Volumes and Issues
Home » Semiconductors » Year 2022, issue 11 » Article p. 823
<<<>>>
Maximum hopping direct current conductivity via hydrogen-like impurities in semiconductors
Russian version
DOI: 10.21883/SC.2022.11.54957.9945
Poklonski N. A. 1, Vyrko S. A. 1, Anikeev I. I.1, Zabrodskii A. G. 2
1Belarusian State University, Minsk, Republic of Belarus
2Ioffe Institute, St. Petersburg, Russia
Email: poklonski@bsu.by, vyrko@bsu.by, ilyaanikeev35@mail.ru, Andrei.Zabrodskii@mail.ioffe.ru
PDF
A quasi-classical model for calculating DC (direct current) electrical conductivity in crystalline semiconductors with hydrogen-like impurities is developed at the transition from band conduction to impurity hopping conduction with decreasing temperature. This transition from the minimum band conductivity to the maximum hopping conductivity via impurities has the form of a characteristic "kink" in the temperature dependence of the electrical resistivity. The idea of the calculation is to preliminarily determine the transition temperature Tj using the standard approach within the framework of the two-band model. The shift of the top of the v-band (the bottom of the c-band) into the depth of the band gap due to the formation of a quasi-continuous band of allowed energy values from the excited states of acceptors (donors) is taken into account. This leads to a decrease in the value of a thermal ionization energy of the majority shallow impurities due to a decrease in the maximum localization radius of a hole on an acceptor (an electron on a donor) with increasing impurity concentration. The values of the observed maximum hopping conductivity and drift hopping mobility corresponding to the temperature Tj are calculated. The numerical calculation within the framework of the proposed model is consistent with the known experimental data on the electrical conductivity and Hall coefficient of moderately compensated p-Ge crystals doped by neutron transmutation and non-intentionally compensated metallurgically doped n-Ge, as well as n- and p-Si crystals on the insulator side of the Mott insulator-metal concentration phase transition. Keywords: bulk crystals of germanium and silicon, hydrogen-like acceptors and donors, holes and electrons, band and hopping motion of charge carriers.
  1. H. Zhu, J. Zhu, W. Hu, Y. Xiao, J. Shen, Q. Li, K. Zhang, K. Deng, T. He, H. Wu, N. Li, W. Lu. J. Appl. Phys. Lett., 119, 191104 (2021)
  2. Y. Chen, B. Wang, Y. Zang, C. Zhang, H. Zhang, Y. Yuan, D. Zhou, L. Hou, M. Pan, X. Wang. IEEE J. Quant. Electron., 56 (3), 4000506 (2020)
  3. L.A. Reichertz, J.W. Beeman, B.L. Cardozo, N.M. Haegel, E.E. Haller, G. Jakob, R. Katterloher. Proc. SPIE, 5543, 231 (2004)
  4. S. Datta. Phys. Rev. Lett., 44 (12), 828 (1980)
  5. M. Pollak. Phys. Status Solidi B, 230 (1), 295 (2002)
  6. V.F. Gantmakher, V.T. Dolgopolov. Phys. Usp., 51 (1), 3 (2008)
  7. P. Stallinga. Adv. Mater., 23 (30), 3356 (2011)
  8. N.A. Poklonski, S.A. Vyrko, O.N. Poklonskaya, A.G. Zabrodskii. J. Appl. Phys., 110 (12), 123702 (2011)
  9. N.A. Poklonski, S.A. Vyrko, O.N. Poklonskaya, A.G. Zabrodskii. Semiconductors, 50 (6), 722 (2016)
  10. A.L. Efros, B.I. Shklovskii. J. Phys. C: Solid State Phys., 8 (4), L49 (1975)
  11. N.F. Mott. Phil. Mag., 19 (160), 835 (1969)
  12. A.G. Zabrodskii. Phil. Mag. B, 81 (9), 1131 (2001)
  13. N.A. Poklonski, S.A. Vyrko, O.N. Poklonskaya, A.I. Kovalev, A.G. Zabrodskii. J. Appl. Phys., 119 (24), 245701 (2016)
  14. B.I. Shklovskii, A.L. Efros. Electronic Properties of Doped Semiconductors (Berlin, Springer, 1984)
  15. I. Shlimak. Is Hopping a Science? Selected Topics of Hopping Conductivity (World Scientific, Singapore, 2015)
  16. N.F. Mott. Impurity bands in silicon and germanium. In: M.A. Kastner, G.A. Thomas, S.R. Ovshinsky (eds). Disordered Semiconductors (London, Plenum, 1987) p. 3
  17. N.A. Poklonski, S.A. Vyrko, A.G. Zabrodskii. Phys. Solid State, 46 (6), 1101 (2004)
  18. N.A. Poklonski, S.A. Vyrko, A.I. Kovalev, A.N. Dzeraviaha. J. Phys. Commun., 2 (1), 015013 (2018)
  19. N. Mott. J. Phys. C: Solid State Phys., 20 (21), 3075 (1987)
