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Spin-dependent intravalley and intervalley electron-phonon scatterings in germanium

  • Semiconductors
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Abstract

The spin-dependent electron-phonon scattering in the L and Γ valleys of germanium crystals has been investigated theoretically. For this purpose, the 16 × 16 k · p Hamiltonian correctly describing the electron dispersion in the vicinity of the L point of the Brillouin zone in germanium in the lowest conduction bands and the highest valence bands has been constructed. This Hamiltonian facilitates the analysis of the spin-dependent properties of conduction electrons. Then, the electron scatterings by phonons in the L and Γ valleys, i.e., intra-L valley, intra-Γ valley, inter-L-Γ valley, and inter-L-L valley scatterings, have been considered successively. The scattering matrix expanded in powers of the electron wave vectors counted from the centers of the valleys has been constructed using the invariant method for each type of processes. The numerical coefficients in these matrices have been found by the pseudopotential method. The partial contributions of the Elliott and Yafet mechanisms to the spin-dependent electron scattering have been analyzed. The obtained results can be used in studying the optical orientation and relaxation of hot electrons in germanium.

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References

  1. I. Žutić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004).

    Article  ADS  Google Scholar 

  2. M. W. Wu, J. H. Jiang, and M. Q. Weng, Phys. Rep. 493, 61 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  3. P. Y. Yu, and M. Cardona, Fundamentals of Semiconductors: Physics and Materials Properties, 3rd ed. (Springer-Verlag, New York, 2001).

    Google Scholar 

  4. D. Culcer, L. Cywi ski, Q. Li, X. Hu, and S. Das Sarma, Phys. Rev. B: Condens. Matter 80, 205302 (2009).

    Article  ADS  Google Scholar 

  5. N. W. Gray and A. Tiwari, Appl. Phys. Lett. 98, 102112 (2011).

    Article  ADS  Google Scholar 

  6. K. R. Jeon, B. C. Min, I. J. Shin, C. Y. Park, H. S. Lee, Y. H. Jo, and S. C. Shin, Appl. Phys. Lett. 98, 262102 (2011).

    Article  ADS  Google Scholar 

  7. B. T. Jonker, G. Kioseoglou, A. T. Hanbicki, C. H. Li, and P. E. Thompson, Nat. Phys. 3, 542 (2007).

    Article  Google Scholar 

  8. I. Appelbaum, B. Huang, and D. J. Monsma, Nature (London) 447, 295 (2007).

    Article  ADS  Google Scholar 

  9. L. Grenet, M. Jamet, P. Noé, V. Calvo, J. M. Hartmann, L. E. Nistor, B. Rodmacq, S. Auffret, P. Warin, and Y. Samson, Appl. Phys. Lett. 94, 032502 (2009).

    Article  ADS  Google Scholar 

  10. S. P. Dash, S. Sharma, R. S. Patel, M. P. de Jong, and R. Jansen, Nature (London) 462, 491 (2009).

    Article  ADS  Google Scholar 

  11. E. J. Loren, B. A. Ruzicka, L. K. Werake, H. Zhao, H. M. van Driel, and A. L. Smirl, Appl. Phys. Lett. 95, 092107 (2009).

    Article  ADS  Google Scholar 

  12. J. Rioux and J. E. Sipe, Phys. Rev. B: Condens. Matter 81, 155215 (2010).

    Article  ADS  Google Scholar 

  13. E. J. Loren, J. Rioux, C. Lange, J. E. Sipe, H. M. van Driel, and A. L. Smirl, Phys. Rev. B: Condens. Matter 84, 214307 (2011).

    Article  ADS  Google Scholar 

  14. P. Li and H. Dery, Phys. Rev. Lett. 107, 107203 (2011).

    Article  ADS  Google Scholar 

  15. A. Jain, L. Louahadj, J. Peiro, J. C. Le Breton, C. Vergnaud, A. Barski, C. Beigné, L. Notin, A. Marty, V. Baltz, S. Auffret, E. Augendre, H. Jaffrés, J. M. George, and M. Jamet, Appl. Phys. Lett. 99, 162102 (2011).

