Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


For citation:

Filippov V. V., Zavorotniy A. A. Mathematical modeling of the electric field in anisotropic semiconductors during Hall measurements. Izvestiya of Saratov University. Physics , 2023, vol. 23, iss. 4, pp. 354-364. DOI: 10.18500/1817-3020-2023-23-4-354-364, EDN: MMFANT

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.12.2023
Full text:
(downloads: 107)
Language: 
Russian
Article type: 
Article
UDC: 
537.311.332
EDN: 
MMFANT

Mathematical modeling of the electric field in anisotropic semiconductors during Hall measurements

Autors: 
Filippov Vladimir Vladimirovich, Lipetsk State Pedagogical University named after P.P. Semenov-Tyan-Shansky
Zavorotniy Anatoliy A., Lipetsk State Technical University
Abstract: 

Background and Objectives: Modern discrete functional semiconductor devices and structural elements of micro- and nanoelectronics use materials with anisotropy of electrical properties. In particular, such materials are crystalline thermoelectrics, layered graphite structures, strained silicon. In the practical application of these semiconductors, it becomes necessary to measure their kinetic coefficients, however, the electrodynamics of these media differs from isotropic ones, which requires the correction of existing methods for measuring the specific conductivity and concentration of the main charge carriers. The paper presents a technique for solving the Neumann problem with inhomogeneous boundary conditions for the electric field potential in a rectangular region in a relatively weak magnetic field in a linear approximation. Materials and Methods: The boundary value problem considered in the paper occurs in the analysis of measurements of the Hall effect by probe methods. Using the perturbation theory and the Fourier method, an expression for the Hall field potential is obtained, presented in rectangular coordinates as a series of harmonic functions, convenient for further practical use. Results: Practically important expressions for the analysis of Hall measurements by probe methods have been obtained for anisotropic samples with flat boundaries. An analysis of the obtained solution and computer simulation of the electric potential in anisotropic semiconductor wafers with flat boundaries have been performed. Conclusion: An experimental verification of the obtained distributions of potentials and practical recommendations on the application of the obtained theoretical expressions are presented.

