Table of Contents Author Guidelines Submit a Manuscript
Advances in Condensed Matter Physics
Volume 2017, Article ID 5038462, 12 pages
https://doi.org/10.1155/2017/5038462
Research Article

Low Temperature Conductivity in -Type Noncompensated Silicon below Insulator-Metal Transition

1Belarusian State University of Informatics and Radioelectronics, P. Browka 6, 220013 Minsk, Belarus
2Belarusian State University, Nezalezhnastsi Av. 4, 220030 Minsk, Belarus
3National Research Nuclear University (MEPHI), Kashirskoe Highway 31, Moscow 115409, Russia

Correspondence should be addressed to S. L. Prischepa; yb.riusb@apehcsirp

Received 17 November 2016; Revised 4 January 2017; Accepted 22 January 2017; Published 14 February 2017

Academic Editor: Da-Ren Hang

Copyright © 2017 A. L. Danilyuk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. V. Löhneysen, “Metal-insulator transition in heavily doped semiconductors,” Current Opinion in Solid State and Materials Science, vol. 3, no. 1, pp. 5–15, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. V. Dobrosavljevic, N. Trivedi, and J. M. Jr. Valles, Conductor-Insulator Quantum Phase Transitions, Oxford University Press, 2012. View at Publisher · View at Google Scholar
  3. N. F. Mott, Metal-Insulator Transitions, Taylor & Francis, London, UK, 2nd edition, 1990.
  4. P. P. Edwards and M. J. Sienko, “Universality aspects of the metal-nonmetal transition in condensed media,” Physical Review B, vol. 17, no. 6, pp. 2575–2581, 1978. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Fritzche, The Metal Non-Metal Transition in Disordered Systems, Edited by L. F. Friedman and D. P. Tunstall, University of St. Andrews, St. Andrews, UK, 1979.
  6. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, Springer, Berlin, Germany, 1984.
  7. A. L. Efros and B. I. Shklovskii, “Coulomb gap and low temperature conductivity of disordered systems,” Journal of Physics C: Solid State Physics, vol. 8, no. 4, pp. L49–L51, 1975. View at Publisher · View at Google Scholar · View at Scopus
  8. A. L. Efros, “Coulomb gap in disordered systems,” Journal of Physics C, vol. 9, no. 11, pp. 2021–2030, 1976. View at Publisher · View at Google Scholar · View at Scopus
  9. J. R. Friedman, Y. Zhang, P. Dai, and M. P. Sarachik, “Magnetic-field-induced crossover from Mott variable-range hopping to weakly insulating behavior,” Physical Review B, vol. 53, no. 15, pp. 9528–9531, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. J. Zhang, W. Cui, M. Juda et al., “Hopping conduction in partially compensated doped silicon,” Physical Review B, vol. 48, no. 4, pp. 2312–2319, 1993. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Fujimoto, H. Kobori, T. Ohyama et al., “Crossover from positive to negative magnetoresistance by the rise of electron temperature for Si:Sb in the variable-range hopping regime,” Physica B: Condensed Matter, vol. 324, no. 1–4, pp. 1–8, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Aharony, Y. Zhang, and M. P. Sarachik, “Universal crossover in variable range hopping with Coulomb interactions,” Physical Review Letters, vol. 68, no. 26, pp. 3900–3903, 1992. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Meir, “Universal crossover between Efros-Shklovskii and mott variable-range-hopping regimes,” Physical Review Letters, vol. 77, no. 26, pp. 5265–5267, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. R. Rosenbaum, N. V. Lien, M. R. Graham, and M. Witcomb, “A useful Mott-Efros-Shklovskii resistivity crossover formulation for three-dimensional films,” Journal of Physics Condensed Matter, vol. 9, no. 29, pp. 6247–6256, 1997. View at Publisher · View at Google Scholar · View at Scopus
