Dynamics of Optical Excitations in Semiconductors

  • Rainer G. Ulbrich
Part of the NATO ASI Series book series (NSSB, volume 340)


A quantum ħω of optical excitation will drive a solid out of thermal equilibrium provided that ħω≫ kT. Here T is the temperature of the solid, and kT characterizes the mean energy of its thermally excited degrees of freedom. The condition is usually met, even far above room temperature, for optical interband transitions in semiconductors. During and after the absorption process a number of electronic and vibronic excited states will be populated and interact with each other. These excitations will subsequently relax towards equilibrium, through exchange of momentum and energy with the rest of the system. In this chapter we shall discuss the elementary steps in this sequence, and the role of optical spectroscopy as a powerful tool for their experimental study.


Gallium Arsenide Pair Density Ultrashort Light Pulse Valence Band State Pair Excitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1.1]
    Sadao Adachi “GaAs, AlAs and AlxGal™xAs: Material Parameters for use in research and device applications”, J.Appl.Phys.58, R1 (1985).CrossRefGoogle Scholar
  2. [1.2]
    J. Blakemore “Semiconducting and other major properties of gallium arsenide”, J.Appl.Phys.53, R123.Google Scholar
  3. [1.3]
    see e.g “Ultrafast Phenomena VIII”, Springer Series in Chemical Physics (Springer, Berlin, 1992).Google Scholar
  4. [1.4]
    A similar impact of coherent laser spectroscopy occurred in chemistry, see e.g. the issue on “Femtochemistry” in Physical Chemistry, Vol.97 (1993).Google Scholar
  5. [1.5]
    J. Shah “Ultrafast Luminescence Spectroscopy”, in: Modern Problems in Condensed Matter Sciences, eds. V.M. Agranovich and A.A. Maradudin, Vol.35 (North-Holland, Amsterdam, 1992), Ch.2.Google Scholar
  6. [1.6]
    H. Heinrich, G. Bauer, F. Kuchar (eds.) “Physics and Technology of Submicron Structures”, Solid State Sciences Vol. 83 (Springer, Berlin, 1988).Google Scholar
  7. [1.7]
    C. Weisbuch, B. Vinter “Quantum Semiconductor Structures:Fundamentals and Applications” (Academic Press, Boston, 1991).Google Scholar
  8. [1.8]
    Mark A. Reed, Wiley P. Kirk (eds.) “Nanostructure Physics and Fabrication” (Academic Press, New York, 1989) Ch.2.Google Scholar
  9. [2.1]
    N.W. Ashcroft, N.D. Mermin, “Solid State Physics” (Holt, Rhinehart and Winston, Philadelphia, 1981), Ch.8.Google Scholar
  10. [2.2]
    N.W. Ashcroft, N.D. Mermin, Appendix M; see also R.E. Peierls “Quantum Theory of Solids” (Clarendon Press, Oxford, 1965), Ch.6.4.Google Scholar
  11. [2.3]
    P. Lee and T.V. Ramakrishnan “Disordered Electronic Systems”, Rev.Mod.Phys. 57, 287(1985).CrossRefGoogle Scholar
  12. [2.4]
    M.L. Cohen and V. Heine, Solid State Physics Vol.24 (Academic Press, New, York, 1970).Google Scholar
  13. [2.5]
    C. Radin and L.S. Schulman “Periodicity of Classical Ground States”, Phys.Rev.Lett. 51, 752 (1983)MathSciNetCrossRefGoogle Scholar
