Abstract

Numerical calculations were carried out of the energy levels of electrons and holes in thin films of pure bismuth under extreme size quantizations. Also included were the energy quantizations due to a magnetic field applied perpendicular to the films. Real bismuth energy band structures, including the non-parabolic energy-momentum relationship for electrons, were used throughout the calculations. In sufficiently thin films, the charge carriers perform essentially two-dimensional motions. The transition from a state of three-dimensional motions to a state of two-dimensional motions was discussed for a film of an arbitrary orientation with respect to the crystallographic axes. The magnetic field effect upon such a transition was also discussed and presented numerically.

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