  20. A.M. Mathai. An Introduction to Geometrical Probability: Distributional Aspects with Applications (Amsterdam, Gordon and Breach Science Publishers, 1999)
  21. N.A. Poklonski, S.A. Vyrko, A.N. Dzeraviaha. J. Belarusian State Univ. Phys., N 2, 28 (2020) (in Russian)
  22. N.A. Poklonski, A.N. Dzeraviaha, S.A. Vyrko, A.G. Zabrodskii, A.I. Veinger, P.V. Semenikhin. AIP Advances, 11 (5), 055016 (2021)
  23. N.L. Lavrik, V.P. Voloshin. J. Chem. Phys., 114 (21), 9489 (2001)
  24. K.S. Shifrin. J. Phys. (USSR), 8 (1-6), 242 (1944)
  25. D.V. Eddolls. Phys. Status Solidi, 17 (1), 67 (1966)
  26. G.E. Stillman, C.M. Wolfe. Thin Sol. Films, 31 (1-2), 69 (1976)
  27. A.L. Khomkin, A.S. Shumikhin. Phys. Usp., 64 (11), 1125 (2021)
  28. G.E. Norman, I.M. Saitov. Phys. Usp., 64 (11), 1094 (2021)
  29. A.A. Likal'ter. Phys. Usp, 43 (8), 777 (2000)
  30. K.W. Boer, U.W. Pohl. Semiconductor Physics (Cham, Springer, 2018)
  31. P.Y. Yu, M. Cardona. Fundamentals of Semiconductors. Physics and Materials Properties (Heidelberg, Springer, 2010)
  32. N.A. Poklonski, S.A. Vyrko, V.I. Yatskevich, A.A. Kocherzhenko. J. Appl. Phys., 93 (12), 9749 (2003)
  33. N.A. Poklonski, A.A. Kocherzhenko, S.A. Vyrko, A.T. Vlassov. Phys. Status Solidi B, 244 (10), 3703 (2007)
  34. E. Conwell, V.F. Weisskopf. Phys. Rev., 77 (3), 388 (1950)
  35. N.A. Poklonski, S.A. Vyrko, A.N. Dzeraviaha. Semiconductors, 52 (6), 692 (2018)
  36. O. Madelung (ed.). Semiconductors: Data Handbook (Berlin, Springer, 2004)
  37. S. Adachi. Properties of Group-IV, III-V and II-VI Semiconductors (Chichester, Wiley, 2005)
  38. M. Levinshtein, S. Rumyantsev, M. Shur (eds). Handbook Series on Semiconductor Parameters (Singapore, World Scientific, 1996)
  39. J.S. Blakemore. Semiconductor Statistics (N.Y., Dover, 2002)
  40. M.V. Alekseenko, A.G. Zabrodskii, L.M. Shterengas. Semiconductors, 32 (7), 720 (1998)
  41. H. Matsuura, Y. Kondo, K. Iida, A. Hidaka, S. Ji, K. Eto, K. Kojima, T. Kato, S. Yoshida, H. Okumura. Jpn. J. Appl. Phys., 60, 031008 (2021)
  42. A. Avdonin, P. Skupinski, K. Grasza. Physica B, 483, 13 (2016)
  43. H. Fritzsche, M. Cuevas. Phys. Rev., 119 (4), 1238 (1960)
  44. H. Fritzsche, M. Cuevas. In Proc. Int. Conf. on Semicond. Phys., Prague, 1960 (Prague, Pub. Czech. Acad. Sci., 1961) p. 222
  45. H.C. Thomas, B. Covington. J. Appl. Phys., 48 (8), 3434 (1977)
  46. A.G. Zabrodskii, A.G. Andreev, M.V. Alekseenko. Sov. Phys. Semicond., 26 (3), 244 (1992)
  47. A.G. Andreev, V.V. Voronkov, G.I. Voronkova, A.G. Zabrodskii, E.A. Petrova. Semiconductors, 29 (12), 1162 (1995)
  48. A.G. Zabrodskii, A.G. Andreev, S.V. Egorov. Phys. Status Solidi B, 205 (1), 61 (1998)
  49. L.V. Govor, V.P. Dobrego, N.A. Poklonskii. Sov. Phys. Semicond., 18 (11), 1292 (1984)
  50. R. Rentzsch, O. Chiatti, M. Muller, A.N. Ionov. Phys. Status Solidi B, 230 (1), 237 (2002)
  51. H. Fritzsche. J. Phys. Chem. Solids, 6 (1), 69 (1958)
  52. E.A. Davis, W.D. Compton. Phys. Rev., 140 (6A), A2183 (1965)
  53. K.R. Atkins, R. Donovan, R.H. Walmsley. Phys. Rev., 118 (2), 411 (1960)
  54. G.A. Swartz. J. Phys. Chem. Solids, 12 (3-4), 245 (1960)
  55. R.K. Ray, H.Y. Fan. Phys. Rev., 121 (3), 768 (1961)
  56. T.G. Castner, N.K. Lee, H.S. Tan, L. Moberly, O. Symko. J. Low Temp. Phys., 38 (3-4), 447 (1980)
  57. T.M. Lifshits. Instrum. Exp. Tech., 36 (1), 1 (1993)
  58. A.G. Zabrodskii, M.V. Alekseenko. Semiconductors, 28 (1), 101 (1994)
  59. N.A. Poklonski, S.A. Vyrko, A.I. Kovalev. Doklady of the National Academy of Sciences of Belarus, 62 (4), 406 (2018) (in Russian).

Подсчитывается количество просмотров абстрактов ("html" на диаграммах) и полных версий статей ("pdf"). Просмотры с одинаковых IP-адресов засчитываются, если происходят с интервалом не менее 2-х часов.

Дата начала обработки статистических данных - 27 января 2016 г.

Publisher:

Ioffe Institute

Institute Officers:

Director: Sergei V. Ivanov

Contact us:

26 Polytekhnicheskaya, Saint Petersburg 194021, Russian Federation
Fax: +7 (812) 297 1017
Phone: +7 (812) 297 2245
E-mail: post@mail.ioffe.ru