title: Namangan Institute of Engineering and Technology nammti uz - bet 248
text: Fig.1. The form of the Gaussian function, the
  energy derivative of the Fermi-Dirac function and
  the Lorentz function at a temperature of T=300 K.
  Fig.2. The form of the Gaussian function, the
  derivative of the Fermi-Dirac function with
  respect to energy and the Lorentz function at a
  temperature of T=100 K.
  Namangan Institute of Engineering and Technology
  nammti.uz
  10.25.2023
  Pg.229
  Fig.3. The form of the Gaussian function, the derivative of the Fermi-Dirac function with respect
  to energy and the Lorentz function at a temperature of T=4 K.
  As can be seen from these figures, at low temperatures, the height of the distribution of the
  Gaussian function is higher than the height of the Lorentz function and the height of the derivative
  of the Fermi-Dirac function. From Fig. 2 and 3, it can be seen that at high temperatures, the height
  of the peak of the Gaussian function is also greater than the height of the Lorentz function and the
  height of the derivative of the Fermi-Dirac function.
  This is an important result, indicating that the distribution of the Gaussian function is much
  more efficient and tends to the ideal δ - Dirac function more quickly than the Lorentz functions and
  the derivative of the Fermi-Dirac function.
  References:
  1.
  Erkaboev, U.I., Rakhimov, R.G. Determination of the dependence of the oscillation of
  transverse electrical conductivity and magnetoresistance on temperature in heterostructures based
  on quantum wells. East European Journal of Physics, 2023(3), pp.133–145.
  2.
  Erkaboev, U.I., Rakhimov, R.G. Simulation of temperature dependence of oscillations of
  longitudinal magnetoresistance in nanoelectronic semiconductor materials. e-Prime - Advances in
  Electrical Engineering, Electronics and Energy, 2023, 5, 100236.
  3.
  Gulyamov, G., Erkaboev, U.I., Rakhimov, R.G., Mirzaev, J.I., Sayidov, N.A. Determination
  of the dependence of the two-dimensional combined density of states on external factors in
  quantum-dimensional heterostructures. Modern Physics Letters B, 2023, 37(10), 2350015
  4.
  Erkaboev, U.I., Rakhimov, R.G., Sayidov, N.A., Mirzaev, J.I. Modeling the temperature
  dependence of the density oscillation of energy states in two-dimensional electronic gases under
  the impact of a longitudinal and transversal quantum magnetic fields. Indian Journal of Physic, 2023,
  97(4), pp.1061–1070.
  5.
  Erkaboev, U.I., Sayidov, N.A., Negmatov, U.M., Mirzaev, J.I., Rakhimov, R.G. Influence
  temperature and strong magnetic field on oscillations of density of energy states in heterostructures
  with quantum wells HgCdTe/CdHgTe. E3S Web of Conferences. 2023. Vol.401,Article ID 01090
  6.
  Erkaboev, U.I., Sayidov, N.A., Negmatov, U.M., Rakhimov, R.G., Mirzaev, J.I. Temperature
  dependence of width band gap in In
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