  15. L. R. Wienkes, C. Blackwell, and J. Kakalios, “Electronic transport in doped mixed-phase hydrogenated amorphous/ nanocrystalline silicon thin films,” Applied Physics Letters, vol. 100, no. 7, Article ID 072105, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Skinner, T. Chen, and B. I. Shklovskii, “Theory of hopping conduction in arrays of doped semiconductor nanocrystals,” Physical Review B—Condensed Matter and Materials Physics, vol. 85, no. 20, Article ID 205316, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Nakatsuji, V. Dobrosavljević, D. Tanasković, M. Minakata, H. Fukazawa, and Y. Maeno, “Mechanism of hopping transport in disordered mott insulators,” Physical Review Letters, vol. 93, no. 14, Article ID 146401, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Salvato, M. Lucci, I. Ottaviani et al., “Transport mechanism in granular Ni deposited on carbon nanotubes fibers,” Physical Review B, vol. 86, no. 11, Article ID 115117, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. F. A. Zwanenburg, A. S. Dzurak, A. Morello et al., “Silicon quantum electronics,” Reviews of Modern Physics, vol. 85, no. 3, pp. 961–1019, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. E. Prati, K. Kumagai, M. Hori, and T. Shinada, “Band transport across a chain of dopant sites in silicon over micron distances and high temperatures,” Scientific Reports, vol. 6, Article ID 19704, 2016. View at Publisher · View at Google Scholar · View at Scopus
  21. N. V. Agrinskaya and V. I. Kozub, “Universal description of crossover between the Mott regime and the Coloumb-gap regime in hopping conductivity: application to compensated CdTe,” Journal of Experimental and Theoretical Physics, vol. 89, no. 6, pp. 1125–1129, 1999. View at Publisher · View at Google Scholar · View at Scopus
  22. N. V. Lien and R. Rosenbaum, “General crossovers from two-dimensional Mott T−1/3 to soft-gap Tν variable-range hopping,” Physical Review B—Condensed Matter and Materials Physics, vol. 56, no. 23, pp. 14960–14963, 1997. View at Publisher · View at Google Scholar · View at Scopus
  23. N. Van Lien and R. Rosenbaum, “General resistance crossover expressions for three-dimensional variable-range hopping,” Journal of Physics Condensed Matter, vol. 10, no. 27, pp. 6083–6090, 1998. View at Publisher · View at Google Scholar · View at Scopus
  24. P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Reviews of Modern Physics, vol. 57, no. 2, pp. 287–337, 1985. View at Publisher · View at Google Scholar · View at Scopus
  25. A. Aharoni and D. Stauffer, Introduction to Percolation Theory, Taylor & Francis, London, UK, 2nd edition, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  26. B. I. Shklovskii and A. L. Efros, “Impurity band and conductivity of compensated semiconductors,” Soviet Physics—Journal of Experimental and Theoretical Physics, vol. 33, no. 2, pp. 468–474, 1971. View at Google Scholar
  27. V. Ambegaokar, B. I. Halperin, and J. S. Langer, “Hopping conductivity in disordered systems,” Physical Review B, vol. 4, no. 8, pp. 2612–2620, 1971. View at Publisher · View at Google Scholar · View at Scopus
  28. I. S. Beloborodov, A. V. Lopatin, V. M. Vinokur, and K. B. Efetov, “Granular electronic systems,” Reviews of Modern Physics, vol. 79, no. 2, pp. 469–518, 2007. View at Publisher · View at Google Scholar · View at Scopus
