Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Semiconductor excitons in new light

Abstract

Excitons are quasi-particles that form when Coulomb-interacting electrons and holes in semiconductors are bound into pair states. They have many features analogous to those of atomic hydrogen. Because of this, researchers are interested in exploring excitonic phenomena, from optical, quantum-optical and thermodynamic transitions to the possible condensation of excitons into a quantum-degenerate state. Excitonic signatures commonly appear in the optical absorption and emission of direct-gap semiconductor systems. However, the precise properties of incoherent exciton populations in such systems are difficult to determine and are the subject of intense debate. We review recent contributions to this discussion, and argue that to obtain detailed information about exciton populations, conventional experimental techniques should be supplemented by direct quasi-particle spectroscopy using the relatively newly available terahertz light sources. Finally, we propose a scheme of quantum-optical excitation to generate quantum-degenerate exciton states directly.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Excitonic absorption spectra for a GaAs-type quantum-well system.
Figure 2: Resonant excitation dynamics.
Figure 3: The influence of exciton populations on ‘excitonic’ photoluminescence spectra in quantum wells.
Figure 4: Excitonic THz absorption spectra.
Figure 5: Quantum degenerate exciton distribution generated by resonant excitation with incoherent light.

Similar content being viewed by others

References

  1. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors 4th edn (World Scientific, Singapore, 2004).

    Google Scholar 

  2. Klingshirn, C. Semiconductor Optics 2nd edn (Springer, Berlin, 2005).

    Google Scholar 

  3. Schäfer, W. & Wegener, M. Semiconductor Optics and Transport Phenomena (Springer, Berlin, 2002).

    Google Scholar 

  4. Zimmermann, R. Many-Particle Theory of Highly Excited Semiconductors (Teubner, Leipzig, 1987).

    Google Scholar 

  5. Frenkel, J. On the transformation of light into heat in solids. II. Phys. Rev. 37, 1276–1294 (1931).

    Google Scholar 

  6. Wannier, G. H. The structure of electronic excitation levels in insulating crystals. Phys. Rev. 52, 191–197 (1937).

    Google Scholar 

  7. Elliott, R. J. in Polarons and Excitons (eds Kuper, C. G. & Whitefield, G. D.) 269–293 (Oliver and Boyd, Edinburgh, 1963).

    Google Scholar 

  8. Knox, R. S. in Solid State Phys. Suppl. 5 (eds Seitz, F. & Turnbull, D.) (Academic, New York, 1963).

    Google Scholar 

  9. Dexter, D. I. & Knox, R. S. Excitons (Wiley, New York, 1981).

    Google Scholar 

  10. Lampert, M. A. Mobile and immobile effective-mass-particle complexes in nonmetallic solids. Phys. Rev. Lett. 1, 450–453 (1958).

    Google Scholar 

  11. Moskalenko, S. A. The theory of Mott exciton in alkali-halide crystals. Opt. Spektrosk. 5, 147–155 (1958).

    Google Scholar 

  12. Klingshirn, C. & Haug, H. Optical properties of highly excited direct gap semiconductors. Phys. Rep. 70, 315–410 (1981).

    Google Scholar 

  13. Rashba, E. L. & Sturge, M. D. Excitons (North-Holland, Amsterdam, 1982).

    Google Scholar 

  14. Hönerlage, B., Levy, R., Grun, J. B., Klingshirn, C. & Bohnert, K. The dispersion of excitons, polaritons, and biexcitons in direct-gap semiconductors. Phys. Rep. 124, 161–253 (1985).

    Google Scholar 

  15. Blatt, J. M., Boer, K. W. & Brandt, W. Bose–Einstein condensation of excitons. Phys. Rev. 126, 1691–1692 (1962).

    Google Scholar 

  16. Moskalenko, S. A. Reversible optico-hydrodynamic phenomena in a nonideal exciton gas. Sov. Phys. Solid State 4, 199–204 (1962).

