Electronic structure of boron

Abstract

Using a recently developed tight-binding theory with universal matrix elements, the electronic structure of α-rhombohedral boron and B 4C are calculated. The universal matrix elements, which correspond to matrix elements between Wannier functions in the zincblende structure, were found to be inappropriate for the unusual icosahedral unit found in α-rhombohedral boron and B 4C. However, a simple, approximate prescription relating universal matrix elements to matrix elements between nonorthogonal atomic orbitals is derived. The nonorthogonality does not separate into an additive, two-body repulsion as it does in the zincblende structure, and so must be included explicitly in the diagonalization of the Hamiltonian. This prescription is found to well characterize the internal energy levels, the equilibrium spacing and force constant of an icosahedron of boron. The cohesion and equilibrium spacings calculated for an icosahedron and the remaining bonding units in α-rhombohedral boron and B 4C agree well with experimental values: the cohesion is overestimated by the same ratio as for carbonrow semiconductors. Normal mode frequencies calculated for B 12H = 12, B 12D = 12 and B 12Cl = 12 are in good agreement with measured frequencies.