Theory of Coherent Phonon Oscillations in Bulk GaAs

  • Alex V. Kuznetsov
  • Christopher J. Stanton

Abstract

In this chapter we discuss the theory of coherent phonon oscillations in semiconductors with emphasis on bulk GaAs. We first present and solve a phenomenological model that predicts oscillations after carriers are rapidly created by an ultrafast laser pulse. Next, we present a microscopic justification of the phenomenological model that is applicable to both polar and nonpolar semiconductors. We show that for nonpolar semiconductors such as Ge, the coherent lattice displacement is related to a quantum-mechanical average of a single phonon creation operator, and we derive the equation of motion for the coherent phonon amplitude. Our results show that the coherent oscillations are not caused by synchronous motion between different modes, but are instead due to a multiphonon process within a single mode that leads to a macroscopic occupation of that mode. Finally, we look at the specific case of GaAs, which is a polar material. In GaAs the driving force for the oscillations is the screening of a DC surface depletion electric field by photoexcited electrons and holes. We formulate and present a microscopic theory for the plasmon-phonon oscillations. Our results show that for an idealized situation with homogeneous plasma density, plasmon-like oscillations should dominate the transient behavior over the LO phonon oscillations. This does not agree with experiments. To get agreement with experiment, the inhomogeneous density-distribution generated by the laser pulse must be taken into account. When one accounts for the inhomogeneous density of the laser pulse, then the density-dependent plasmon oscillations average out, leaving only density-independent LO phonon oscillations present in the transient optical response.