    Google Scholar 

  17. Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP-USSR 27, 521 (1968).

    Google Scholar 

  18. Ivanov, C. I., Barentzen, H. & Girardeau, M. D. On the theory of dense exciton systems. Physica A 140, 612–628 (1987).

    Google Scholar 

  19. Kira, M. et al. Quantum theory of nonlinear semiconductor microcavity luminescence explaining ‘boser’ experiments. Phys. Rev. Lett. 79, 5170–5173 (1997).

    Google Scholar 

  20. Combescot, M. & Betbeder-Matibet, O. Scattering rates and lifetime of exact and boson excitons. Phys. Rev. Lett. 93, 016403 (2004).

    Google Scholar 

  21. Kira, M., Jahnke, F. & Koch, S. W. Microscopic theory of excitonic signatures in semiconductor photoluminescence. Phys. Rev. Lett. 81, 3263–3266 (1998).

    Google Scholar 

  22. Khitrova, G., Gibbs, H. M., Jahnke, F., Kira, M. & Koch, S. W. Nonlinear optics of normal-mode-coupling semiconductor microcavities. Rev. Mod. Phys. 71, 1591–1639 (1999).

    Google Scholar 

  23. Kira, M., Hoyer, W., Stroucken, T. & Koch, S. W. Exciton formation in semiconductors and the influence of a photonic environment. Phys. Rev. Lett. 87, 176401 (2001).

    Google Scholar 

  24. Koch, S. W., Meier, T., Hoyer, W. & Kira, M. Theory of the optical properties of semiconductor nanostructures. Physica E 14, 45–52 (2002).

    Google Scholar 

  25. Kira, M. & Koch, S. W. Exciton-population inversion and terahertz gain in semiconductors excited to resonance. Phys. Rev. Lett. 93, 076402 (2004).

    Google Scholar 

  26. Lindberg, M. & Koch, S. W. Effective Bloch equations for semiconductors. Phys. Rev. B 38, 3342–3350 (1988).

    Google Scholar 

  27. Schmitt-Rink, S., Chemla, D. S. & Haug, H. Nonequilibrium theory of the optical Stark effect and spectral hole burning in semiconductors. Phys. Rev. B 37, 941–955 (1988).

    Google Scholar 

  28. Lysenko, V. G. & Revenko, V. I. Exciton spectrum in case of high-density non-equilibrium carriers in CdS crystals. Fiz. Tverd. Tela 20, 2144–2147 (1978).

    Google Scholar 

  29. Gibbs, H. M. et al. Saturation of the free exciton resonance in GaAs. Solid State Commun. 30, 271–275 (1979).

    Google Scholar 

  30. Fehrenbach, G. W., Schäfer, W., Treusch, J. & Ulbrich, R. G. Transient optical spectra of a dense exciton gas in a direct-gap semiconductor. Phys. Rev. Lett. 57, 1281–1284 (1982).

    Google Scholar 

  31. Lee, Y. H. et al. Room-temperature optical nonlinearities in GaAs. Phys. Rev. Lett. 57, 2446–2449 (1986).

    Google Scholar 

  32. Schmitt-Rink, S., Chemla, D. S. & Miller, D. A. B. Linear and nonlinear optical properties of semiconductor quantum wells. Adv. Phys. 38, 89–188 (1989).

    Google Scholar 

  33. Rappen, T., Mohs, G. & Wegener, M. Polariton dynamics in quantum wells studied by femtosecond four-wave mixing. Phys. Rev. B 47, 9658–9662 (1993).

    Google Scholar 

  34. Pekar, S. I. On the theory of additional electromagnetic waves in crystals in the exciton absorption region. Sov. Phys. Solid State 4, 953–960 (1962).

    Google Scholar 

  35. Chemla, D. S., Bigot, J.-Y., Mycek, M.-A. & Weiss, S. Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells. Phys. Rev. B 50, 8439–8453 (1994).

