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Namangan Institute of Engineering and Technology
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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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