Namangan Institute of Engineering and Technology

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Bog'liq ТўпламNamangan Institute of Engineering and Technology
nammti.uz
10.25.2023
Pg.230
7.
Erkaboev, U., Rakhimov, R., Mirzaev, J., Sayidov N., Negmatov, U., Abduxalimov, M.
Calculation of oscillations in the density of energy states in heterostructural materials with quantum
wells. AIP Conference Proceedings. 2023. Vol.2789, Article ID 040055
8.
Erkaboev, U., Rakhimov, R., Mirzaev, J., Sayidov N., Negmatov, U., Mashrapov, A.
Determination of the band gap of heterostructural materials with quantum wells at strong magnetic
field and high temperature. AIP Conference Proceedings. 2023. Vol.2789, Article ID 040056
9.
Erkaboev, U.I., Rakhimov, R.G., Negmatov, U.M., Sayidov, N.A., Mirzaev, J.I. Influence of
a strong magnetic field on the temperature dependence of the two-dimensional combined density
of states in InGaN/GaN quantum well heterostructures. Romanian Journal of Physics, 2023, 68(5-
6),614
DETERMINING THE FORBIDDEN BAND GAP OF QUANTUM WELL HETEROSTRUCTURED
MATERIALS UNDER THE INFLUENCE OF A STRONG MAGNETIC FIELD AND HIGH TEMPERATURE
R.G.Rakhimov
Namangan Institute of Engineering and Technology
Annotation. In this article, the temperature dependence of the band gap width in an In
x
Ga
1-
x
As quantum well in the presence of a transverse strong magnetic field is investigated. A new
method for determining the band gap width of a GaAs/In
x
Ga
1-x
As heterostructure based on an
In
x
Ga
1-x
As quantum well in the presence of a magnetic field and temperature is proposed. An
analytical expression is obtained for calculating the band gap width of a rectangular quantum well
at various magnetic fields and temperatures.
Keywords: heterostructure, band gap width, quantum well, transverse strong magnetic field,
temperature, nanoscale semiconductor materials.
In the absence of a transverse quantizing magnetic field, the energy spectrum of charge
carriers in the allowed zone of the quantum well
,
e
h
n
n
E
E
and the envelope wave function for
electrons and holes
,
e
h
n
n
are easily found from the one-electron Schrodinger equation:
2
2
2
2
2
2
(z)
(z)
(z)
2
(z)
(z)
(z)
2
e
e
e
c
n
n
n
e
h
h
h
V
n
n
n
h
E
E
m
z
E
E
m
z
(1)
Here m
e
, m
h
are the effective masses of electrons and holes. E
c
, E
V
are the edges of the
conduction band and valence band of the quantum well, and E
c
(z), E
V
(z) are functions describing the
profile of the quantum well. The movement of charge carriers in the conduction band and valence
band of the quantum well along the XY plane remains unlimited, otherwise the energy spectrum of
electrons and holes in such a plane will be quasi-continuous. But the motion of electrons and holes
along the Z axis will be quantized. Hence , the parabolic law of dispersion of the total energy of
electrons and holes in the allowed zone of a quantum well has the following form:
2
2
2
2
2
2
2
2
2
2
2
2
2
2
,
, d, n
2
2
,
, d, n
2
2
e
c
e
e
c
ex
ey
e
e
e
p
V
h
h
V
hx
hy
h
h
h
E
E k
E
k
k
n
m
m d
E
E k
E
k
k
n
m
m d
(2)
Let us now consider the temperature dependence of the discrete Landau levels of electrons
and holes in the conduction band and the valence band of a quantum well. Transverse quantizing
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