Theory of the Valence Band Splittings at k=0 in Zinc-Blende and Wurtzite Structures

A theory of the valence band splittings at k=0 in zinc-blende and wurtzite structures is proposed, in which the wurtzite levels are treated as perturbations of those in zinc blende. Starting from one-electron Hamiltonians for the two structures, the two-parameter formulas originally derived by Hopfield are obtained, with a minimum of approximations, along with explicit expressions for the parameters in terms of Hamiltonian matrix elements. The two-parameter formulas are compared with experimental data and agreement is found to be good. A simple tight-binding (linear combination of atomic orbitals), $3p$ valence band, point-ion lattice model is used to calculate an effective charge for ZnS from the known valence band splittings in the wurtzite and zinc-blende dimorphs; a value of $2.3e$ is obtained.