Fig.1. The form of the Gaussian function, the
energy derivative of the Fermi-Dirac function and
the Lorentz function at a temperature of T=300 K.
Fig.2. The form of the Gaussian function, the
derivative of the Fermi-Dirac function with
respect to energy and the Lorentz function at a
temperature of T=100 K.
Namangan Institute of Engineering and Technology
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10.25.2023
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Fig.3. The form of the Gaussian function, the derivative of the Fermi-Dirac function with respect
to energy and the Lorentz function at a temperature of T=4 K.
As can be seen from these figures, at low temperatures, the height of the distribution of the
Gaussian function is higher than the height of the Lorentz function and the height of the derivative
of the Fermi-Dirac function. From Fig. 2 and 3, it can be seen that at high temperatures, the height
of the peak of the Gaussian function is also greater than the height of the Lorentz function and the
height of the derivative of the Fermi-Dirac function.
This is an important result, indicating that the distribution of the Gaussian function is much
more efficient and tends to the ideal δ - Dirac function more quickly than the Lorentz functions and
the derivative of the Fermi-Dirac function.
References:
1.
Erkaboev, U.I., Rakhimov, R.G. Determination of the dependence of the oscillation of
transverse electrical conductivity and magnetoresistance on temperature in heterostructures based
on quantum wells. East European Journal of Physics, 2023(3), pp.133–145.
2.
Erkaboev, U.I., Rakhimov, R.G. Simulation of temperature dependence of oscillations of
longitudinal magnetoresistance in nanoelectronic semiconductor materials. e-Prime - Advances in
Electrical Engineering, Electronics and Energy, 2023, 5, 100236.
3.
Gulyamov, G., Erkaboev, U.I., Rakhimov, R.G., Mirzaev, J.I., Sayidov, N.A. Determination
of the dependence of the two-dimensional combined density of states on external factors in
quantum-dimensional heterostructures. Modern Physics Letters B, 2023, 37(10), 2350015
4.
Erkaboev, U.I., Rakhimov, R.G., Sayidov, N.A., Mirzaev, J.I. Modeling the temperature
dependence of the density oscillation of energy states in two-dimensional electronic gases under
the impact of a longitudinal and transversal quantum magnetic fields. Indian Journal of Physic, 2023,
97(4), pp.1061–1070.
5.
Erkaboev, U.I., Sayidov, N.A., Negmatov, U.M., Mirzaev, J.I., Rakhimov, R.G. Influence
temperature and strong magnetic field on oscillations of density of energy states in heterostructures
with quantum wells HgCdTe/CdHgTe. E3S Web of Conferences. 2023. Vol.401,Article ID 01090
6.
Erkaboev, U.I., Sayidov, N.A., Negmatov, U.M., Rakhimov, R.G., Mirzaev, J.I. Temperature
dependence of width band gap in In
x
Ga
1-x
As quantum well in presence of transverse strong
magnetic field. E3S Web of Conferences. 2023. Vol.401, Article ID 04042
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