Keywords

Nickel Recombination Coherence GaAs Refraction 

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References

  1. [1]
    P.C. Becker, H.L. Fragnito, C.H. Brito Cruz, J. Shah, R.L. Fork, J.E. Cunningham, J.E. Henry, and C.V. Shank. it Appl. Phys. Lett., 53:2089, 1988.CrossRefGoogle Scholar
  2. [2]
    M. Rosker, F. Wise, and C.L. Tang. Appl. Phys. Lett., 49:1726, 1986.CrossRefGoogle Scholar
  3. [3]
    R.W. Schoenlein, W.Z. Lin, S.D. Brorson, E.P. Ippen, and J.G. Fujimoto. Appl. Phys. Lett., 51:1191, 1987.CrossRefGoogle Scholar
  4. [4]
    W.H. Knox, C. Hirlimann, D.A.B. Miller, J. Shah, D.S. Chemla, and C.V. Shank. Phys. Rev. Lett., 56:1191, 1986.CrossRefGoogle Scholar
  5. [5]
    J.L. Oudar, A. Migus, D. Hulin, G. Grillon, J. Etchepare, and A. Antonetti. Phys Rev. Lett., 53:384, 1984.CrossRefGoogle Scholar
  6. [6]
    P.C. Becker, H.L. Fragnito, C.H. Brito Cruz, R.L. Fork, J.E. Cunningham, J.E. Henry, and C.V. Shank. Phys. Rev. Lett., 61:1647, 1988.CrossRefGoogle Scholar
  7. [7]
    M.C. Nuss, D.H. Auston, and F. Capasso. Phys. Rev. Lett., 58:2355, 1987.CrossRefGoogle Scholar
  8. [8]
    H. Hang and S. Koch. Quantum Theory of the Optical and Electronic Properties of Semiconductors. World Scientific, Singapore, 1990.Google Scholar
  9. [9]
    E.M. Conwell. Solid State Physics, Advances and Applications, page 110. Academic Press, London, 1967. Hight Field Transport in Semiconductor.Google Scholar
  10. [10]
    K. Seeger, Semiconductor Physics. Springer Verlag, Berlin, 1982.Google Scholar
  11. [11]
    J.S. Blakemore. Semiconductor Statistics. Dover, New York, 1987.Google Scholar
  12. [12]
    C.J. Stanton, D.W. Bailey, and K. Hess. Phys. Rev. Lett., 65:231, 1990.CrossRefGoogle Scholar
  13. [13]
    D.W. Bailey, C.J. Stanton, and K. Hess. Phys. Rev., B 42:3423, 1990, and references therein.Google Scholar
  14. [14]
    M. Ulman, D.W. Bailey, L.H. Acioli, F.G. Vallee, C.J. Stanton, E.P. Ippen, and J.G. Fujimoto. Phys. Rev., B 47:10267, 1993.Google Scholar
  15. [15]
    G.D. Sanders, C.J. Stanton, and Y.C. Chang. Phys. Rev. B 48:11067, 1993.Google Scholar
  16. [16]
    D.W. Bailey and C.J. Stanton. Appl. Phys. Lett, 60:880, 1992.CrossRefGoogle Scholar
  17. [17]
    C.J. Stanton, and D.W. Phys. Rev., B 48:1624, 1993.Google Scholar
  18. [18]
    A.V. Kuznetsov and C.J. Stanton, Phys. Rev., B48: 10828, 1993.Google Scholar
  19. [19]
    C.S. Kim, C.J. Stanton, and A.V. Kuznetsov. Semicond. Sci. Technol., 9:436, 1994.CrossRefGoogle Scholar
  20. [20]
    T. Kuhn and F. Rossi. Phys. Rev., B 46:7496, 1992.Google Scholar
  21. [21]
    T. Kuhn and F. Rossi, Phys. Rev. Lett. 69:977, 1992.CrossRefGoogle Scholar
  22. [22]
    R.T. Phillips, editor, Coherent Optical Interations in Semiconductors. Plenum, New York, 1994.Google Scholar
  23. [23]
    M. Nisoli, S. Desilvestri, O. Svelto, R. Szipocs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz. Opt. Lett., 22:522, 1997.CrossRefGoogle Scholar
  24. [24]
    A.M. Weiner, J.P. Heritage, and E.M. Kirschner. J. Opt. Soc. Am. B, 5:1568, 1988.Google Scholar
  25. [25]
    A. Efimov, C. Schaffer, and D.H. Reitze, J. Opt. Soc. Am. B, 12:1968, 1995.CrossRefGoogle Scholar
  26. [26]
