title: Namangan Institute of Engineering and Technology
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  Bog'liq ТўпламNamangan Institute of Engineering and Technology
  nammti.uz
  10.25.2023
  Pg.224
  TEMPERATURE DEPENDENCE OF THE SPECTRAL DENSITY OF STATES IN SEMICONDUCTORS
  IN QUANTIZING MAGNETIC FIELDS
  R.G.Rakhimov
  Namangan Institute of Engineering and Technology
  Annotation: In this article, a mathematical model for Shubnikov-de Haas oscillations in
  semiconductors upon absorption of microwave radiation is obtained and its temperature
  dependence is studied. A two-dimensional image of microwave magnetoabsorption oscillations in
  narrow-gap semiconductors is constructed. Using a mathematical model, oscillations of microwave
  magnetoabsorption are considered for various values of the electromagnetic field. The calculation
  results are compared with experimental data. The proposed model explains the experimental
  results in semiconductor structures at various temperatures.
  Keywords: semiconductor, electron gas, oscillation, microwave, Landau levels, electric field,
  mathematical model, Shubnikov-de Haas oscillations.
  Let us now consider the temperature dependence of the spectral density of states in
  quantizing magnetic fields using the distribution of the Gaussian, Lorentzian and the energy
  derivative of the Fermi-Dirac function. In work [1], oscillations of the spectral density of states in
  narrow-gap semiconductors were studied. The following expression was obtained for the density of
  energy states in quantizing magnetic fields for narrow-gap semiconductors:
  max
  3
  2
  1
  2
  2
  3
  2
  0
  2
  1
  ( )
  ,
  2
  1
  (2)
  (
  )
  2
  N
  g
  k
  N
  g
  E
  E
  m
  eH
  N
  E H
  mc
  E
  eH
  E
  N
  E
  mc
  (1)
  Here,
  ,
  k
  N
  E H
  is the spectral density of states for the zone with the Kane dispersion law, H
  is the magnetic field strength, E is the energy of a free electron and hole in a quantizing magnetic
  field, N is the number of Landau levels, and E
  g
  is the band gap of the semiconductor.
  This formula is applicable only for narrow-gap (
  0.6
  g
  E
  eV
  ) materials. As can be seen from
  this formula, if
  g
  E
  (for wide-gap semiconductors) then
  2
  0
  g
  E
  E
  and
  2
  0
  g
  E
  E
  , then formula
  (4) turns into the density of states of the band with a parabolic dispersion law [2]:
  max
  3
  2
  1
  2
  3
  2
  0
  ( )
  1
  ,
  2
  1
  (2)
  (
  )
  2
  N
  s
  N
  m
  eH
  N
  E H
  mc
  eH
  E
  N
  mc
  (2)
  If the energy spectrum of electrons is discrete, then the density of energy states is equal to
  the sum of δ-functions concentrated at points of the spectrum Е
  i
  , whose amplitude is
  ),
  0
  (
  )
  0
  (
  2
  `
  2
  i
  i
  si
  N
  where
  ( )
  i
  x
  are the eigenfunctions normalized to unity [3]:
  )
  (
  )
  (
  i
  i
  si
  s
  E
  E
  N
  E
  N
  (3)
  In the general case, the spectral density of energy states is a set of δ - functional peaks located
  from each other by ħ
  c
  in a quantizing magnetic field [4].
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