A new method for determining the bandgap in semiconductors in presence of external action taking into account lattice vibrations

This article proposes a new method of calculating conductivity in semiconductors, taking into account lattice oscillations and thermal smears under the influence of temperature and magnetic fields. It is shown that the dependence of the effective electron mass on energy and temperature affects the temperature dependence of the bandgap in a strong magnetic field. With the help of numerical experiments and using experimental results, graphs of the temperature dependence of the bandgap in the absence and the presence of a magnetic field were obtained. The theoretical results are compared with experimental results. It is shown that to explain the dependence of the bandgap, it is necessary to take into account the contribution of thermal broadening of energy levels. It was found that the total change in the bandgap is determined by both the interaction of electrons with lattice vibrations and the thermal broadening of energy levels in the allowed bands.