Migration of electrons via triple-charged defects of crystal matrix

  • Nikolai A. Poklonski Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-0799-6950
  • Aliaksandr N. Dzeraviaha Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-0021-4303
  • Sergey A. Vyrko Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Aliaksandr I. Kavaleu Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0003-2711-2005

Abstract

The study of semiconductor materials with point radiation defects of the crystal structure in three charge states (–1), (0), (+1) is important for determining the conditions of their radiation resistance under the influence of gamma rays, fast electrons, etc. Such defects are self-sufficient to ensure electrical neutrality of the material under conditions of ionization equilibrium, that issue determines the radiation resistance of materials. In silicon and diamond crystals, such irradiation-induced defects during their accumulation stabilize the Fermi level in the vicinity of one third of the band gap from the top of the valence band. The purpose of the work is an analytical description of the stationary hopping electron transfer in a semiconductor, taking into account the joint migration of both the single electrons and the pairs of electrons over these triple-charged defects. A crystalline semiconductor is considered as a matrix containing immobile point defects of one sort in the prevailing concentration. For the first time in the drift-diffusion approximation, a phenomenological theory is constructed of coexisting migration of both the single electrons (transitions from the charge state (–1) to state (0) and from the state (0) to state (+1)), and the electron pairs (transitions from the state (–1) to state (+1)) by means of their hopping between such defects when an external stationary electric field is applied to the semiconductor. In the linear approximation, analytical expressions are obtained for the screening length of a static electric field and the length of the hopping diffusion of electrons migrating via such defects. It is shown that the additional contribution of the hopping transport of electron pairs leads to a decrease in the screening length and also changes the diffusion length.

Author Biographies

Nikolai A. Poklonski, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (physics and mathematics), full professor; professor at the department of semiconductor physics and nanoelectronics, faculty of physics

Aliaksandr N. Dzeraviaha, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

postgraduate student at the department of semiconductor physics and nanoelectronics, faculty of physics

Sergey A. Vyrko, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics); senior researcher at the laboratory of physics of electronic materials, department of semiconductor physics and nanoelectronics, faculty of physics

Aliaksandr I. Kavaleu, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics); senior lecturer at the department of semiconductor physics and nano-electronics, faculty of physics

References

  1. Brudnyi VN. Charge neutrality in semiconductors: defects, interfaces, surface. Russian Physics Journal. 2013;56(7):754 –756. DOI: 10.1007/s11182-013-0095-4.
  2. Yamaguchi M. Radiation-resistant solar cells for space use. Solar Energy Materials and Solar Cells. 2001;68(1):31–53. DOI: 10.1016/S0927-0248(00)00344-5.
  3. Poklonski NA, Vyrko SA, Zabrodskii AG. Calculation of capacitance of self-compensated semiconductors with intercenter hops of one and two electrons (by the example of silicon with radiation defects). Semiconductors. 2008;42(12):1388 –1394. DOI: 10.1134/S1063782608120038.
  4. Poklonski NA, Kovalev AI, Vyrko SA, Vlasov AT. Semiconductor diode with hopping migration of electrons via point defects of crystalline matrix. Doklady of the National Academy of Sciences of Belarus. 2017;61(3):30 –37. Russian.
  5. Poklonski NA, Kovalev AI, Vyrko SA. Drift and diffusion of electrons via two-level (triple-charged) point defects in crystalline semiconductors. Doklady of the National Academy of Sciences of Belarus. 2014;58(3):37– 43. Russian.
  6. Poklonski NA, Vyrko SA, Kovalev AI. Stationary hopping migration of bipolarons via «soft» point defects in partly disordered semiconductors. Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series. 2014;3:91–96. Russian.
  7. Pollak M. Hopping – past, present and future (?). Physica Status Solidi B. 2002;230(1):295–304. DOI: 10.1002/1521-3951(200203)230:1<295::AID- PSSB295>3.0.CO;2-C.
  8. Shlimak I. Is hopping a science? Selected topics of hopping conductivity. Singapore: World Scientific; 2015. 156 p. DOI: 10.1142/9522.
  9. Poklonski NA, Vyrko SA, Kovalev AI, Dzeraviaha AN. Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands. Journal of Physics Communications. 2018;2:015013. DOI: 10.1088/2399-6528/aa8e26.
  10. Korn GA, Korn TM. Mathematical handbook for scientists and engineers: definitions, theorems, and formulas for reference and review. New York: Dover; 2000. xx+1130 p.
  11. Arnol’d VI. Ordinary differential equations. Berlin: Springer; 1992. 334 p. Russian edition: Arnol’d VI. Obyknovennye differentsial’nye uravneniya. Moscow: Moskovskii tsentr nepreryvnogo matematicheskogo obrazovaniya; 2014. 341 p.
  12. Farlow SJ. An introduction to differential equations and their applications. New York: Dover; 2006. 640 p. (Dover Books on Mathematics).
  13. Poklonskii NA, Lopatin SYu. Stationary hopping photoconduction among multiply charged impurity atoms in crystals. Physics of the Solid State. 1998;40(10):1636 –1640. DOI: 10.1134/1.1130623.
  14. Manifacier JC, Henisch HK. The concept of screening length in lifetime and relaxation semiconductors. Journal of Physics and Chemistry of Solids. 1980;41(11):1285–1288. DOI: 10.1016/0022-3697(80)90166-3.
  15. Warner RM. Normalization in semiconductor problems. Solid-State Electronics. 1985;28(5):529–530. DOI: 10.1016/0038-1101(85)90118-2.
Published
2020-02-05
Keywords: crystalline semiconductor, triple-charged point defects, hopping of single electrons, hopping of electron pairs, screening length, diffusion length
Supporting Agencies The work was supported by the Belarusian National Research Program «Fizmattekh», Belarusian Republican Foundation for Fundamental Research (grant No. F19RM-054), and by the European Union Framework Programme for Research and Innovation Horizon 2020 (grant No. H2020-MSCA-RISE-2019-871284 SSHARE).
How to Cite
Poklonski, N. A., Dzeraviaha, A. N., Vyrko, S. A., & Kavaleu, A. I. (2020). Migration of electrons via triple-charged defects of crystal matrix. Journal of the Belarusian State University. Physics, 1, 41-53. https://doi.org/10.33581/2520-2243-2020-1-41-53