    Article  ADS  Google Scholar 

  16. J. M. Tang, B. T. Collins, and M. E. Flatté, Phys. Rev. B: Condens. Matter 85, 045202 (2012).

    Article  ADS  Google Scholar 

  17. F. Pezzoli, F. Bottegoni, D. Trivedi, F. Ciccacci, A. Giorgioni, P. Li, S. Cecchi, E. Grilli, Y. Song, M. Guzzi, H. Dery, and G. Isella, Phys. Rev. Lett. 108, 156603 (2012).

    Article  ADS  Google Scholar 

  18. A. Jain, C. Vergnaud, J. Peiro, J. C. Le Breton, E. Prestat, L. Louahadj, C. Portemont, C. Ducruet, V. Baltz, A. Marty, A. Barski, P. Bayle-Guillemaud, L. Vila, J.-P. Attané, E. Augendre, H. Jaffrès, J.-M. George, and M. Jamet, Appl. Phys. Lett. 101, 022402 (2012).

    Article  ADS  Google Scholar 

  19. P. Li, Y. Song, and H. Dery, Phys. Rev. B: Condens. Matter 86, 085202 (2012).

    Article  ADS  Google Scholar 

  20. P. Li, D. Trivedi, and H. Dery, Phys. Rev. B: Condens. Matter 87, 115203 (2013).

    Article  ADS  Google Scholar 

  21. Y. Zhou, W. Han, L. T. Chang, F. Xiu, M. Wang, M. Oehme, I. A. Fischer, J. Schulze, R. K. Kawakami, and K. L. Wang, Phys. Rev. B: Condens. Matter 84, 125323 (2011).

    Article  ADS  Google Scholar 

  22. C. Tahan, M. Friesen, and R. Joynt, Phys. Rev. B: Condens. Matter 66, 035314 (2002).

    Article  ADS  Google Scholar 

  23. M. S. Sherwin, A. Imamoglu, and T. Montroy, Phys. Rev. A: At., Mol., Opt. Phys. 60, 3508 (1999).

    Article  ADS  Google Scholar 

  24. A. R. Calderbank and P. W. Shor, Phys. Rev. A: At., Mol., Opt. Phys. 54, 1098 (1996).

    Article  ADS  Google Scholar 

  25. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A: At., Mol., Opt. Phys. 54, 3824 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  26. D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, Phys. Rev. Lett. 81, 2152 (1998).

    Article  ADS  Google Scholar 

  27. A. R. Cameron, P. Riblet, and A. Miller, Phys. Rev. Lett. 76, 4793 (1996).

    Article  ADS  Google Scholar 

  28. J.-M. Jancu, R. Scholz, F. Beltram, and F. Bassani, Phys. Rev. B: Condens. Matter 57, 6493 (1998).

    Article  ADS  Google Scholar 

  29. Y. H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, Nature (London) 437, 1334 (2005).

    Article  ADS  Google Scholar 

  30. M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group Theory: Application to the Physics of Condensed Matter (Springer-Verlag, Berlin, 2008).

    Google Scholar 

  31. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors (Nauka, Moscow, 1972; Wiley, New York, 1974).

    Google Scholar 

  32. L. C. L. Y. Voon and M. Willatzen, The k · p-Method: Electronic Properties of Semiconductors (Springer-Verlag, Berlin, 2009).

    Google Scholar 

  33. Y. Song and H. Dery, Phys. Rev. B: Condens. Matter 86, 085201 (2012).

    Article  ADS  Google Scholar 

  34. Y. Yafet, in Solid State Physics, Ed. by F. Seitz and D. Turnbull (Academic, New York, 1963), Vol. 14, p. 1.

  35. M. Lax and J. J. Hopfield, Phys. Rev. 124, 115 (1961).

    Article  ADS  MATH  Google Scholar 

  36. M. Lax, Phys. Rev. [Sect] A 138, 793 (1965).

    MathSciNet  ADS  Google Scholar 

  37. J. Birman, Theory of Crystal Space Groups and Lattice Dynamics: Infra-Red and Raman Optical Processes of Insulating Crystals (Springer-Verlag, Heidelberg, 1974; Mir, Moscow, 1978), Vol. 1.