  14. J. Miekisz and C. Radin “Why solids are not really crystalline”, Phys.Rev.B 39, 1950 (1989).MathSciNetCrossRefGoogle Scholar
  15. [2.7]
    P. Fulde, “Electron Correlations in Molecules and Solids” Springer Series in Solid State Sciences, Vol.100 (Springer, Berlin, 1993).Google Scholar
  16. [2.8]
    J.C. Phillips “Bands and Bonds in Semiconductors” (Academic Press, New York, 1973) Ch.7.Google Scholar
  17. [2.9]
    F. Bassani, G. Pastori Parravicini “Electronic States and Optical Transitions in Solids” (Pergamon Press, Oxford, 1975).Google Scholar
  18. [2.10]
    P.W. Anderson, “Concepts in Solids” (Benjamin Publishers, London, 1978) Ch.2.Google Scholar
  19. [2.11]
    O. Madelung “Introduction to Solid State Theory” Vol.1, Springer Series in Solid State Science (Springer, Berlin, 1978)CrossRefGoogle Scholar
  20. [2.12]
    M. Lanoo, in: “Materials Science and Technology” Vol.4 (eds. R.W. Kahn, P. Haasen, E.J. Kramer, Verlag Chemie, Weinheim, 1991),Ch.l.Google Scholar
  21. [2.13]
    M. Born and J.R. Oppenheimer, Ann.d.Physik 84, 457 (1927).MATHCrossRefGoogle Scholar
  22. [2.14]
    A.A. Maradudun in: “Dynamical Properties of Solids” (eds. G.K. Horton and A.A. Maradudin, North Holland, Amsterdam, 1974) p.1Google Scholar
  23. [2.15]
    R.E. Peierls “Quantum Theory of Solids” (Clarendon Press, Oxford, 1965), Ch.2.Google Scholar
  24. [2.16]
    M. Born and K. Huang “Dynamical Theory of Crystal Lattices” (Clarendon Press, Oxford, 1985) Ch.4.Google Scholar
  25. [2.17]
    J. Ziman “Electrons and Phonons” (Oxford University Press, Oxford, 1963) Ch.7.Google Scholar
  26. [2.18]
    D. Adler “Electronic Phase Transitions”, in: “Essays in Physics” (eds. G.K.T. Tonn and G.N. Fowler, Academic Press, London, 1970) Vol.1, p.33.Google Scholar
  27. [2.19]
    L. Pauling and E.B. Wilson “Introduction to Quantum Mechanics” (Dover Publications, New York, 1963) Ch.32.Google Scholar
  28. [2.20]
    W. Schaefer “Theory of Dense Nonequilibrium Exciton Systems”, in: “Optical Nonlinearities and Instabilities in Semiconductors” (ed. H. Haug, Academic Press, New York, 1988) Ch.6.Google Scholar
  29. [2.21]
    H. Haug “Microscopic Theory of the Optical Band Edge Nonlinearities”, (ed. H. Haug, Academic Press, New York, 1988) Ch. 3.Google Scholar
  30. [2.21a]
    R. Zimmermann “Many Particle Theory of Highly Excited Semiconductors” (B.G. Teubner Verlagsgesellschaft, Leipzig, 1988).Google Scholar
  31. [2.22]
    J.P. Dahl and J. Avery “Local Density Approximations in Quantum Chemistry and Solid State Physics” (Plenum Press, New York, 1984)Google Scholar
  32. R. Dreizler, E.U. Gross “Density Functional Theory” (Springer, Berlin, 1990).MATHCrossRefGoogle Scholar
  33. [2.23]
    L.D. Landau, E.M. Lifshitz “Lehrbuch der Theoretischen Physik” Vol.III (Akademie-Verlag, Leipzig, 1966) p.251.Google Scholar
  34. [2.24]
    P. Hohenberg and W. Kohn, Phys.Rev. 136, B864 (1964)MathSciNetCrossRefGoogle Scholar
  35. W. Kohn and L.J. Sham, Phys.Rev. 140, A1133(1965).MathSciNetCrossRefGoogle Scholar
  36. [2.25]
    see, e.g. W. Hanke and L.J. Sham, Phys.Rev. B21, 4656 (1980).Google Scholar
