Investigation of the Lorenz number and the carrier concentration of the GaAs semiconductor depending on temperature

Yıl 2021, , 89 - 97, 31.12.2021

Ebru Çopuroğlu

https://doi.org/10.54187/jnrs.1013381

Öz

As is known, semiconductors are insulators under normal conditions but can become conductive with external excitation. Considering the effects of acting on these materials, the number of free electrons and the electrical conductivity will increase with increasing temperature. The increase in the concentration of free electrons in the semiconductor can be shown as the increase in electrical conductivity. If a semiconductor is exposed to an electric field with increasing concentration, we can have an idea about how the number of free electrons or the speed of free electrons will be affected. It is well known that it is necessary to calculate two-parameter Fermi functions to solve the properties of kinetic effects and electron transport phenomena in semiconductors. Effective methods have been developed for the calculation of two-parameter Fermi functions in literature. In this study, analytical calculations for the Lorenz number and the carrier concentration of the GaAs semiconductor were made using the two-parameter Fermi function.

Anahtar Kelimeler

Hall Coefficient, Fermi integral, Carrier concentration, Semiconductors

Kaynakça

• C. Kittel, Introduction to solid state physics, John Wiley & Sons. Inc., Sixth Edition, New York, 1986.
• N. W. Ashcroft, N.D. Mermin, Solid state physics, Philadelphia Pa., New York, 1976.
• H. P. Myers, Introductory solid state physics. CRC Press, London, 1997.
• E. O. Kane, Band structure of indium antimonide, Journal of Physics and Chemistry of Solids, 1(4), (1957) 249–261.
• B. Šantić, B., U. V. Desnica, Thermoelectric effect spectroscopy of deep levels—application to semi‐insulating GaAs, Applied Physics Letters, 56(26), (1990) 2636–2638.
• L. Zhu, R. Ma, L. Sheng, M. Liu, D. N. Sheng, Universal thermoelectric effect of Dirac fermions in graphene, Physical Review Letters, 104(7), (2010) 076804.
• D. Segal, Thermoelectric effect in molecular junctions: A tool for revealing transport mechanisms, Physical Review B, 72(16), (2005) 165426.
• P. E. Nielsen, P. L. Taylor, Theory of thermoelectric effects in metals and alloys, Physical Review B, 10(10), (1974) 4061.
• G. Sansone, A. Ferretti, L. Maschio, Ab initio electronic transport and thermoelectric properties of solids from full and range-separated hybrid functionals, The Journal of Chemical Physics, 147(11), (2017) 114101.
• B. M. Askerov, F. M. Gashimzade, Determination of parameters of degenerate semiconductors, Physica Status Solidi (b), 21(2), (1967) 155–158.
• B. M. Askerov, Kinetic effects in semiconductors, Science, Leningrad, 1970.
• B. M. Askerov, Electron transport phenomena in semiconductors. World Scientific, London, 1994.
• H. S. Kim, Z. M. Gibbs, Y. Tang, H. Wang, G. J. Snyder, Characterization of Lorenz number with Seebeck coefficient measurement, APL materials, 3(4), (2015) 041506.
• M. Thesberg, H. Kosina, N. Neophytou, On the Lorenz number of multiband materials, Physical Review B, 95(12), (2017) 125206.
• P. J. Price, Theory of transport effects in semiconductors: Thermoelectricity, Physical Review, 104(5), (1956) 1223.
• A. Putatunda, D. J. Singh, Lorenz number in relation to estimates based on the Seebeck coefficient, Materials Today Physics, 8, (2009) 49–55.
• O. S. Gryazanov, Tables for the calculation of kinetic coefficients in semiconductor, Nauka, Leningrad, 1971.
• W. Zawadzki, R. Kowalczyk, J. Kolodziejczak, The Generalized Fermi‐Dirac integrals, Physica Status Solidi (b), 10(2), (1965) 513–518.
• G. Rzadkowski, S. Łepkowski, A generalization of the Euler-Maclaurin summation formula: an application to numerical computation of the Fermi-Dirac integrals, Journal of Scientific Computing, 35(1), (2008) 63–74.
• I. I. Guseinov, B. A. Mamedov, B. A. Unified treatment for accurate and fast evaluation of the Fermi–Dirac functions, Chinese Physics B, 19(5), (2010) 050501.
• B. A. Mamedov, E. Copuroglu, Unified analytical treatments of the two-parameter Fermi functions using binomial expansion theorem and incomplete gamma functions, Solid State Communications, 245, (2016) 42–49.
• I. M. Ryzhik, I. S. Gradshteyn, Tables of integrals and sums, series, and products, Academic Press, New York, 1980.
• E. Çopuroğlu, I. M. Askerov, A. Aslan, Analytical calculation of temperature dependence of the Lorenz number in semiconductors, Journal of Science and Arts, 20(1), (2020)197–202.
• M. Shur, Physics of semiconductor devices, Englewood Cliffs, Prentice-Hall, 1990.