    P. Leisching, P.H. Bolivar, W. Beck, Y. Dhaibi, F. Bruggerman, R. Schwendler, H. Kurz, K. Leo, and K. Kohier, Phys. Rev., B 50:14389, 1994.Google Scholar
  27. [27]
    T. Dekorsey, R. Ott, H. Kurz, and K. Kohler. Phys. Rev., B 51:17275, 1995.Google Scholar
  28. [28]
    K. Leo, T.C. Damen, J. Shah, E.O. Gobel, and K. Kohier. Appl. Phys. Lett., 57:19, 1990.CrossRefGoogle Scholar
  29. [29]
    S.T. Cundiff, A. Knorr, J. Feldmann, S.W. Koch, E.O. Gobel, and H. Nickel. Phys. Rev. Lett., 73:1178. 1994.CrossRefGoogle Scholar
  30. [30]
    J. Feldmann, M. Koch, E.O. Gobel, F. Jahnke, T. Meier, W. Schafer, P. Thomas, S. W. Koch, H. Nickel, S. Luttgen, W. Stolz, Semicond. Sci. Technol., 9:1965, 1994.CrossRefGoogle Scholar
  31. [31]
    K. Leo, J. Shah, E.O. Gobel, T.C. Damen, S. Schmitt-Rink, W. Schafer, and K. Kohler, Phys. Rev. Lett, 66:201, 1991.CrossRefGoogle Scholar
  32. [32]
    H.G. Roskos, M.C. Nuss, J. Shah, K. Leo, D.A.B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, Phys. Rev. Lett., 68:2216, 1992.CrossRefGoogle Scholar
  33. [33]
    A. Bonvalet, J. Nagle, V. Berger, A. Migus, J.-L. Martin, and M. Joffe, Phys. Rev. Lett., 76:4692, 1996.CrossRefGoogle Scholar
  34. [34]
    A.V. Kuznetsov and C.J. Stanton. Phys. Rev. Lett., 73:3243, 1994.CrossRefGoogle Scholar
  35. [35]
    A.V. Kuznetsov and C. J. Stanton. Phys. Rev., B 52:7555, 1995Google Scholar
  36. [36]
    W.A. Kutt, W. Albrecht, and H. Kurz. IEEE J. Quantum Electronics, QE-28:2434, 1992.CrossRefGoogle Scholar
  37. [37]
    R. Merlin, Solid State Comm., 102:207, 1997.CrossRefGoogle Scholar
  38. [38]
    H.J. Zeiger, J. Vidal, T.K. Cheng, E.P. Ippen, G. Dresselhaus, and M.S. Dresselhaus, Phys. Rev., B 45:768,1992.Google Scholar
  39. [39]
    G.C. Cho, W. Kutt, and H. Kurz, Phys. Rev. Lett, 65:764, 1990.CrossRefGoogle Scholar
  40. [40]
    W. Kutt, G.C. Cho, T. Pfeifer, and H. Kurz. Semicond. Sci. Technol., 7:B77, 1992.CrossRefGoogle Scholar
  41. [41]
    T. Pfeifer, W. Kutt, H. Kurz, and H. Scholz. Phys. Rev. Lett., 69:3248, 1992.CrossRefGoogle Scholar
  42. [42]
    T.K. Cheng, J. Vidal, H.J. Zeiger, G. Dresselhaus, M.S. Dresselhaus, and E.P. Ippen. Appl. Phys. Lett., 59:1923, 1991.CrossRefGoogle Scholar
  43. [43]
    W. Albrecht, Th. Kruse, and H. Kurz. Phys. Rev. Lett., 69:1451, 1992.CrossRefGoogle Scholar
  44. [44]
    T. Dekorsy, T. Pfeifer, W. Kutt, and H. Kurz. Phys. Rev., B 47:3842, 1993.Google Scholar
  45. [45]
    D.N. Mirlin, I.J. Karlik, L.P. Nikitin, I.I. Reshina, and V.F. Sapega. Solid State Commun., 37:757, 1981.CrossRefGoogle Scholar
  46. [46]
    R.G. Ulbrich, J.A. Kash, and J.C. Tsang. Phys. Rev. Lett, 62:949, 1989.CrossRefGoogle Scholar
  47. [47]
    Y.S. Sun and C.J. Stanton. Phys. Rev., B 43:2284, 1990.Google Scholar
  48. [48]
    O. Madelung, editor. Data in Science and Technology: Semiconductors, Group IV Elements and III-V Compunds. Springer Verlag, Berlin 1991.Google Scholar
  49. [49]
    R. Scholz, T. Pfeifer, and H. Kurz. Phys. Rev., B 47:16229, 1993.Google Scholar
  50. [50]
    The coupling constant Mkqα is related to the deformation potential matrix element C that represents the change in energy of the state {α, k} due to the presence of lattice displacement: \( M_{{\rm{kq}}}^a = C_{\rm{k}}^a \sqrt {\frac{h}{{2\rho V\omega q}}} \cdot \) Google Scholar
  51. [51]
