Simplified LCAO Method for Zincblende, Wurtzite, and Mixed Crystal Structures

Abstract

The tight-binding (LCAO) method is a convenient, if qualitative, way of comparing energy bands in the zincblende and wurtzite structures. Using this method it is shown that wurtzite states along $\Gamma -{\Gamma }^{\prime }$ ("$c$" direction in the zone) can be obtained by perturbing corresponding zincblende states along $\Gamma -\Lambda$ ([111] zone direction). The perturbation is the difference of crystal potential, $V^{\prime }=V\left(\mathrm{ZB}\right)-V\left(\mathrm{Wur}\right)$, which takes the zincblende structure into the wurtzite and results in a splitting and shifting of these corresponding states. For perpendicular to these directions the correspondence of vectors and of states is not so clear, although some comparison can still be made.