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.233
  INFLUENCE OF A QUANTIZING MAGNETIC FIELD ON THE FERMI ENERGY OSCILLATIONS IN TWO-
  DIMENSIONAL SEMICONDUCTORS
  R.G.Rakhimov
  Namangan Institute of Engineering and Technology
  Annotation. In this article we investigated the effects of quantizing magnetic field and
  temperature on Fermi energy oscillations in nanoscale semiconductor materials. It is shown that
  the Fermi energy of a nanoscale semiconductor material in a quantized magnetic field is quantized.
  The distribution of the Fermi-Dirac function is calculated in low-dimensional semiconductors at
  weak magnetic fields and high temperatures. The proposed theory explains the experimental results
  in two-dimensional semiconductor structures with a parabolic dispersion law.
  Keywords: semiconductor, Fermi energy, quantizing magnetic field, dispersion law, two-
  dimensional semiconductor structure, 2D electron gas.
  In k-space isoenergic surfaces E(k)=const are closed and are represented in the form of a
  sphere. The allowed energy states have a constant density V/8π
  3
  and are distributed in k-space.
  Here, V is the volume of the crystal. Since two opposite orientations of the spin of the electron state
  are responsible for each value of k, then the wave numbers of all states that will be filled have values
  no more than k
  F
  in the volume of the crystal V, according to the Pauli principle and k
  F
  is determined:
  3
  3
  3
  4
  2
  3
  8
  d
  F
  V
  k
  N
  (1)
  From here
  1
  2
  3
  3
  3
  d
  F
  N
  k
  V
  (2)
  Here, N
  3d
  is the electron concentration for a three-dimensional electron gas.
  If the system of electrons is due to the Fermi-Dirac statistics, then the energy in the ground
  state, i.e., at absolute temperature, is called maximum:
  2
  2
  2
  F
  F
  k
  E
  m
  (3)
  E
  F
  - called Fermi energy for 3D electron gas. The Fermi surface will have a spherical shape with
  a radius of k
  F
  for the isotopic dispersion law. The expressions given above were obtained only for
  bulk materials and do not consider changes in the oscillations of the Fermi energy in two-
  dimensional electron gases.
  Now, consider the dependence of the Fermi energy on the quantizing magnetic field in two-
  dimensional electron gases. In the absence of a magnetic field in two-dimensional electron gases,
  the electron energy is quantized along the Z-axis, so the electron moves freely only in the XY plane.
  These quantizations are called dimensional quantization. However, if the magnetic induction B is
  directed perpendicular to the XY plane, then the free energy of the electron is also quantized along
  the XY plane.
  The question arises: how will the Fermi energy change in two-dimensional electron gases in
  the presence of a quantizing magnetic field.
  For a 2D electron gas, the allowed energy states have a constant density S/4π
  2
  and are
  distributed in the XY plane. Here, S is the surface area of the crystal. Then, using formulas (1) and
  (2), we determine the electron concentration for a two-dimensional electron gas:
  2
  2
  2
  2
  2
  4
  4
  d
  F
  L
  N
  k
  (4)
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