Abstract:
We obtain continuous analytical expressions approximating the Fermi–Dirac integrals of orders j=−1/2,1/2,1,3/2,2,5/2,3,7/2 in a convenient form for calculation with reasonable accuracy (1÷4)% in a wide range of the degeneration in this paper. An approach based on the least square method for approximation was used. The demands to the approximation of integrals, to the range of variation of order j and to the definitional domain are considered in terms of the use of Fermi–Dirac integrals to determine the properties of metals and semiconductors.
Citation:
O. N. Koroleva, A. V. Mazhukin, V. I. Mazhukin, P. V. Breslavskiy, “Analytical approximation of the Fermi–Dirac integrals of half-integer and integer orders”, Mat. Model., 28:11 (2016), 55–63; Math. Models Comput. Simul., 9:3 (2017), 383–389
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F. Lanzini, H. O. Di Rocco, “An implementation of the average atom model using the thermodynamic consistency condition: application to Ar”, Acta Phys. Pol. A, 134:6 (2018), 1126–1133
O. N. Koroleva, A. V. Mazhukin, “Thermophysical characteristics of an electron gas of silicon in the region of phase transformations”, Keldysh Institute preprints, 2018, 73–27
N. N. Kalitkin, S. A. Kolganov, “Calculation of the Fermi–Dirac functions with exponentially convergent quadratures”, Math. Models Comput. Simul., 10:4 (2018), 472–482
O. N. Koroleva, A. V. Mazhukin, “Determination of thermal conductivity and heat capacity of silicon electron gas”, Math. Montisnigri, 40 (2017), 99–109
O. N. Koroleva, V. I. Mazhukin, A. V. Mazhukin, “Calculation of silicon band gap by means of Fermi-Dirac integrals”, Math. Montisnigri, 38 (2017), 49–62
O. N. Koroleva, A. V. Mazhukin, “Determination of transport properties of silicon electron gas”, Math. Montisnigri, 39 (2017), 57–66
A. V. Mazhukin, O. N. Koroleva, V. I. Mazhukin, A. V. Shapranov, “Continual and molecular dynamics approaches in determining thermal properties of silicon”, Third International Conference on Applications of Optics and Photonics, Proceedings of SPIE, 10453, ed. M. Costa, SPIE-Int. Soc. Optical Engineering, 2017, UNSP 104530Y
Mazhukin V.I., Koroleva O.N., Mazhukin A.V., Aleshchenko Yu.A., “Effect of Degenerate Carriers on Si Band Gap Narrowing”, Bull. Lebedev Phys. Inst., 44:7 (2017), 198–201
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