Temperature dependence of quantum effects in narrow zone semiconductors

TEMPERATURE DEPENDENCE OF QUANTUM EFFECTS IN NARROW ZONE SEMICONDUCTORS
This article discusses quantum oscillations of longitudinal electrical conductivity, magnetic susceptibility oscillations, and electronic heat capacity oscillations for narrow-gap semiconductors. A theory is developed of the temperature dependence of quantum oscillation phenomena in narrow-gap semiconductors, taking into account the thermal smearing of Landau levels. The proposed model explains the experimental results in semiconductor structures at various temperatures.
Temperature dependence of longitudinal conductivity oscillations in narrow-gap semiconductors
It is known that with the help of oscillation phenomena it is possible to determine the basic physical quantities (longitudinal conductivity, magnetic susceptibility, thermoelectric power and other transport phenomena) in a quantizing magnetic field. In particular, oscillations of longitudinal electrical conductivity and oscillations of magnetic susceptibility provide valuable information on the energy spectra of free electrons in semiconductor structures. In a strong magnetic field, the longitudinal conductivity is determined using the following expression [103;С.330-400]:
(1)
Here, N is the number of Landau levels, is the cyclotron frequency, and is the momentum relaxation time. E is the energy of a free electron in a quantizing magnetic field. Integrand factor - the energy derivative of the Fermi-Dirac function takes on the character of a delta function at low temperatures.