  29. E. Dagotto, Nanoscale Phase Separation and Colossal Magnetoresistance, Springer, Berlin, Germany, 2002.
  30. D. Shahar, D. C. Tsui, M. Shayegan, E. Shimshoni, and S. L. Sondhi, “A different view of the quantum hall plateau-to-plateau transitions,” Physical Review Letters, vol. 79, no. 3, pp. 479–482, 1997. View at Publisher · View at Google Scholar · View at Scopus
  31. S. H. Pan, J. P. ONeal, R. L. Badzey et al., “Microscopic electronic inhomogeneity in the high-T superconductor Bi Sr CaCu O,” Nature (London), vol. 413, no. 6853, pp. 282–285, 2001. View at Google Scholar
  32. M. M. Qazilbash, A. Tripathi, A. A. Schafgans et al., “Nanoscale imaging of the electronic and structural transitions in vanadium dioxide,” Physical Review B, vol. 83, no. 16, Article ID 165108, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. P. Dai, Y. Zhang, and M. P. Sarachik, “Low-temperature transport in the hopping regime: evidence for correlations due to exchange,” Physical Review Letters, vol. 69, no. 12, pp. 1804–1806, 1992. View at Publisher · View at Google Scholar · View at Scopus
  34. H. Fritzsche and M. Cuevas, “Impurity conduction in transmutation-doped p-type germanium,” Physical Review, vol. 119, no. 4, pp. 1238–1245, 1960. View at Publisher · View at Google Scholar · View at Scopus
  35. R. K. Ray and H. Y. Fan, “Impurity conduction in silicon,” Physical Review, vol. 121, no. 3, pp. 768–779, 1961. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Inada, H. Yamamoto, M. Gibo et al., “Crossover from Efros-Shklovskii variable range hopping to nearest-neighbor hopping in silicon nanocrystal random network,” Applied Physics Express, vol. 8, no. 10, Article ID 105001, 2015. View at Publisher · View at Google Scholar · View at Scopus
  37. H. Fritzsche, “Electrical properties of germanium semiconductors at low temperatures,” Physical Review, vol. 99, no. 2, pp. 406–419, 1955. View at Publisher · View at Google Scholar · View at Scopus
  38. A. S. Ioselevich, “Spin polarons and variable range hopping in magnetically disordered systems,” Physical Review Letters, vol. 71, no. 7, pp. 1067–1070, 1993. View at Publisher · View at Google Scholar · View at Scopus
  39. J. H. Davies, “The density of states in the coulomb gap,” Philosophical Magazine B, vol. 52, no. 3, pp. 511–520, 1985. View at Publisher · View at Google Scholar · View at Scopus
  40. M. Pollak, “The Coulomb gap: a review, and new developments,” Philosophical Magazine Part B, vol. 65, no. 4, pp. 657–667, 1992. View at Publisher · View at Google Scholar · View at Scopus
  41. C. Yamanouchi, “Hall coefficient and resistivity in the intermediate impurity conduction of n-type germanium,” Journal of the Physical Society of Japan, vol. 20, no. 6, pp. 1029–1034, 1965. View at Publisher · View at Google Scholar · View at Scopus
  42. H. Nishimura, “Impurity conduction in the intermediate concentration region,” Physical Review, vol. 138, no. 3A, pp. A815–A821, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  43. E. M. Gershenzon, A. P. Mel’nikov, R. I. Rabinovich, and N. A. Serebryakova, “H-like impurity centers and molecular complexes created by them in semiconductors,” Soviet Physics—Uspekhi, vol. 23, no. 10, pp. 684–698, 1980. View at Publisher · View at Google Scholar · View at Scopus
  44. A. Kurobe and H. Kamimura, “Correlation effects on variable range hopping conduction and the magnetoresistance,” Journal of the Physical Society of Japan, vol. 51, no. 6, pp. 1904–1913, 1982. View at Publisher · View at Google Scholar · View at Scopus
  45. T. G. Castner, N. K. Lee, G. S. Cieloszyk, and G. L. Salinger, “Dielectric anomaly and the metal-insulator transition in n-type silicon,” Physical Review Letters, vol. 34, no. 26, pp. 1627–1630, 1975. View at Publisher · View at Google Scholar · View at Scopus
  46. A. Ferreira Da Silva, “Metal-insulator transitions in doped silicon and germanium,” Physical Review B, vol. 37, no. 9, pp. 4799–4800, 1988. View at Publisher · View at Google Scholar · View at Scopus
  47. I. Terry, T. Penney, S. Von Molnr, and P. Becla, “Low-temperature transport properties of Cd0.91Mn0.09Te:In and evidence for a magnetic hard gap in the density of states,” Physical Review Letters, vol. 69, no. 12, pp. 1800–1803, 1992. View at Publisher · View at Google Scholar · View at Scopus
