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.259
  where b is the parameter that determines the effective half-width of the distribution in the
  form of hyperbolic secant. In [3, 5] it was shown that in the case when the density
  distribution of electronic states at the boundaries of the valence and conduction bands has a
  power dependence, they can be written as follows:
  1
  )
  )(
  (
  )
  (
  n
  g
  C
  V
  E
  N
  g
  , here ε≤ε
  V
  (4)
  2
  )
  )(
  (
  )
  (
  n
  g
  V
  C
  E
  N
  g
  , here ε
  С
  ≤ε (5)
  where N (εV) and N (εC) are effective values of the density of
  states in the valence band and in the conduction band, εV is the
  highest border of the valence band, and εC is the lower boundary
  of the conduction band. E
  g
  – is the energy width of the mobility
  gap (the width of the forbidden zone). Considering that the density
  distribution of states at the boundaries of the allowed zones can
  be parabolic or linear [1, 6], then n1 and n2 are ½ and 1. When
  the densities of electronic states of the allowed bands correspond
  to the Gaussian distribution, they can be written as follows [1, 6]:
  for the valence band
  2
  exp
  V
  V
  a
  N
  g
  , (6)
  for conduction band
  2
  exp
  C
  C
  a
  N
  g
  , (7)
  As is known, the integral of the Gaussian distribution does not
  have an analytical solution; therefore, to obtain analytical solutions
  of the defect absorption spectra, one can apply the distributions in
  the form of a hyperbolic secant: for the valence bands
  ))
  (
  exp(
  ))
  (
  exp(
  )
  (
  2
  )
  (
  V
  V
  V
  b
  b
  N
  g
  , (8)
  for conduction band
  ))
  (
  exp(
  ))
  (
  exp(
  )
  (
  2
  )
  (
  C
  C
  C
  b
  b
  N
  g
  ,
  (9)
  As shown in [6], the distribution of electronic states in the tails of allowed bands is
  exponential and is described by the following expressions: for the tail of the valence band
  ))
  (
  exp(
  )
  (
  )
  (
  1
  V
  V
  N
  g
  when ε
  V
  <ε; (10)
  and for the tail of the conduction band
  ))
  (
  exp(
  )
  (
  )
  (
  2
  C
  C
  N
  g
  when ε<ε
  C
  ; (11)
  where β
  1
  - and β
  2
  are the parameters that determine the curvature of the tails of the valence
  and conduction bands.
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