Effects ofp−dhybridization on the valence band of I-III-VI2chalcopyrite semiconductors

The electronic structure of the valence band at the Brillouin-zone center of the I-III-${\mathrm{VI}}_2$ chalcopyrite compounds has been calculated using a model developed by adding the effects of $p-d$ hybridization and the crystal field to the Hamiltonian of the Kane model. Two important parameters in the model are the energy separation $E$ between the $p$ and $d$ levels and the interaction $M$ between these levels. It is shown that three previous models (Tell and Bridenbaugh, Kildal, and the linear hybridization model) can be derived as special cases of the present model. The model has been used to analyze the available data on some 13 compounds. It is shown that the dimensionless parameters $\frac{M}{E}$ and $\frac{\Delta E_g}{E}$, where $\Delta E_g$ is the band-gap anomaly, show a smooth variation with the fractional $d$ character of the valence band and appear to be characteristic of the structure. Values of the deformation potentials $b_p$ and $b_d$ averaged over all of the compounds have been determined and found to be $b_p=(-0.8\mathrm{}\pm 0.2)$ eV and $b_d=(-4.3\mathrm{}\pm 1.5)$ eV.