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.231
  magnetic fields affect the energy spectrum of charge carriers in the allowed zone of a rectangular
  quantum well. This effect leads to serious changes in the edges of the conduction band and the
  valence band of the quantum well, which is reflected in the oscillations of the density of energy
  states. In this case, the movement of charge carriers in the valence band and in the conduction band
  of the quantum well along the XY plane becomes limited, and the energy of charge carriers in this
  direction is quantized. Hence, in a transverse quantizing magnetic field, the energy of free charge
  carriers in the allowed zone of the quantum well, without taking into account spin, can be written:
  2
  2
  2
  2
  2
  2
  2
  2
  2
  2
  1
  ,
  , d, n
  2
  2
  1
  ,
  , d, n
  2
  2
  e
  L
  p
  L
  d
  e
  e
  e
  c
  c
  e
  c
  c
  e
  e
  d
  h
  h
  h
  V
  c
  h
  V
  c
  h
  h
  E
  E
  E
  N
  n
  m d
  E
  E
  E
  N
  n
  m d
  ( 3)
  Here
  L
  e
  N
  and
  L
  h
  N
  are the number of Landau levels of electrons and holes in the conduction
  band and in the valence band of the quantum well. The oscillations of the density of energy states
  in the conduction band and the valence band of the quantum well in a unit of the energy range are
  an essential characteristic of low-dimensional semiconductor materials. In particular, a change in
  the energy spectrum of charge carriers leads to a change in the oscillation of the density of states
  in the allowed zones under the action of a quantizing magnetic field.
  In the presence of a transverse quantizing magnetic field, the temperature dependence of the
  energy state density oscillations can be used to study the temperature dependence of the band gap
  width of a quantum well. We decompose the density oscillations of the energy states of the
  quantum well, including the conduction band and the valence band, into a series according to the
  formula (3).
  For the conduction band of a quantum well:
  2
  2
  2
  2
  2
  , 2
  ,
  2
  ,
  1
  2
  2
  1
  , , ,
  exp
  L
  L
  e
  e
  e
  c
  c
  e
  e
  c
  d
  S Z
  N
  N
  E
  E
  N
  N
  m d
  eB
  N
  E B T d
  kT
  kT
  (4)
  For the valence band of a quantum well:
  2
  2
  2
  2
  2
  V, 2
  ,
  2
  ,
  1
  2
  2
  1
  , , ,
  exp
  L
  L
  h
  h
  h
  V
  c
  h
  h
  d
  S Z
  N
  N
  E
  E
  N
  N
  m d
  eB
  N
  E B T d
  kT
  kT
  (5)
  Expression (3) shows the dependences of the energy of the charge carriers on the transverse
  quantizing magnetic field and on the thickness of the quantum well with the parabolic law of
  dispersion. This energy spectrum changes fundamentally in the size of the quantum well and the
  strong quantizing magnetic field. The motion of free electrons and holes in the XY plane becomes
  quantized, while the motion along Z remains discrete. From this it can be seen that under the action
  of a transverse quantizing magnetic field , the valence band and the conduction band of the
  quantum well are split into a number of zero-dimensional subzones. In addition, using the
  expressions
  T
  E
  T
  E
  T
  E
  g
  v
  с
  and formula (2), it is possible to calculate the width of the band gap
  of a quantum well under the influence of a magnetic field:
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