Semiclassical and Quantum Electronic Transport in Nanometer-Scale Structures: Empirical Pseudopotential Band Structure, Monte Carlo Simulations and Pauli Master Equation

  • Massimo V. Fischetti
  • Bo Fu
  • Sudarshan Narayanan
  • Jiseok Kim
Chapter

Abstract

The study of electronic transport in nanometer-scale devices requires an accurate knowledge of the excitation spectrum (i.e., the band structure) of the systems and, for short devices, a formulation of transport which transcends the semiclassical Boltzmann formulation. Here we show that the use of ‘judiciously’ chosen empirical pseudopotentials, coupled to the supercell method, can provide a sufficiently accurate description of the band structure of thin semiconductor films, hetero-structures, nanowires, and carbon-based structures such as graphene, graphene nanoribbons, and nanotubes. We discuss semiclassical Monte Carlo simulations employing the supercell-pseudopotential band structure, considering transport in thin Si bodies. This example illustrates the importance of the full-band approach since in this case it yields the low value of the saturated high-field electron drift velocity, observed experimentally but never predicted when employing effective-mass band structures. Finally, we discuss a mixed envelope-supercell approach to deal with open systems within the full-band supercell scheme and review the Master-equation approach to quantum transport. Finally, we present some results of fully dissipative quantum transport using, for now, the effective mass approximation, emphasizing the role of impurity scattering in determining the ‘quantum access resistance’ in thin-body devices.

Keywords

Pseudopotentials Electron transport Nanostructures 

Notes

Acknowledgements

One of the authors (MVF) would like to thank Steve Laux, Seonghoon Jin, and Eric Polizzi for help and stimulating discussions. This work has been supported in part by SRC, MARCO/MSD FCRP, and Samsung Electronics Corporation, Ltd.