    Google Scholar 

  36. Schultheis, L., Sturge, M. D. & Hegarty, J. Photon-echoes from two-dimensional excitons in GaAs-AlGaAs quantum wells. Appl. Phys. Lett. 47, 995–997 (1985).

    Google Scholar 

  37. Schultheis, L., Kuhl, J., Honold, A. & Tu, C. W. Ultrafast phase relaxation of excitons via exciton–exciton and exciton–electron collisions. Phys. Rev. Lett. 57, 1635–1638 (1986).

    Google Scholar 

  38. Schultheis, L., Kuhl, J., Honold, A. & Tu, C. W. Picosecond phase coherence and orientational relaxation of excitons in GaAs. Phys. Rev. Lett. 57, 1797–1800 (1986).

    Google Scholar 

  39. Stolz, H. Time Resolved Light Scattering from Excitons (Springer, Berlin, 1994).

    Google Scholar 

  40. Shah, J. Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, Berlin, 1996).

    Google Scholar 

  41. Chemla, D. S. & Shah, J. Many-body and correlation effects in semiconductors. Nature 411, 549–557 (2001).

    Google Scholar 

  42. Smirl, A. L. in Ultrafast Phenomena in Semiconductors (ed. Tsen, K.-T.) 443–507 (Springer, New York, 2001).

    Google Scholar 

  43. Kuhl, J. et al. in Coherent Optical Interactions in Semiconductors (ed. Phillips, R. T.) 1–31 (Plenum, New York, 1994).

    Google Scholar 

  44. Stolz, H., Schwarze, D., von der Osten, W. & Weimann, G. Transient resonant Rayleigh scattering from electronic states in disordered systems: excitons in GaAs/AlxGa1−xAs multiple-quantum-well structures. Phys. Rev. B 47, 9669–9675 (1993).

    Google Scholar 

  45. Haacke, S., Tayler, R. A., Zimmermann, R., Bar-Joseph, I. & Deveaud, B. Resonant femtosecond emission from quantum well excitons: the role of Rayleigh scattering and luminescence. Phys. Rev. Lett. 78, 2228–2231 (1997).

    Google Scholar 

  46. Birkedahl, D. & Shah, J. Femtosecond spectral interferometry of resonant secondary emission from quantum wells: resonance Rayleigh scattering in the nonergodic regime. Phys. Rev. Lett. 81, 2372–2375 (1998).

    Google Scholar 

  47. Garro, N., Snelling, M. J., Kennedy, S. P., Phillips, R. T. & Ploog, K. H. Coherent effects in resonant quantum-well emission. Phys. Rev. B 60, 4497–4500 (1999).

    Google Scholar 

  48. Langbein, W., Hvam, J. M. & Zimmermann, R. Time resolved speckle analysis: a new approach of coherence and dephasing of optical excitations in solids. Phys. Rev. Lett. 82, 1040–1043 (1999).

    Google Scholar 

  49. Runge, E. Excitons in semiconductor nanostructures. Solid State Phys. 57, 149–305 (2002).

    Google Scholar 

  50. Thränhardt, A., Kuckenburg, S., Knorr, A., Meier, T. & Koch, S. W. Quantum theory of phonon-assisted exciton formation and luminescence in semiconductor quantum wells. Phys. Rev. B 62, 2706–2720 (2000).

    Google Scholar 

  51. Peyghambarian, N. et al. Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure. Phys. Rev. Lett. 53, 2433–2436 (1984).

    Google Scholar 

  52. Meier, T. & Koch, S. W. Analysis of excitonic absorption changes induced by incoherent exciton and electron–hole pair populations. Phys. Status Solidi B 221, 211–214 (2000).

    Google Scholar 

  53. Kusano, J., Segawa, Y., Aoyagi, Y., Namba, S. & Okamoto, H. Extremely slow energy relaxation of a two-dimensional exciton in a GaAs superlattice structure. Phys. Rev. B 40, 1685–1691 (1989).

