title: COMPARISON OF THE DISTRIBUTIONS OF THE LORENTZ, GAUSSIAN FUNCTIONS AND THE
text: Namangan Institute of Engineering and Technology
  nammti.uz
  10.25.2023
  Pg.228
  In many works consider the Shubnikov-de Haas and de Haas-van Alphen oscillations in bulk
  and nanosized semiconductors at different temperatures and at different pressures. For example,
  in [1–3], a method was developed for determining the temperature dependence of the
  thermodynamic density of states in a quantizing magnetic field. These methods are used to study
  quantum oscillation phenomena in semiconductors at various temperatures. However, these works
  did not investigate the influence of the microwave field (microwave radiation absorption) on the
  temperature dependence of quantum oscillation phenomena in semiconductors using the Gaussian,
  Lorentzian and energy derivative of the Fermi-Dirac function.
  The purpose of this work is to compare the distributions of the Lorentz, Gaussian functions
  and the derivative of the Fermi-Dirac function with respect to energy at different temperatures.
  Let us consider the dependence of the static distribution function on energy at various
  temperatures. The distribution functions of Gauss, Lorentz and the energy derivative of the Fermi-
  Dirac function for energy levels
  E
  i
  is determined by the following expression:
  2
  2
  1
  ,
  exp
  i
  E
  E
  Gauss E T
  kT
  kT
  (1)
  2
  2
  1
  ,
  1
  i
  Lorentz E T
  E
  E
  kT
  (2)
  0
  2
  exp (
  ) /
  ( , , )
  1
  1 exp (
  ) /
  E
  kT
  f E
  T
  E
  kT
  E
  kT
  (3)
  Here,
  ,
  Gauss E T
  is the Gaussian distribution function, is the Lorentz distribution function,
  f
  0
  (
  E)/
  E is the energy derivative of the Fermi-Dirac distribution function. Now consider the
  temperature dependence of the distribution of the Gaussian, Lorentzian and Fermi-Dirac functions.
  Figures 1, 2 and 3 show the dependences of the distributions of the Gaussian function, Lorentz
  function and the derivative of the Fermi-Dirac function on energy at various temperatures
  Т
  1
  =300
  К,
  Т
  2
  =100
  К,
  Т
  3
  =4
  К.