  37. [2.26]
    M. Lanoo, in: “Materials Science and Technology” Vol.4 (eds. R.W. Kahn, P. Haasen, E.J. Kramer, Verlag Chemie, Weinheim, 1991),Ch.l.Google Scholar
  38. [2.27]
    J.R. Chelikowsky and M.L. Cohen “Electronic Structure of GaAs”, Phys.Rev. B14, 556 (1976)Google Scholar
  39. M.L. Cohen and J.R. Chelikowsky, “Electronic Structure and Optical Properties of Semiconductors” Springer Solid State Sciences Vol.75 (Springer, Berlin, 1988).Google Scholar
  40. [2.28]
    J.D. Dow “Final-State Interactions in the Optical Spectra of Solids: Elements of Exciton Theory”, in: “New Developments in the Optical Properties of Solids” (ed. B. Seraphin, North Holland Publishing Company, Amsterdam, 1976) Ch.2.Google Scholar
  41. [2.29]
    W. Hanke “The Role of Electron-Hole Interaction in the Optical Spectra of Semiconductors and Insulators”, in: Advances in Solid State Physics, Vol.19 (Vieweg, Braunschweig, 1979) p.43.Google Scholar
  42. [3.1]
    W.A. Harrison “Electronic Structure and the Properties of Solids” (W.H. Freeman, San Francisco, 1980) Ch.9.Google Scholar
  43. [3.2]
    E.O. Kane, in: Semiconductors and Semimetals, Vol.1 (eds. R.K. Willardson and A.C. Beer, Academic Press, New York, 1966) p.75.CrossRefGoogle Scholar
  44. [3.3]
    P. Lawaetz “Valence Band Parameters in Cubic Semiconductors”, Phys.Rev. B4, 3760 (1971).Google Scholar
  45. [3.4]
    C. Hermann and C. Weisbuch “k.p perturbation theory in III-V compounds and alloys: a reexamination”, Phys.Rev.B 15, 823 (1977).CrossRefGoogle Scholar
  46. [3.5]
    D.des Cloizeaux “Linear Response, Generalized Susceptibility and Dispersion Theory”, in: Theory of Condensed Matter (IAEA, Vienna, 1968)Google Scholar
  47. F. Stern in: Solid State Physics Vol.15 (eds. F. Seitz, D. Turnbull, Academic Press, New York, 1963) p.299.Google Scholar
  48. [3.6]
    M. Cardona “Optical Constants of Insulators: Dispersion Relations”, in: Optical Properties of Solids (eds. S. Nudelman and S.S. Mitra, Plenum Press, New York, 1969) Ch.6.Google Scholar
  49. [3.7]
    J.D. Jackson “Classical Electrodynamics” (J. Wiley and sons, New York, 1975) Ch.7.MATHGoogle Scholar
  50. [3.8]
    R. Kubo, J.Phys.Soc.Japan 12, 570 (1957).MathSciNetCrossRefGoogle Scholar
  51. [3.9]
    F. Wooten “Optical Properties of Solids” (Academic Press, New York, 1972) Ch.5.Google Scholar
  52. [4.1]
    N.F. Mott, Phil.Mag. 6, 287 (1961).CrossRefGoogle Scholar
  53. [4.2]
    R.J. Elliott “Intensity of Optical Absorption by Excitons”, Phys.Rev. 108, 1384 (1957).CrossRefGoogle Scholar
  54. [4.3]
    Y. Toyozawa “Interaction between Elementary Excitations and Spectral Line Shapes” in: S. Nakajima, Y. Toyozawa and R. Abe “The Physics of Elementary Excitations” (Springer, Berlin, 1980) p.317.Google Scholar
  55. [4.4]
    J.O. Dimmock “Excitons”, in: Semiconductors and Semimetals Vol.3 (eds. R.K. Willardson and A.C. Beer, Academic Press, New York, 1967) Ch.5.Google Scholar
  56. [4.5]
