Fermi energy and electron density in a narrow strip of semimetal bismuth†

Abstract

In an ultrathin film of semimetal bismuth, the electrons and holes would perform two-dimensional motions in the film plane due to the quantum size effect. When the width is reduced while the length is kept fixed, the film turns itself into a narrow strip and its two-dimensional energy spectrum would be subject to another quantum size effect. Numerical evaluations have been carried out of the Fermi energy and of the electron/hole density in a narrow strip of bismuth as functions of the variable width. Both functions exhibit oscillatory variations in accordance with the size effect. Both the vanishing-wave-function and the vanishing-gradient boundary conditions have been studied and contrasting results have been obtained. As the width is sufficiently reduced, the semimetallic strip would become semiconducting if the vanishing-wave-function boundary condition is applied; or the strip would become highly conductive if the vanishing-gradient boundary condition is applied.