Chemical-bond approach to the electric susceptibility of semiconductors

A simple model-independent method is developed to relate chemical bonds to the dielectric constant and other physical properties of tetrahedral semiconductors with the minimum number of parameters possible. For this purpose, we express ${\epsilon }_1\mathrm{}\left(0\right)\mathrm{}$, via the Kramers-Kronig relation, as a function of the zeroth and the first moments of ${\epsilon }_2\left(\omega \right)$. The first moment is determined by the $f$ sum rule while the zeroth moment can be calculated if the valence- and conduction-band wave functions are known. Since conduction bands are inadequately described by models that are analytically simple, we bypass the problem by using completeness to eliminate the conduction band entirely. The result is an expression for ${\epsilon }_1\mathrm{}\left(0\right)\mathrm{}$ which involves only valenceband wave functions. Since working in a localized representation is more convenient than in the Bloch representation, we introduce a generalized Wannier function of bonding character for the valence bands. Realizing that this is appropriate for only those semiconductors like diamond in which the bonding-antibonding coupling is weak, we build into our Wannier function the lacking antibonding character via a power-series expansion in the quantity $\frac{V_1}{V_2}$ (Hall-Weaire parameters). Using Herman-Skillman values for the atomic orbitals, we obtain numerical results that agree with experiment to about 10%.