    R.J. Elliott “Theory of Excitons I”, in: Polarons and Excitons (eds. C.G. Kuper and G.D. Whitfield, Oliver and Boyd, Edinburgh, 1963) p.269.Google Scholar
  57. [4.6]
    K. Cho “Excitons”, in: Topics in Applied Physics, Vol.14 (Springer, Berlin, 1979)Google Scholar
  58. [4.7]
    E.I. Rashba, M.D. Sturge “Excitons” (North Holland, Amsterdam, 1982)Google Scholar
  59. [4.8]
    J.J. Hopfield “Resonant Scattering of Polaritons as Composite Particles”, Phys.Rev. 182, 945 (1969).CrossRefGoogle Scholar
  60. [4.9]
    R.G. Ulbrich “Dense Nonequilibrium Excitations: Band Edge Absorption Spectra of Highly Excited Gallium Arsenide”, in: “Optical Nonlinearities and Instabilities in Semiconductors” (ed. H. Haug, Academic Press, New York, 1988) Ch.5.Google Scholar
  61. [4.10]
    C. Weisbuch and R.G. Ulbrich “Resonant Light Scattering Mediated by Excitonic Polaritons in Semiconductors”, in: “Light Scattering in Solids III” Topics in Applied Physics Vol.51 (eds. M. Cardona and G. Güntherodt, Springer, Berlin, 1982) Ch.7.Google Scholar
  62. [4.11]
    J.J. Hopfield “Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals”, Phys.Rev. 112, 1555 (1958).MATHCrossRefGoogle Scholar
  63. [4.12]
    W.C. Tait “Quantum Theory of a Basic-Light-Matter Interaction”, Phys.Rev. B5, 648 (1972)MathSciNetGoogle Scholar
  64. R.G. Ulbrich and G.W. Fehrenbach “Polariton Wavepacket Propagation in the Exciton Resonance of a Semiconductor”, Phys.Rev.Lett. 13, 963 (1979)CrossRefGoogle Scholar
  65. J. Aaviksoo “Time-resolved studies of excitonic polaritons”, Journal of Luminescence 48&49, 57(1991).CrossRefGoogle Scholar
  66. [4.15]
    P.M. Platzman and P.A. Wolff “Waves and Interactions in Solid State Plasmas”, in: Solid State Physics Vol.13 (Academic Press, New York, 1973) Ch.1.Google Scholar
  67. [4.16]
    J. Appel and A.W. Overhauser, “Acoustic plasma modes”, Phys.Rev. B26, 507 (1982).Google Scholar
  68. [4.17]
    R. Zimmermann “The Dynamical Stark Effect of Excitons”, in: Advances in Solid State Physics Vol.30 (Vieweg, Braunschweig, 1990)Google Scholar
  69. [4.18]
    M. Rice in: Solid State Physics Vol.32 (Academic Press, New York, 1977) p.1.Google Scholar
  70. [4.19]
    H. Haug and S. Schmitt-Rink, Progr.Quant.Electr. 9, 3 (1984).CrossRefGoogle Scholar
  71. [4.20]
    H. Haug and S. Schmitt-Rink “Basic Mechanisms of the Optical Nonlinearities of Semiconductors Near the Band Edge”, J.Opt.Soc.Am. B2, 1135 (1985).Google Scholar
  72. [4.21]
    P. Debye and E. Hueckel, Phys.Z. 24, 185 (1923)MATHGoogle Scholar
  73. P. Debye and E. Hueckel, Phys.Z. 24, 305 (1923).Google Scholar
  74. [4.22]
    C. Comte and P. Nozieres, “Exciton Bose condensation: the ground state of an electron-hole gas” J.Physique 43, 1069 (1982)CrossRefGoogle Scholar
  75. C. Comte and P. Nozieres, “Exciton Bose condensation: the ground state of an electron-hole gas” J.Physique 43, 1083(1982).CrossRefGoogle Scholar
  76. [4.23]
    M. Combescot and J. Bok “Crystalline, Amorphous and Liquid Silicon”, in: Cohesive Properties of Semiconductors under Laser Irradiation, NATO ASI Series Vol.E69 (Nijhoff Publishers, den Haag, 1983) p.289.CrossRefGoogle Scholar
