Hole-majority condition in thin films of semimetal bismuth

Experimental evidence suggested that the charge-neutrality condition in thin films of semimetal bismuth may be violated due to energy band distortion and that holes are the majority charge carriers. We have made calculations of the electron and hole densities, the Fermi energy, and the electric conductivity as functions of the film thickness and the temperature, using a hole-majority model in contrast to previous work of this kind. Results are presented and they are in fairly good agreement with existing experimental data. The electron density would go down to zero at zero temperature in sufficiently thin films leading to a "semimetal-semiconductor" transition. Two different boundary conditions that size quantize the energy spectra have been alternately employed and results compared. The quantum-mechanical background of the boundary conditions has been discussed.