    Ch. Kittel. Quantum Theory of Solids. Wiley, New York, 1963.Google Scholar
  52. [52]
    E.C.G. Sudarshan J.R. Klauder. Fundamentals of Quantum Optics. Benjamin, New York, 1968.Google Scholar
  53. [53]
    C. Cohen-Tannoudiji, B. Diu, and F. Laloe. Quantum Mechanics. Wiley, New York, 1977.Google Scholar
  54. [54]
    H J. Eichler, P. Gunther, and D.W. Pohl, Laser Induced Transient Gratings. Springer, Berlin, 1986.Google Scholar
  55. [55]
    V.A. Kochelap, V.N. Sokolov, and B.Yu. Vengalis. Phase Transistions in Semiconductors with Deformational Electron-Phonon Interaction. Naukova Dumka, Kiev, 1984.Google Scholar
  56. [56]
    J.A. Kash and J.C. Tsang. Solid State Electron., 31:419, 1989.CrossRefGoogle Scholar
  57. [57]
    T. Pfeifer, T. Dekorsy, and W. Kutt and H. Kurz. Appl. Phys. A, 55:482, 1992.CrossRefGoogle Scholar
  58. [58]
    H. Heesel, S. Hunsche, H. Mikkelsen, T. Dekorsy, K. Leo, and H. Kurz. Phys. Rev., B 47:16000, 1993.Google Scholar
  59. [59]
    T. Dekorsy, H. Heesel, T. Pfeifer, H. Mikkelsen, W. Kutt, K. Leo, and H. Kurz. Opt. Soc. Am. Proc. Ultrafast Opt Optoelectron., 14:129, 1993.Google Scholar
  60. [60]
    R. Scholz and A. Stahl. Phys. Status Solidi, B 168:123, 1991.CrossRefGoogle Scholar
  61. [61]
    A. Mooradian and A.L. McWhorter. Phys. Rev. Lett., 19:849, 1967.CrossRefGoogle Scholar
  62. [62]
    M. Born and K. Huang. Dynamical Theory of Crystal Lattices. Oxford University Press, Oxford, 1954.Google Scholar
  63. [63]
    F. Vallee and F. Bogani. Phys. Rev., B 43:12049, 1991.Google Scholar
  64. [64]
    C.L. Collins and P.Y. Yu. Solid State Communications, 51:123, 1984.CrossRefGoogle Scholar
  65. [65]
    P. Lorain and D. R. Corson. Electromagnetic Fields and Waves. W.H. Freeman, San Francisco, 1970.Google Scholar
  66. [66]
    F. Wooten. Optical Properties of Solids. Academic Press, San Diego, 1972.Google Scholar
  67. [67]
    C.J. Stanton and D.W. Bailey. Monte Carlo Device Simulation: Full Band and Beyond, page 67. Kluwer Academic, Boston, 1991. Edited by K. Hess.CrossRefGoogle Scholar
  68. [68]
    S. Zollner, K.D. Myers, J.M. Dolan, and C.J. Stanton. Thin Solid Films, 313–314:313, 1998.Google Scholar
  69. [69]
    S. Zollner, K.D. Myers, K.G. Jesnon, J.M. Dolan, D.W. Bailey, and C.J. Stanton. Solid State Comm., 104:51, 1997.CrossRefGoogle Scholar
  70. [70]
    C.J. Stanton and D.W. Bailey. Phys. Rev., B 45:8369, 1992.Google Scholar
  71. [71]
    C.C. Shih and A. Yariv. J. Phys. C, 15:825, 1982.CrossRefGoogle Scholar
  72. [72]
    T. Pfeifer, T. Dekorsy, W. Kutt, and H. Kurz. Phonon Scattering in Condensed Matter VII, page 110. Springer, Berlin, 1993. Edited by: M. Meissner and R. O. Pohl.CrossRefGoogle Scholar
  73. [73]
    R. Kerssting, J.N. Heyman, G. Strasser, and K. Unterrainer. Phys. Rev., B 58:4553, 1998.Google Scholar
  74. [74]
    T. Dekorsey, A.M.T. Kim, G.C. Cho, H. Kurz, A. V. Kuznetsov, and A. Forster. Phys. Rev., B: 1531, 1996.Google Scholar
  75. [75]
    I.I. Mazin, A.I. Liechtenstein, O. Jepsen, O.K. Andersen, and C.O. Rodriguez. Phys.Rev., B 49:9210, 1994.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Alex V. Kuznetsov
  • Christopher J. Stanton

There are no affiliations available

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