  77. [4.24]
    R. Zimmermann, K. Kilimann, W.D. Kraeft, D. Kremp, G. Roepke, “Dynamical Screening and Self-Energy of Excitons in the Electron-Hole Plasma” phys.stat.sol. b90, 175 (1978).Google Scholar
  78. [4.26] L.D. Landau and E.M. Lifschitz “Lehrbuch der Theoretischen Physik” Vol.III (Akademie Verlag, Berlin, 1966) p.122 ff.Google Scholar
  79. [5.1]
    J.J. Hopfield “Aspects of Polaritons”, Proc.Int.Conf.Phys.Semiconductors, Kyoto 1966 (J.Phys.Soc.Japan Vol.21, Suppl., 1966) p.77Google Scholar
  80. [5.2]
    S. Pekar “Exciton Dispersion in Crystals”, Soviet Physics JETP 6, 785 (1958)MathSciNetGoogle Scholar
  81. [5.3]
    V.M. Agranovitch and V.L. Ginzburg “Spatial Dispersion in Crystal Optics and the Theory of Excitons” (Interscience, New York, 1966)Google Scholar
  82. V.M. Agranovitch and V.M. Ginzburg “Crystal Optics with Spatial Dispersionand Excitons” (Springer, Berlin, 1984).Google Scholar
  83. [5.4]
    H. Fröhlich, “Theory of Dielectrics — Dielectric Constant and Dielectric Loss” (Oxford University Press, Oxford, 1949).Google Scholar
  84. [5.5]
    see the chapter by S. Haroche in this volume.Google Scholar
  85. [5.6]
    M. Lindberg, R. Binder, and S.W. Koch “Theory of the Semiconductor Photon Echo”, Phys.Rev. A 45, 1865 (1992).CrossRefGoogle Scholar
  86. [5.7]
    H. Haug, S.W. Koch “Quantum Theory of the Optical and Electronic Properties of Semiconductors” 2nd ed. (World Scientific, Singapore, 1993) Ch.13.Google Scholar
  87. [5.8]
    L. Allen and J.H. Eberly “Optical Resonance and Two-Level Atoms” (Wiley, New York, 1975).Google Scholar
  88. [5.9]
    A. Mysyrowicz, D. Hulin, A. Antonetti, A. Migus, W.T. Masselink, and H. Morkoc, “Dynamical Stark Effect of Excitons”, Phys.Rev.Lett. 55, 1335 (1985).CrossRefGoogle Scholar
  89. [5.10]
    R.G. De Voe and R.G. Brewer, “Optical Coherent Transients by Laser Frequency Switching” Phys.Rev.Lett. 40, 862 (1978)CrossRefGoogle Scholar
  90. R.G. Brewer, in: “Nonlinear Spectroscopy” Proc.Int.School Physics Enrico Fermi, Course 64 (ed. N. Bloembergen, North Holland, Amsterdam, 1977).Google Scholar
  91. [5.11]
    Marc D. Levenson “Introduction to Nonlinear Laser Spectroscopy” (Academic Press, New York, 1982) Ch.6.Google Scholar
  92. [5.12]
    R. Zimmermann “Many Particle Theory of Highly Excited Semiconductors” (Teubner, Leipzig, 1987) Chs.3 and 5.Google Scholar
  93. [5.13]
    J.C. Phillips “Bands and Bonds in Semiconductors” (Academic Press, New York, 1973) Ch.7.Google Scholar
  94. [5.14]
    A.V. Kuznetsov “Interactions of ultrashort light pulses with semiconductors: Effective Bloch equations with relaxation and memory effects”, Phys.Rev. B44, 8721 (1991)Google Scholar
  95. [5.14]
    M. Koch, J. Feldmann, G. von Plessen, E.O. G’bel, and P. Thomas “Quantum Beats versus Polarization Interference: An Experimental Distinction”, Phys.Rev.Lett. 69, 3631 (1992)CrossRefGoogle Scholar
  96. J. Feldmann, in: Advances in Solid State Physics Vol.32 (ed. U. Rössler, Vieweg, Braunschweig, 1992) p.81.Google Scholar
