Abstract
Three-dimensional quantizations of the energy spectrum can be realized in semimetal bismuth by applying a magnetic field perpendicular to a bismuth thin film. Numerical calculations were made of the chemical potential and the carrier (electrons and holes) density in three-dimensionally quantized bismuth films. The nonparabolic, ellipsoidal electronic band model for bismuth was used. The chemical potential and carrier density were evaluated as functions of temperature, film thickness, and magnetic field intensity. Comparison of the calculated results and experimental data suggests that the energy-band model would remain valid in thin films and the localized electrons would amount to 1% (order of magnitude) of the carrier density. The electrons would assume two-dimensional motions once the film thickness is reduced below about 350 A\r{}.
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