Extrema positions of charge carrier band spectrum in thin bismuth films

Many studies report an increase in charge carrier concentration in thin bismuth films as their thickness decreases at low temperatures. These results are obtained on the basis of data on resistivity, magnetoresistance, Hall coefficient, and thermal EMF measured in these films. The calculation is most often carried out within the framework of the two-band approximation assuming the quadraticity of the dispersion law of electrons and holes. Using these approximations, it is possible to estimate the change in the position of energy extremes relative to the chemical potential in these films based on concentration values of charge carriers. This article presents all these calculations and analyses the extrema movement of the charge carrier band spectrum in bismuth films with a change in their thickness.