References

  1. 1.
    H. Ajiki and T. Ando, Jap. J. Appl. Phys. 62, 1255 (1993).Google Scholar
  2. 2.
    T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).CrossRefGoogle Scholar
  3. 3.
    V. Barone, O. Hod, and G. Scuseria, Nano Letters 6, 2748 (2006).CrossRefGoogle Scholar
  4. 4.
    L. Bellaiche, S.-H. Wei, and A. Zunger, Phys. Rev. B 54, 17568 (1996).CrossRefGoogle Scholar
  5. 5.
    L. Bellaiche, L.-W. Wang, S.-H. Wei, and A. Zunger, Appl. Phys. Lett. 74, 1842 (1999).CrossRefGoogle Scholar
  6. 6.
    X. Blase, L. X. Benedict, E. L. Sherly, and S. G. Louie, Phys. Rev. Lett. 72, 1878 (1994).CrossRefGoogle Scholar
  7. 7.
    M. Brandbyge, J.-L. Mozos, P. Ordejón, J. Taylor, and K. Strokbo, Phys. Rev. B 65, 165401 (2002).CrossRefGoogle Scholar
  8. 8.
    L. Brey and H. A. Fertig, Phys. Rev. B 73, 235411 (2006).CrossRefGoogle Scholar
  9. 9.
    L. G. Bulusheva, A. V. Okotrub, D. A. Romanov, and D. Tomanek, J. Phys. Chem. A 102, 975 (1998).CrossRefGoogle Scholar
  10. 10.
    H. J. Choi and J. Ihm, Phys. Rev. B 59, 2267 (1999).CrossRefGoogle Scholar
  11. 11.
    P. Courrieu, Neural Inf. Processing - Letters and Reviews 8, 25 (2005).Google Scholar
  12. 12.
    G. Dresselhaus, M. Dresselhaus, and J. G. Madrovies, Carbon 4, 433 (1966).CrossRefGoogle Scholar
  13. 13.
    D. Esseni and P. Palestri, Phys. Rev. B 72, 165342 (2005).CrossRefGoogle Scholar
  14. 14.
    M. Ezawa, Phys. Rev. B 73, 045432 (2006).CrossRefGoogle Scholar
  15. 15.
    M. Ezawa, Phys. Stat. Sol. (c) 4, 489 (2007).CrossRefGoogle Scholar
  16. 16.
    M. V. Fischetti and S. E. Laux, Phys. Rev. B 38, 9721 (1988).CrossRefGoogle Scholar
  17. 17.
    M. V. Fischetti and S. E. Laux, Phys. Rev. B 48, 2244 (1993).CrossRefGoogle Scholar
  18. 18.
    M. V. Fischetti, J. Appl. Phys. 83, 270 (1998).CrossRefGoogle Scholar
  19. 19.
    M. V. Fischetti, Phys. Rev. B 59, 4901 (1999).CrossRefGoogle Scholar
  20. 20.
    W. R. Frensley, Rev. Mod. Phys. 63, 215 (1991).CrossRefGoogle Scholar
  21. 21.
    J. T. Frey and D. J. Doren, “TubGen 3.3 Web Interface”, http://turin.nss.udel.edu/research/tubegenonline.html
  22. 22.
    Bo Fu and M. V. Fischetti, Dissipative Quantum Transport Using the Pauli Master Equation, in Proc. International Workshop on Computational Electronics (2009), http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=5091106\&isnumber=5091070.Google Scholar
  23. 23.
    M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996).CrossRefGoogle Scholar
  24. 24.
    P. Giannozzi et al., J. Phys.: Cond. Matter 21, 395502 (2009).Google Scholar
  25. 25.
    G. Gilat and L. J. Raubenheimer, Phys. Rev. 144, 390 (1966).CrossRefGoogle Scholar
  26. 26.
    M. J. Gilbert and D. K. Ferry, IEEE Trans. Nanotechnol. 4 355, (2005).CrossRefGoogle Scholar
  27. 27.
    O. Gulseren, T. Yildirim, and S. Caraci, Phys. Rev. B 65, 153405 (2002).CrossRefGoogle Scholar
  28. 28.
    D. Gunlycke, P. A. Areshkin, J. Li, J. M. Mintmire, and C. T. White, Nano Letters 7, 3608 (2007).CrossRefGoogle Scholar
  29. 29.
    L. H. Hemstreet Jr., C. Y. Fong, and M. L. Cohen, Phys. Rev. B 2, 2054 (1970).CrossRefGoogle Scholar
  30. 30.
    L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).MATHGoogle Scholar
  31. 31.
    E. Kan, Z. Li, J. Yang, and J. G. Hou, J. Am. Chem. Soc. 130, 4224 (2008).CrossRefGoogle Scholar
  32. 32.
    L. V. Keldysh, Zh. Éksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JEPT 20, 1018 (1965)].Google Scholar
  33. 33.
    B. Khoshnevisan and Z. S. Tabatabaean, Appl. Phys. A 92, 371 (2008).CrossRefGoogle Scholar
  34. 34.
    M. Kohn and J. M. Luttinger, Phys. Rev. 98, 915 (1955).CrossRefGoogle Scholar
  35. 35.
    W. Kohn and J. M. Luttinger, Phys. Rev. 108, 590 (1957).MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    Y. Kurokawa, S. Nomura, T. Takemori, and Y. Aoyagi, Phys. Rev. B 61, 12616 (2000).CrossRefGoogle Scholar
  37. 37.
