Eigen energies and eigen states of conduction electrons in pure bismuth under size and magnetic field quantizations

Abstract

The effect of size quantizations on the energy spectrum of electrons in bismuth thin films, oriented perpendicular to the trigonal axis, was studied. The non-parabolic ellipsoidal energy-momentum model for bismuth electrons was used. The Schrödinger equation was set up for films either in the absence or in the presence of a transverse magnetic field. The Schrödinger equation was solved to fit either the vanishing-wave-function or the vanishing-gradient boundary condition. The effect of the off-diagonal element in the effective mass tensor on the energy spectrum was demonstrated. The charge carriers would assume two-dimensional motions in ultrathin bismuth films under the application of vanishing-gradient boundary conditions.