Double quantum size effects on the energy spectra of charge carriers in thin wires of pure bismuth

Abstract

The energy spectra of electrons and holes in a thin wire of bismuth are subject to two dimensional size quantizations. Because of the highly anisotropic energy-momentum relationship for bismuth electrons, exact solutions to the Schrödinger equation satisfying appropriate boundary conditions in connection with the quantum size effects are generally difficult to obtain. A perturbation method has been applied to obtain the energy subbands under the double size quantizations. Numerical evaluations have been carried out of the possible quantum-size-induced semimetal to semiconductor transitions. General features of the anisotropic size dependence of the Fermi energy and of the electron density and the identifications of the associated quantum oscillations are presented.