Reference: 
  1. Marenkin S. F., Trukhan V. M. Fosfidy, arsenidy tsinka i kadmiya [Phosphides, zinc and cadmium arsenides]. Minsk, Varaskin, 2010. 224 p. (in Russian).
  2. Gridnev S. A., Kalinin Yu. E., Makagonov V. A., Shuvaev A. S. Promising thermoelectric Materials. International Scientific Journal for Alternative Energy and Ecology, 2013, no. 1-2 (118), pp. 117–125.
  3. Yang J., Li J., Zhang C., Feng Z., Shi B., Zhai W., Yan Y., Wang Y. Excellent thermoelectric performance of BaMgSi driven by low lattice thermal conductivity: A promising thermoelectric material. Journal of Alloys and Compounds, 2020, vol. 827, pp. 154342. https://doi.org/10.1016/j.jallcom.2020.154342
  4. Wang C., Zheng C., Gao G. Bulk and Monolayer ZrS3 as Promising Anisotropic Thermoelectric Materials: A Comparative Study. The Journal of Physical Chemistry C, 2020, vol. 124, no. 12, pp. 6536–6543. https://doi.org/10.1021/acs.jpcc.0c00298
  5. Nemov S. A., Ulashkevich Yu. V., Pogumirsky M. V., Stepanova O. S. Reflection from the Side Face of a PbSb2Te4 Crystal. Semiconductors, 2020, vol. 54, iss. 3, pp. 282–284. https://doi.org/10.1134/S1063782620030161
  6. Yapryntsev M. N., Ivanov O. N., Vasil’ev A. E., Zhezhu M. V., Popkov D. A. Synthesis, structure and anisotropy of thermoelectric properties of Bi2Te2.7Se0.3 compound doped with samarium. Semiconductors, 2022, vol. 55, iss. 14, pp. 2121. https://doi.org/10.21883/SC.2022.14.53856.16
  7. Pokhrel T. R., Majumder A. Impact of Work Function Engineering on Strained Silicon Based Double Gated Junction-less Transistor. Silicon, 2022, vol. 14, pp. 10061–10069. https://doi.org/10.1007/s12633-022-01661-3
  8. Beccari A., Visani D. A., Fedorov S. A., Bereyhi M. J., Boureau V., Engelsen N. J., Kippenberg T. J. Strained crystalline nanomechanical resonators with quality factors above 10 billion. Nature Physics, 2022, vol. 18, pp. 436–441. https://doi.org/10.1038/s41567-021-01498-4
  9. Orton J. W., Blood P. The Electrical Characterization of Semiconductors: Measurement of Minority Carrier Properties. Academic Press, London, San Diego, 1990. 735 p.
  10. Batavin V. V., Kontsevoy Yu. A., Fedorovich Yu. V. Izmerenie parametrov poluprovodnikovykh materialov i struktur [Measurement of parameters of semiconductor materials and structures]. Moscow, Radio i svyaz’, 1985. 264 p. (in Russian)
  11. Lugansky L. B., Tsebro V. I. Four-probe methods for measuring the resistivity of samples in the form of rectangular parallelepipeds. Instruments and Experimental Techniques, 2015, vol. 58, no. 1, pp. 118–129. https://doi.org/10.1134/S0020441215010200
  12. Filippov V. V. A four-probe method for joint measurements of components of the tensors of the conductivity and the Hall coefficient of anisotropic semiconductor films. Instruments and Experimental Techniques, 2012, vol. 55, no. 1, pp. 104–109. https://doi.org/10.1134/S0020441212010046
  13. Askerov B. M. Electron Transport Phenomena in Semiconductors. World Scientific, Singapore, New Jersey, London, 1994. 412 p. (Russ. ed.: Moscow, Nauka, 1985. 320 p.). https://doi.org/10.1142/1926
  14. Filippov V. V., Bormontov E. N. Features of the electricfield distribution in anisotropic semiconductor wafers in a transverse magnetic field. Semiconductors, 2013, vol. 47, iss. 7, pp. 884–891. https://doi.org/10.1134/S1063782613070063
  15. Filippov V. V., Mitsuk S. V. Modelling magnetoresistance effect in limited anisotropic semiconductors. Chinese Physics Letters, 2017, vol. 34, no. 7, pp. 077201. https://doi.org/10.1088/0256-307X/34/7/077201
  16. Baranskij P I., Buda I. S., Dakhovsky I. V., Kolomoets V. V. Elektricheskie i gal’vanomagnitnye javlenija v anizotropnykh poluprovodnikakh [Electrical and galvanomagnetic phenomena in anisotropic semiconductors]. Kiev, Naukova dumka, 1977. 270 p. (in Russian).
  17. Landau L. D., Lifshitz E. M. Electrodynamics of Continuous Media. Oxford, Pergamon Press, 1984. 474 p. (Russ. ed.: Moskow, Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, 1982. 621 p.).
  18. Korn G. A., Korn T. M. Mathematical Handbook for Scientists and Engineers. Definitions, Theorems, and Formulas for Reference and Review. Dover Publications, Inc., New York, 2000. 1152 p. (Russ. ed.: Saint Petersburg, Lan’, 2003. 832 p.).
  19. Webster A. Partial Differential Equations of Mathematical Physics: Second edition. Dover Books on Mathematics. Dover Publications, Inc., New York, 2016. 464 p.
  20. Gurevich Yu. G., Kucherenko V. V., Ramires de Areiano E. A problem with directional derivative in the theory of galvanomagnetic effects. Mathematical Notes, 1999, vol. 65, pp. 436–446. https://doi.org/10.1007/BF02675357
  21. Gonzalez G., Gurevich Yu. G., Prosentsov V. V. New mechanism of magnetoresistance in bulk semiconductors: Boundary condition effects. Solid State Communications, 1996, vol. 97, no. 12, pp. 1069–1072. https://doi.org/10.1016/0038-1098(96)00032-4
  22. Kibirev V. V. Basic boundary value problems of potential theory. Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, Informatika [Bulletin of the Buryat State University. Mathematics, Computer Science], 2015, no. 2, pp. 22–29 (in Russian).
  23. Filippov V. V., Vlasov A. N. Probe Measurements of the Potential Distribution in Anisotropic Semiconductor Crystals and Films. Russian Microelectronics, 2013, vol. 42, no. 7, pp. 428–432. https://doi.org/10.1134/S1063739712070190
  24. Makarov E. G. Inzhenernye raschety v Mathcad 15 [Engineering calculations in Mathcad 15]. Saint Petersburg, Piter, 2011. 402 p. (in Russian).
  25. Maxfield B. Essential Mathcad for Engineering, Science, and Math. 2nd edition. Elsevier Science, Academic Press, 2009. 501 p.
  26. Lazarev V. B., Shevchenko V. Ya., Grinberg Ya. Kh., Sobolev V. V. Poluprovodnikovye soedineniya gruppy AIIBV [Semiconductor compounds of the AIIBV group]. Moscow, Nauka, 1977. 148 p. (in Russian).
  27. Filippov V. V., Zavorotny A. A., Tigrov V. P. Modified Van der Pauw method of measuring the electrical conductivity tensor of anisotropic semiconductor films. Russian Physics Journal, 2019, vol. 62, no. 1, pp. 105–113. https://doi.org/10.1007/s11182-019-01689-w
Received: 
07.04.2023
Accepted: 
20.05.2023
Published: 
25.12.2023