  97. [5.15]
    D. Kim, J. Shah, A. Vinattieri, T. Damen, D.A.B. Miller, W. Schäfer,and L. Pfeiffer “Femtosecond Pulse Distortion in Quantum Wells: Intensity and Phase Sensitive Measurements”, Talk QPD18-1/40 presented at CLEO 1993.Google Scholar
  98. [6.1]
    F. Wooten “Optical Properties of Solids” (Academic Press, New York, 1972) Chs.3 and 5.Google Scholar
  99. [6.1a]
    B. Laks, G.F. Neumark, A. Hangleiter and S.T. Pantelides, Phys.Rev.Lett. 61, 1229 (1988).CrossRefGoogle Scholar
  100. [6.1b]
    K. Ridley “Quantum Processes in Semiconductors” (Oxford Science Publications, Oxford, 1993) Ch.3Google Scholar
  101. R.P. Feynman “Statistical Mechanics” (W.A. Benjamin, Reading, 1972) Ch.4.Google Scholar
  102. [6.1c]
    see e.g. Proc. 5th Int.Conf. on Hot Carriers in Semiconductors, Boston, 1987 (Pergamon Press, New York, 1988) Ch.4.Google Scholar
  103. [6.1d]
    see Ref.l.l.Google Scholar
  104. [6.1e]
    A. Stahl and I. Balslev, “Electrodynamics of the Semiconductor Band Edge” (Springer, Berlin, 1986).Google Scholar
  105. [6.2]
    H.J. Eichler “Forced Light Scattering at Laser-Induced Gratings — a Method for Investigation of Optically Excited Solids”, in: “Advances in Solid State Physics” Vol.18 (Vieweg Verlag, Braunschweig, 1978) p.241.Google Scholar
  106. [6.3]
    E.P. Ippen and C.V. Shank, in: “Ultrashort Light Pulses”, Topics in Applied Physics Vol.18 (ed. S.L. Shapiro, Springer, Berlin, 1977)Google Scholar
  107. see also “Laser-Induced Dynamic Gratings” (ed. H.J. Eichler, Springer Series in Optical Sciences Vol.50, 1986) Ch.7.Google Scholar
  108. [6.4]
    M. Born and E. Wolf “Principles of Optics” (Pergamon Press, Oxford, 1970) Ch.10.Google Scholar
  109. [6.5]
    S. Freundt, PhD thesis, University Goettingen, 1994 (unpublished).Google Scholar
  110. [6.6]
    G. Böhne, S. Freundt, S. Arlt, D. Pfister, and R.G. Ulbrich, “Phase and Amplitude of Coherently Driven Interband Polarization in Gallium Arsenide”, Int.Conf.Phys.Semiconductors, Vancouver, 1994 (to be published).Google Scholar
  111. [6.7]
    Landolt-Börnstein “Numerical Data and Functional Relationships in Science and Technology”, Group III, Vols.17a,b (Berlin, Springer, 1982).Google Scholar
  112. [6.8]
    P. Grosse “Freie Elektronen in Festkörpern” (Springer, Berlin,1979), Ch.3. [6.9] see the chapter by C. Andreani in this volume.CrossRefGoogle Scholar
  113. [6.10]
    A. Knorr, R. Binder, M. Lindberg and S.W. Koch “Theoretical Study of Resonant Ultrashort-Pulse Propagation in Semiconductors”, Phys.Rev.A 46, 7179(1992).CrossRefGoogle Scholar
  114. [6.11]
    P.A. Harten, A. Knorr, J.P. Sokoloff, F. Brown de Colstoun, S.G. Lee, R. Jin, E.M. Wright, G. Kithorova, H.M. Gibbs, S.W. Koch, and N. Peyghambarian “Propagation-Induced Escape from Adiabatic Following in a Semiconductor”, Phys.Rev.Lett. 9, 852 (1992).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Rainer G. Ulbrich
    • 1
  1. 1.IV. Physikalisches InstitutGeorg-August-Universität GöttingenGöttingenGermany

Personalised recommendations