    Google Scholar 

  54. Damen, T. C. et al. Dynamics of exciton formation and relaxation in GaAs quantum wells. Phys. Rev. B 42, 7434–7438 (1990).

    Google Scholar 

  55. Blom, P. W. M., van Hall, P. J., Smit, C., Cuypers, J. P. & Wolter, J. H. Selective exciton formation in thin GaAs/AlxGa1−xAs quantum wells. Phys. Rev. Lett. 71, 3878–3881 (1993).

    Google Scholar 

  56. Kumar, R., Vengurlekar, A. S., Prabhu, S. S., Shah, J. & Pfeiffer, L. N. Picosecond time evolution of free electron–hole pairs into excitons in GaAs quantum wells. Phys. Rev. B 54, 4891–4897 (1996).

    Google Scholar 

  57. Nüsse, S., Haring Bolivar, P., Kurz, H., Klimov, V. & Levy, F. Carrier cooling and exciton formation in GaSe. Phys. Rev. B 56, 4578–4583 (1997).

    Google Scholar 

  58. Zhao, H. & Kalt, H. in Optics of Semiconductors and their Nanostructures (eds Kalt, H. & Hetterich, M.) 19–45 (Springer, Berlin, 2004).

    Google Scholar 

  59. Szczytko, J. et al. Determination of the exciton formation in quantum wells from time-resolved interband luminescence. Phys. Rev. Lett. 93, 137401 (2004).

    Google Scholar 

  60. Szczytko, J. et al. Origin of excitonic luminescence in quantum wells: direct comparison of the exciton population and Coulomb correlated plasma models. Phys. Rev. B. 71, 195313 (2005).

    Google Scholar 

  61. Hayes, G. R. & Deveaud, B. Is luminescence from quantum wells due to excitons? Phys. Status Solidi A 190, 637–640 (2002).

    Google Scholar 

  62. Selbmann, P. E., Gulia, M., Rossi, F., Molinari, E. & Lugli, P. H. Coupled free-carrier and exciton relaxation in optically excited semiconductors. Phys. Rev. B 54, 4660–4673 (1996).

    Google Scholar 

  63. Gulia, M., Rossi, F., Molinari, E., Selbmann, P. E. & Lugli, P. H. Phonon-assisted exciton formation and relaxation in GaAs/AlxGa1−xAs quantum wells. Phys. Rev. B 55, R16049–R16052 (1997).

    Google Scholar 

  64. Siantidis, K., Axt, V. M. & Kuhn, T. Dynamics of exciton formation for near band-gap excitations. Phys. Rev. B 65, 035303 (2001).

    Google Scholar 

  65. Hoyer, W., Kira, M. & Koch, S. W. Influence of Coulomb and phonon interaction on the exciton formation dynamics in semiconductor heterostructures. Phys. Rev. B 67, 155113 (2003).

    Google Scholar 

  66. Hoyer, W., Kira, M. & Koch, S. W. in Electron and Photon Confinement in Semiconductor Nanostructures: Proceedings of the International School of Physics “Enrico Fermi”, Course CL (eds Deveaud, B., Quattropani, A. & Schwendimann, P.) 15–62 (IOS Press, Amsterdam, 2003).

    Google Scholar 

  67. Chatterjee, S. et al. Excitonic photoluminescence in semiconductor quantum wells: plasma versus excitons. Phys. Rev. Lett. 92, 067402 (2004).

    Google Scholar 

  68. Hoyer, W. et al. Many-body dynamics and exciton formation studied by time-resolved photoluminescence. Phys. Rev. B 72, 075324 (2005).

    Google Scholar 

  69. Hoyer, W., Kira, M. & Koch, S. W. Influence of bound and unbound electron-hole-pair populations on the excitonic luminescence in semiconductor quantum wells. Preprint at <http://arxiv.org/abs/cond-mat/0604349> (2006).

