We present a detailed study based upon a second-neighbor tight-binding calculation using the same starting point as that used earlier by Stocker and by Shevchik, Tejeda, and Cardona. Parameters are fit to the known bands of the group-IV semiconductors; symmetric matrix elements are assumed constant in isoelectronic series while the variation of antisymmetric matrix elements with polarity is obtained directly from the bond-orbital model of Harrison. Using these parameters, valence bands are obtained for all zinc-blende semiconductors. The agreement with experiment for symmetry-point eigenvalues is comparable to that of the empirical-pseudopotential method though the bands are obtained analytically. As expected, agreement for effective masses and for nonsymmetric points is not as good. From the various symmetry-point expressions for the bands several relationships between eigenvalues within a given band are obtained. By dissecting the interbond matrix elements into matrix elements between $s p^3$ hybrids, a number of relations between eigenvalues in different materials are obtained; these take the form of dependence upon polarity for isoelectronic series and dependence upon bond length for compounds of equal valence difference. Additional insight into the origin of these trends is obtained by further dissecting the interhybrid matrix elements into matrix elements between atomic orbitals. It is found that the convergence of the tight-binding calculation increases with increasing polarity but is quite insensitive to metallicity; an explanation for these tendencies is given.

• Received 25 November 1974

DOI:https://doi.org/10.1103/PhysRevB.11.3006