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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.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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