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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.237
calculation by formula
experimental data
Fig.1. The dependence of the band gap on the magnetic field in InAs
Figure 2 shows the CDS oscillations as a function of temperature in InSb with a nonparabolic
dispersion law. In this figure, the oscillations of the combined density of states start from E=ħω=0.27
eV with a non-quadratic dispersion law. Here, E=ħω is the photon energy. Figure 3 shows the
temperature dependence of the oscillations of the combined density of states with a parabolic
dispersion law. As can be seen from these figures, at high temperatures, the Landau level peaks are
almost invisible and coincide with the density of states in the absence of a magnetic field (Fig. 4).
The theoretical calculation of the contribution from lattice expansion performed by Bardeen
and Shockley shows that the band gap at high temperatures varies linearly with temperature. Based
on the theoretical consideration of the electron-phonon interaction carried out by Vasiliev and
Adams, Varshni proposed the following formula for describing the dependence of the band gap on
temperature:
2
( )
(0)
g
g
aT
E T
E
T
(2)
In works [2–4], the temperature dependence of the band gap in new materials was studied in
detail. It is shown that the band gap decreases with increasing temperature.
Hence, by substituting formula (2) into equation (1), we can calculate the temperature
dependence of the spectrum of a fan diagram in semiconductors:
2
max
1
[
( )]
4[
( )] (
)
(3)
2
g
g
c
E T
E T
N
This formula is the temperature dependence of the fan diagram, taking into account the
combined density of states.
0,0
5,0
10,0
15,0
20,0
25,0
0,0
10,0
20,0
B, T
И
зм
ен
ен
ие
E
g,
m
eV
расчет по формуле (4.14),
экспериментальные данные [126; C.1805-1808]
0,0
5,0
10,0
15,0
20,0
25,0
0,0
10,0
20,0
B, T
И
зм
ен
ен
ие
E
g,
m
eV
расчет по формуле (4.14),
экспериментальные данные [126; C.1805-1808]
0,0
5,0
10,0
15,0
20,0
25,0
0,0
10,0
20,0
B, T
И
зм
ен
ен
ие
E
g,
m
eV
расчет по формуле (4.14),
экспериментальные данные [126; C.1805-1808]
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