  48. H. Vinzelberg, A. Heinrich, C. Gladun, and D. Elefant, “Activated conduction in Amorphous Cr-SiOx Thin films,” Philosophical Magazine B, vol. 65, no. 4, pp. 651–656, 1992. View at Publisher · View at Google Scholar · View at Scopus
  49. R. W. van der Heijden, G. Chen, A. T. A. M. de Waele, H. M. Gijsman, and F. P. B. Tielen, “Simple activated transport in ion-implanted Si:As at temperatures below 0.5 K,” Solid State Communications, vol. 78, no. 1, pp. 5–8, 1991. View at Publisher · View at Google Scholar · View at Scopus
  50. J.-J. Kim and H. J. Lee, “Observation of a nonmagnetic hard gap in amorphous In/InOx films in the hopping regime,” Physical Review Letters, vol. 70, no. 18, pp. 2798–2801, 1993. View at Publisher · View at Google Scholar · View at Scopus
  51. V. Voegele, S. Kalbitzer, and K. Böhringer, “Observation of correlation effects in the hopping transport in amorphous silicon,” Philosophical Magazine B, vol. 52, no. 2, pp. 153–168, 1985. View at Publisher · View at Google Scholar · View at Scopus
  52. K. G. Lisunov, E. K. Arushanov, C. Kloc, U. Malang, and E. Bucher, “Hopping conductivity in p-type β-FeSi2,” Physica Status Solidi (B) Basic Research, vol. 195, no. 1, pp. 227–236, 1996. View at Publisher · View at Google Scholar · View at Scopus
  53. K. G. Lisunov, E. Arushanov, G. A. Thomas, E. Bucher, and J. H. Schön, “Variable-range hopping conductivity and magnetoresistance in n-CuGaSe2,” Journal of Applied Physics, vol. 88, no. 7, pp. 4128–4134, 2000. View at Publisher · View at Google Scholar · View at Scopus
  54. A. Fedotov, S. Prischepa, A. Danilyuk, I. Svito, and P. Zukowski, “Spin-polarized and normal hopping magnetoresistance in heavily doped silicon,” Acta Physica Polonica A, vol. 125, no. 6, pp. 1271–1274, 2014. View at Publisher · View at Google Scholar · View at Scopus
  55. K. A. Matveev, L. I. Glazman, P. Clarke, D. Ephron, and M. R. Beasley, “Theory of hopping magnetoresistance induced by Zeeman splitting,” Physical Review B, vol. 52, no. 7, pp. 5289–5297, 1995. View at Publisher · View at Google Scholar · View at Scopus
  56. Y. Meir, “Universal spin-induced magnetoresistance in the variable-range hopping regime,” Europhysics Letters, vol. 33, no. 6, pp. 471–476, 1996. View at Publisher · View at Google Scholar · View at Scopus
  57. S. V. Demishev and A. A. Pronin, “Magnetoresistance of carbon nanomaterials,” Physics of the Solid State, vol. 48, no. 7, pp. 1363–1372, 2006. View at Publisher · View at Google Scholar · View at Scopus
  58. S. V. Demishev, A. D. Bozhko, V. V. Glushkov et al., “Scaling of magnetoresistance of carbon nanomaterials in Mott-type hopping conductivity region,” Physics of the Solid State, vol. 50, no. 7, pp. 1386–1391, 2008. View at Publisher · View at Google Scholar · View at Scopus
  59. B. I. Shklovskiĭ and A. L. Éfros, “Percolation theory and conductivity of strongly inhomogeneous media,” Soviet Physics - Uspekhi, vol. 18, no. 11, pp. 845–862, 1975. View at Publisher · View at Google Scholar · View at Scopus
  60. A. K. Fedotov, I. A. Svito, V. V. Fedotova, A. G. Trafimenko, A. L. Danilyuk, and S. L. Prischepa, “Low-temperature conductivity of silicon doped with antimony,” Semiconductors, vol. 49, no. 6, pp. 705–711, 2015. View at Publisher · View at Google Scholar · View at Scopus
  61. B. Sandow, K. Gloos, R. Rentzsch, A. N. Ionov, and W. Schirmacher, “Electronic correlation effects and the Coulomb gap at finite temperature,” Physical Review Letters, vol. 86, no. 9, pp. 1845–1848, 2001. View at Publisher · View at Google Scholar · View at Scopus
  62. I. Shlimak, M. Kaveh, R. Ussyshkin et al., “Temperature-induced smearing of the Coulomb gap: experiment and computer simulation,” Physical Review Letters, vol. 75, no. 26, pp. 4764–4767, 1995. View at Publisher · View at Google Scholar · View at Scopus
  63. A. L. Danilyuk, A. G. Trafimenko, A. K. Fedotov, I. A. Svito, and S. L. Prischepa, “Negative differential resistance in n-type noncompensated silicon at low temperature,” Applied Physics Letters, vol. 109, no. 22, Article ID 222104, 2016. View at Publisher · View at Google Scholar