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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.219
max
3
2
1
2
2
3
2
0
(
, )
( )
,
(8)
2
(
)
1
(2)
(
4
(
))
2
N
g
n
c
jds
N
g
c
g
h
E
dN h
B
m
N
h
B
dh
h
E
N
E
Here,
,
n
jds
N
h
B
is a CDS with a non-quadratic dispersion law in a quantizing magnetic field.
Figure 1 shows the CDS for InSb (Eg(0)=0.234 eV) in a magnetic field B=5 Tl. As can be seen
from these figures, we observe CDS oscillations starting from hν=0.44 eV with a non-quadratic
dispersion law. Here, hν is the energy of the absorbed photon. Expression (8) can be used to explain
the dependence of the absorption coefficient on the magnetic field for a nonparabolic dispersion
law.
We now compare the CDS oscillations for parabolic and non-parabolic dispersion laws. For
direct allowed transitions, the interband magnetoabsorption coefficient is determined by the
following expression [9]:
2
1/2
2
3/2
2
2
2
2
(0) (
)
(2
1)
(9)
r
H
c
r
g
r
N
m
e
ep
H
E
N
H
m
nc
c
p
- matrix element,
r
m
- reduced effective mass,
r
- reduced effective Bohr magneton.
Landau N-levels.
This expression will be used to calculate the absorption coefficient in the simplest case of a
direct-gap semiconductor, when the parabolic curves E(k) have extrema at k=0.
From expression (9) we obtain CDS oscillations with a quadratic dispersion law:
3/ 2
2
2
1
( ,
)
(
)
(10)
(2
1)
p
r
jds
r
N
g
r
m
N
E H
H
E
N
H
Where,
( ,
)
p
jds
N
E H
- CDS oscillations with a parabolic dispersion law,
is the energies of
the absorbed photon.
Figure 2 shows the change in CDS oscillations for two types of zones. Here, N=0..20, B=2 T, for
InSb. In these figures, in the interval E=0..1.45 eV, we observe 20 Landau levels in the non-parabolic
zone, and in the parabolic zone, the number of Landau levels will be equal to 6. Hence, it can be
seen that with increasing electron energy, the distance between Landau levels decreases, the curve
The CDS moves towards higher CDS values up along the axis of the density of states.
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