    S. E. Laux, A. Kumar and M. V. Fischetti, J. Appl. Phys. 95, 5545 (2004).CrossRefGoogle Scholar
  38. 38.
    Y. Lee, T. Nagata, K. Kakushima, K. Shiraishi, and H. Iwai, “A Study on Electronic Structure of Silicon Nanowires with Diverse Diameters and Orientations for High Performance FET”, Proc. International Workshop on Density Functional Theory, Tokyo, November, p. 83. 2008.Google Scholar
  39. 39.
    C. S. Lent and D. J. Kirkner, J. Appl. Phys. 67, 6353 (1990).CrossRefGoogle Scholar
  40. 40.
    K. Mäder and A. Zunger, Phys. Rev. B 50, 17393 (1994).CrossRefGoogle Scholar
  41. 41.
    A. Mayer, Carbon 42, 2057 (2004).CrossRefGoogle Scholar
  42. 42.
    T. Miyake and S. Saito, Phys. Rev. B 68, 155424 (2003).CrossRefGoogle Scholar
  43. 43.
    T. Miyake and S. Saito, Phys. Rev. B 72, 073404 (2005).CrossRefGoogle Scholar
  44. 44.
    K. Nehari, N. Cavassilas, J. L. Autran, M. Bescond, D. Munteanu, and M. Lannoo, Solid-State Electron. 50, 716 (2006).CrossRefGoogle Scholar
  45. 45.
    N. Neophytou, A. Paul, M. S. Lundstrom, and G. Klimeck, IEEE Trans. Electr. Dev. 55, 1286 (2008).CrossRefGoogle Scholar
  46. 46.
    T. W. Odom, J. Huang, P. Kim, and C. M. Lieber, Nature (London) 391, 62 (1998).Google Scholar
  47. 47.
    T. W. Odom, J. Huang, P. Kim, and C. M. Lieber, J. Phys. Chem. B 104, 2794 (2000).CrossRefGoogle Scholar
  48. 48.
    M. Ouyang, J. Huang, C. L. Cheung, and C. M. Lieber, Science 292, 702 (2001).CrossRefGoogle Scholar
  49. 49.
    A. Pecchia and A. Di Carlo, Rep. Prog. Phys. 67, 1497 (2004).CrossRefGoogle Scholar
  50. 50.
    R. Penrose, Proc. Cambridge Phil. Soc. 51, 406 (1955).MathSciNetMATHCrossRefGoogle Scholar
  51. 51.
    L. Pisani, J. A. Chan, B. Montanari, and N. M. Harrison, Phys. Rev. B 75, 064418 (2007).CrossRefGoogle Scholar
  52. 52.
    E. Polizzi, Phys. Rev. B 79, 115112 (2009).CrossRefGoogle Scholar
  53. 53.
    S. Reich and C. Thomsen, Phys. Rev. B 65, 155411 (2002).CrossRefGoogle Scholar
  54. 54.
    F. Sacconi, M. P. Persson, M. Povolotsky, L. Latessa, A. Pecchia, A. Gagliardi, A. Balint, T. Fraunheim, and A. Di Carlo, J. Comp. Electron. 6, 329 (2007).CrossRefGoogle Scholar
  55. 55.
    K.-I. Sasaki, S. Murakami, and R. Saito, J. Phys. Soc. Jpn. 75, 074713 (2006).CrossRefGoogle Scholar
  56. 56.
    W. Saslow, T. K. Bergstresser, and M. L. Cohen, Phys. Rev. Lett. 16, 354 (1966).CrossRefGoogle Scholar
  57. 57.
    H. Scheel, S. Reich, and C. Thomsen, Phys. Stat. Sol. (b) 242, 2474 (2005).CrossRefGoogle Scholar
  58. 58.
    H. Sevincli, M. Topsakal, and S. Ciraci, Phys. Rev. B 78, 245402 (2008).CrossRefGoogle Scholar
  59. 59.
    M. Sharma, A. Tiwari, and U. S. Sharma, “Ab-initio study of electronic band structure of zigzag single wall carbon nanotubes”, in Proc. “International Workshop on New Trends in Science and Technology”, Ankara, Turkey, Nov. 3-4, 2008, http://ntst08.cankaya.edu/proceedings/proceedings/Manoj/SharmaPaper.doc.Google Scholar
  60. 60.
    Y.-W. Son, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 97, 216803 (2006).CrossRefGoogle Scholar
  61. 61.
    P. E. Trevisanutto, C. Giorgetti, L. Reining, M. Ladisa, and V. Olevano, Phys. Rev. Lett. 101, 226405 (2008).CrossRefGoogle Scholar
  62. 62.
    L. Van Hove, Physica 21, 517 (1955).MathSciNetMATHGoogle Scholar
  63. 63.
    L.-W. Wang and A. Zunger, J. Phys. Chem. 98, 2158 (1994).CrossRefGoogle Scholar
  64. 64.
    L. Yang, C.-H. Park, Y.-W. Son, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 99, 186801 (2007).CrossRefGoogle Scholar
  65. 65.
    S. B. Zhang, C.-Y. Yeh, and A. Zunger, Phys. Rev. B 48, 11204 (1993).CrossRefGoogle Scholar
  66. 66.
    D. Zhang and E. Polizzi, J. Comp. Electr. 7, 427 (2008).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Massimo V. Fischetti
    • 1
  • Bo Fu
  • Sudarshan Narayanan
  • Jiseok Kim
  1. 1.Department of Materials Science and EngineeringUniversity of Texas at DallasRichardsonUSA

Personalised recommendations