    Google Scholar 

  38. E. McCann and V. I. Fal’ko, Phys. Rev. Lett. 108, 166606 (2012).

    Article  ADS  Google Scholar 

  39. H. Ochoa, A. H. C. Neto, V. I. Fal’ko, and F. Guinea, arXiv:1209.4382.

  40. R. J. Elliott, Phys. Rev. 96, 266 (1954).

    Article  ADS  MATH  Google Scholar 

  41. S. Ridene, K. Boujdaria, H. Bouchriha, and G. Fishman, Phys. Rev. B: Condens. Matter 64, 085329 (2001).

    Article  ADS  Google Scholar 

  42. R. Winkler, Spin-Obit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer-Verlag, Berlin, 2003).

    Book  Google Scholar 

  43. V. D. Dymnikov, Phys. Solid State 43(11), 2037 (2001).

    Article  ADS  Google Scholar 

  44. J. Rioux and J. E. Sipe, Physica E (Amsterdam) 45, 1 (2012).

    Article  ADS  Google Scholar 

  45. P. Zhang, J. Zhou, and M. W. Wu, Phys. Rev. B: Condens. Matter 77, 235323 (2008).

    Article  ADS  Google Scholar 

  46. E. L. Ivchenko, Yu. B. Lyanda-Geller, and G. E. Pikus, Sov. Phys. JETP 71(3), 550 (1990).

    Google Scholar 

  47. D. K. Ferry, Phys. Rev. B: Solid State 14, 1605 (1976).

    Article  ADS  Google Scholar 

  48. J. L. Cheng, M. W. Wu, and J. Fabian, Phys. Rev. Lett. 104, 016601 (2010).

    Article  ADS  Google Scholar 

  49. P. Li and H. Dery, Phys. Rev. Lett. 105, 037204 (2010).

    Article  ADS  Google Scholar 

  50. J. L. Cheng, J. Rioux, J. Fabian, and J. E. Sipe, Phys. Rev. B: Condens. Matter 83, 165211 (2011).

    Article  ADS  Google Scholar 

  51. M. M. Rieger and P. Vogl, Phys. Rev. B: Condens. Matter 48, 14276 (1993).

    Article  ADS  Google Scholar 

  52. W. Weber, Phys. Rev. B: Solid State 15, 4789 (1977).

    Article  ADS  Google Scholar 

  53. I. G. Kuleev and I. I. Kuleev, Phys. Solid State 49(3), 437 (2007).

    Article  ADS  Google Scholar 

  54. R. J. Elliott and R. Loudon, J. Phys. Chem. Solids 15, 146 (1960).

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, 96 JinZhai Rd., Hefei, Anhui, 230026, China

    Z. Liu & M. W. Wu

  2. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021, Russia

    M. O. Nestoklon & E. L. Ivchenko

  3. Department of Physics and Institute for Optical Sciences, University of Toronto, 60 St. George Street, Suite 331, Toronto, Ontario, M5S 1A7, Canada

    J. L. Cheng

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  1. Z. Liu
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  4. E. L. Ivchenko
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  5. M. W. Wu
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Original Russian Text © Z. Liu, M.O. Nestoklon, J.L. Cheng, E.L. Ivchenko, M.W. Wu, 2013, published in Fizika Tverdogo Tela, 2013, Vol. 55, No. 8, pp. 1510–1523.

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Liu, Z., Nestoklon, M.O., Cheng, J.L. et al. Spin-dependent intravalley and intervalley electron-phonon scatterings in germanium. Phys. Solid State 55, 1619–1634 (2013). https://doi.org/10.1134/S1063783413080167

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