  70. Gershenzon, E. M., Goltsman, G. N. & Ptitsina, M. G. Investigation of free excitons in Ge and their condensation at submillimeter waves. Zh. Eksp. Teor. Fiz. 70, 224–234 (1976).

    Google Scholar 

  71. Timusk, T., Navarro, R., Lipari, N. O. & Altarelli, M. Far-infrared absorption by excitons in silicon. Solid State Commun. 25, 217–219 (1978).

    Google Scholar 

  72. Groeneveld, R. M. & Grischkowsky, D. Picosecond time-resolved far-infrared experiments on carriers and excitons in GaAs-AlGaAs multiple-quantum wells. J. Opt. Soc. Am. B 11, 2502–2507 (1994).

    Google Scholar 

  73. Cerne, J. et al. Terahertz dynamics of excitons in GaAs/AlGaAs quantum wells. Phys. Rev. Lett. 77, 1131–1134 (1996).

    Google Scholar 

  74. Kubouchi, M., Yoshioka, K., Shimano, R., Mysyrowicz, A. & Kuwata-Gonokami, M. Study of orthoexciton-to-paraexciton conversion in Cu2O by excitonic Lyman spectroscopy. Phys. Rev. Lett. 94, 016403 (2005).

    Google Scholar 

  75. Jörger, M., Fleck, T., Klingshirn, C. & von Baltz, R. Midinfrared properties of cuprous oxide: high-order lattice vibrations and intraexcitonic transitions of the 1s paraexciton. Phys. Rev. B 71, 235219 (2005).

    Google Scholar 

  76. Kira, M., Hoyer, W. & Koch, S. W. Terahertz signatures of the exciton formation dynamics in non-resonantly excited semiconductors. Solid State Commun. 129, 733–736 (2004).

    Google Scholar 

  77. Kaindl, R. A., Carnahan, M. A., Hägele, D., Lövenich, R. & Chemla, D. S. Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas. Nature 423, 734–738 (2003).

    Google Scholar 

  78. Galbraith, I. et al. Excitonic signatures in the photoluminescence and terahertz absorption of a GaAs/AlxGa1−xAs multiple quantum well. Phys. Rev. B 71, 073302 (2005).

    Google Scholar 

  79. Hägele, D., Hübner, J., Rühle, W. W. & Oestreich, M. When do excitons really exist? Physica B 272, 328–330 (1999).

    Google Scholar 

  80. Oestreich, M., Hägele, D., Hübner, J. & Rühle, W. W. Excitons, or no excitons, that is the question. Phys. Status Solidi A 178, 27–32 (2000).

    Google Scholar 

  81. Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron–hole plasma. Nature 414, 286–289 (2001).

    Google Scholar 

  82. Huber, R. et al. Femtosecond formation of coupled phonon-plasmon modes in InP: ultrabroadband THz experiment and quantum kinetic theory. Phys. Rev. Lett. 94, 027401 (2005).

    Google Scholar 

  83. Kira, M. & Koch, S. W. Quantum-optical spectroscopy of semiconductors. Phys. Rev. A 73, 013813 (2006).

    Google Scholar 

  84. Koch, S. W. & Kira, M. Excitons in semiconductors. in Optics of Semiconductors and their Nanostructures (eds Kalt, H. & Hetterich, M.) 1–18 (Springer, Berlin, 2004).

    Google Scholar 

Download references

Acknowledgements

The research in Marburg is partially supported by the Deutsche Forschungsgemeinschaft through the Quantum Optics in Semiconductors Research Group and the Optodynamics Centre at the Philipps-Universität Marburg. We thank W. Hoyer for valuable discussions and collaboration on the exciton-luminescence theory. The Tucson research is financed by NSF (AMOP), AFOSR and DURINT.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. W. Koch.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koch, S., Kira, M., Khitrova, G. et al. Semiconductor excitons in new light. Nature Mater 5, 523–531 (2006). https://doi.org/10.1038/nmat1658

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat1658

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing