title: Namangan Institute of Engineering and Technology
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  Namangan Institute of Engineering and Technology Pdf ko'rish
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  Bog'liq ТўпламNamangan Institute of Engineering and Technology
  nammti.uz
  10.25.2023
  Pg.235
  For an area equal to one (L
  x
  L
  y
  =1) of formula (12), the following is calculated:
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  1
  1
  (
  )
  4
  2
  8
  2
  8
  2
  d
  d
  fz
  fz
  fz
  F
  c
  n
  n
  n
  N
  H
  N
  H c
  eH
  H
  m
  md
  mc
  eH
  md
  md
  (13)
  Here
  2
  2
  (
  )
  d
  cN
  H
  eH
  is the filling factor. This is the number of Landau levels, taking into
  account their spin splitting, in a quantizing magnetic field, at absolute zero temperature, filled with
  electrons. This dimensionless parameter is used to facilitate the discussion of quantum oscillatory
  effects in 2D electron gases.
  As can be seen from formula (13), the Fermi energies are quantized if the filling factor is an
  integer, then the minimum energy quantum will be
  1
  8
  c
  , that is, formula (13) gives the exact value
  of the energy for the first level corresponding to the
  1
  .
  2
  2
  2
  1
  2
  1
  (
  )
  8
  2
  fz
  c
  n
  H
  md
  (14)
  For all other levels, the rigorous theory gives the expression
  2
  2
  2
  2
  1
  (
  )
  8
  2
  fz
  c
  n
  H
  md
  (15)
  Here, the filling factor is an integer
  0,1, 2, 3...
  In addition, in two-dimensional semiconductors, in the presence of a quantizing magnetic
  field, the energy spectrum of electrons is purely discrete. A purely discrete energy spectrum, in this
  case the Fermi energy, is usually characteristic of a quantum dot. In this case, the magnetic induction
  vector will be directed along the Z axis and perpendicularly along the plane of the transverse two-
  dimensional layer. In a transverse quantizing magnetic field, quantum wells become analogous to a
  quantum dot, in which the motion is limited in all three directions.
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