the form n2−1=EdE0(E02−ℏ2ω2), where ℏω is the photon energy, E0 is the single oscillator energy, and Ed is the dispersion energy. The parameter Ed, which is a measure of the strength of interband optical transitions, is found to obey the simple empirical relationship Ed=βNcZaNe, where Nc is the coordination number of the cation nearest neighbor to the anion, Za is the formal chemical valency of the anion, Ne is the effective number of valence electrons per anion (usually Ne=8), and β is essentially two-valued, taking on the "ionic" value βi=0.26±0.04 eV for halides and most oxides, and the "covalent" value βc=0.37±0.05 eV for the tetrahedrally bonded ANB8−N zinc-blende- and diamond-type structures, as well as for scheelite-structure oxides and some iodates and carbonates. Wurtzite-structure crystals form a transitional group between ionic and covalent crystal classes. Experimentally, it is also found that Ed does not depend significantly on either the bandgap or the volume density of valence electrons. The experimental results are related to the fundamental ε2 spectrum via appropriately defined moment integrals. It is found, using relationships between moment integrals, that for a particularly simple choice of a model ε2 spectrum, viz., constant optical-frequency conductivity with high- and low-frequency cutoffs, the bandgap parameter Ea in the high-frequency sum rule introduced by Hopfield provides the connection between the single-oscillator parameters (E0,Ed) and the Phillips static-dielectric-constant parameters (Eg,ℏωp), i.e., (ℏωp)2=EaEd