Quantum size effect and electric conductivity in thin films of pure bismuth

Abstract

Numerical evaluations have been carried out of the electric conductivities at 0 K of electrons and of holes, respectively, in thin films of semimetal bismuth with the film plane normal to the trigonal axis. The ellipsoidal non-parabolic model for the electron energies in bismuth has been used. Different boundary conditions in connection with the quantum size effect on the energy spectrum have been studied. It is shown that the electron contribution dominates the electric conductivity at 0 K in thin films of bismuth. Indirect comparison between the numerical results and existing experimental data seems to suggest that the vanishing-gradient boundary condition might be a better choice when applying size quantizations to the electronic energy spectrum in ultrathin films of bismuth.