Electronic Band Structure of Boron Carbide

Abstract

The tight‐binding approximation is applied to a study of electronic energy bands of the boron carbide B₄C crystal. The 60×60 determinantal secular equation for the energy is reduced by group‐theoretical treatments of the spatial symmetry at certain special values of the wave vector k. Calculations are carried out at two points in the Brillouin zone. At the zone center point there is a substantial energy gap, about 2.5 ev, between the occupied and unoccupied levels, and at the zone boundary point k = (π/a)(1,1,1) this gap becomes very narrow, i.e., about 1 ev. Considering compatibility relations for the types of symmetry, there may be the energy gap, being substantially broad at the zone center point and very narrow at the zone boundary point k = (π/a)(1,1,1), between the all‐filled valence and the all‐empty conduction bands, in accordance with the existence of the complicated structure, the great hardness, and the appreciable electric conductivity of this crystal.