Abstract

An exciton moving in a random potential is a promising model system for the study of localization effects, since its energy spectrum can be measured directly, and there are no complications resulting from Coulomb interaction. This paper reviews our work on the use of nonlinear techniques, such as hole burning and four-wave mixing, to detect the motion of two-dimensional excitons in thin GaAs–AlxGa1−x As heterostructures, in which the random potential comes from fluctuations in layer width. A clear distinction is found between the behavior of excitons below and above the absorption line center. Below the line center, hole burning is easy, and both spectral and spatial diffusion are slow, i.e., the excitons behave as if they are localized; above it the reverse is true. This is strong evidence for a mobility edge at the line center, which is the position predicted classically.

© 1985 Optical Society of America

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  1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492 (1958).
    [CrossRef]
  2. N. F. Mott and E. A. Davis, Electronic Processes in Noncrystalline Materials, 2nd ed. (Clarendon, Oxford, 1979).
  3. P. W. Anderson, “Localization redux,” Physica 117/118B, 30 (1983).
  4. A. F. Ioffe and A. R. Regel, “Noncrystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237 (1960).
  5. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in 2D,” Phys. Rev. Lett. 42, 673 (1979).
    [CrossRef]
  6. D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Nonmetallic conduction in electron inversion layers at low temperatures,” Phys. Rev. Lett. 44, 1153 (1980).
    [CrossRef]
  7. R. G. Wheeler, “Magnetoconductance and weak localization in silicon inversion layers,” Phys. Rev. B 24, 4645 (1981).
    [CrossRef]
  8. D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Magnetoresistance in Si MOSFETs; evidence for weak localization and correlation,” Phys. Rev. B 26, 773 (1982).
    [CrossRef]
  9. N. F. Mott, “Electrical properties of liquid mercury,” Phil. Mag. 13, 989 (1966);see also M. H. Cohen, H. Fritzsche, and S. R. Ovshinsky, “Simple band model for amorphous semiconducting alloys;” Phys. Rev. Lett. 22, 1065 (1969).
    [CrossRef]
  10. B. L. Altshuler, A. G. Aronov, and P. A. Lee, “Interaction effects in disordered Fermi systems in 2D,” Phys. Rev. Lett. 44, 1288 (1980).
    [CrossRef]
  11. N. F. Mott, “The basis of the electron theory of metals, with special reference to the transition metals,” Proc. Phys. Soc. (London) 62, 416 (1949);“On the transition to metallic conduction in semiconductors,” Can. J. Phys. 34, 1356 (1956);“The transition to the metallic state,” Phil. Mag. 6, 287 (1961).
    [CrossRef]
  12. A. E. White, R. C. Dynes, and J. P. Garno, “Low temperature magnetoresistance in 2D Mg films,” Phys. Rev. B 29, 3694 (1984).
    [CrossRef]
  13. E. Arnold, “Disorder induced carrier localization in Si surface layers,” Appl. Phys. Lett. 26, 705 (1974);C. J. Adkins, “The Hall effect in inversion layers,” Phil. Mag. 38, 535 (1978).
    [CrossRef]
  14. N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
    [CrossRef]
  15. A. Y. Cho and J. R. Arthur, “Molecular beam epitaxy,” Prog. Solid State Chem. 10, 157 (1975).
    [CrossRef]
  16. R. D. Dupuis, L. A. Moudy, and P. D. Dapkus, “Preparation and properties of Ga1−x AlxAs–GaAs heterojunctions grown by MOCVD,” in GaAs and Related Compounds, C. N. Wolfe, ed. (Institute of Physics, London, 1979);R. C. Miller, R. D. Dupuis, and P. M. Petroff, “High quality single GaAs quantum wells grown by MOCVD,” Appl. Phys. Lett. 44, 508–510 (1984).
    [CrossRef]
  17. R. Dingle, W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin Alx Ga1−x As–Ga As–Alx Ga1−x As heterostructures,” Phys. Rev. Lett. 33, 827 (1974);R. Dingle, “Confined carrier quantum states in ultra-thin semiconductor heterostructures,” Festkoerperprobleme 15, 21 (1975).
    [CrossRef]
  18. R. C. Miller, D. A. Kleinman, and A. C. Gossard, “Energy gap discontinuities and effective masses for GaAs–Alx Ga1−x As quantum wells,” Phys. Rev. B 29, 7085 (1984).
    [CrossRef]
  19. R. C. Miller, AT&T Bell Laboratories Murray Hill, New Jersey 07974 (personal communication, 1984).
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    [CrossRef]
  21. C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs–Alx Ga1−x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
    [CrossRef]
  22. O. Simpson, “Electronic properties of aromatic hydrocarbons III. Diffusion of excitons,” Proc. R. Soc. London Ser. A 238, 402 (1956).
  23. J. P. Woerdman, “Some optical and electrical properties of a laser-generated free-carrier plasma in Si,” Philips Research Rep. Suppl. No. 7 (1971).
  24. H. J. Eichler, “Forced light scattering at laser-induced gratings—a method for investigation of optically excited solids,” Festkoerperprobleme 18, 241 (1978).
  25. J. R. Salcedo, A. E. Siegman, D. D. Dlott, and M. D. Fayer, “Dynamics of exciton transport in molecular crystals: the picosecond transient grating method,” Phys. Rev. Lett. 41, 131 (1978).
    [CrossRef]
  26. M. D. Fayer, “Exciton coherence,” in Spectroscopy and Exciton Dynamics of Condensed Molecular Systems, V. M. Agranovich and R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983).
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    [CrossRef]
  28. H. Kalt, V. G. Lyssenko, R. Renner, and C. Klingshirn, “Laser-induced gratings and wave mixing in large-gap semiconductors,” J. Opt. Soc. Am. B 2, 1188–1196 (1985).
    [CrossRef]
  29. Y. M. Wong and V. M. Kenkre, “Extension of exciton transport theory for transient grating experiments into the intermediate coherence domain,” Phys. Rev. B 22, 3072 (1980).
    [CrossRef]
  30. M. D. Sturge, J. Hegarty, and L. Goldner, “Localization of 2D excitons in GaAs–AlGaAs quantum-well layers,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).
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    [CrossRef]
  32. R. Kopelman, “Energy transport in mixed molecular crystals,” in Spectroscopy and Excitation Dynamics of Condensed Molecular Systems, V. M. Agranovich and R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983).
  33. G. F. Imbusch and R. Kopelman, “Optical spectroscopy of electronic centers in solids,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 1.
  34. T. Holstein, S. K. Lyo, and R. Orbach, “Excitation transfer in disordered systems,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 2.
  35. E. Cohen and M. D. Sturge, “Fluorescent line narrowing, localized exciton states and spectral diffusion in the mixed semiconductor CdSx Se1−x,” Phys. Rev. B 25, 3828 (1982).
    [CrossRef]
  36. T. Takagahara, “Theoretical study of population dynamics of 2D excitons in GaAs–AlAs quantum well structures,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).
  37. A. J. Grant and E. A. Davis, “Hopping conduction in amorphous semiconductors,” Solid Sate Commun. 15, 563 (1974).
    [CrossRef]
  38. D. E. McCumber and M. D. Sturge, “Linewidth and temperature shift of the R lines in ruby,” J. Appl. Phys. 34, 1682 (1983).
    [CrossRef]
  39. D. Hsu and J. L. Skinner, “On the thermal broadening of zero-phonon impurity lines in absorption and fluorescent spectra,” J. Chem. Phys. 81, 1604 (1984).
    [CrossRef]
  40. Y. Masumoto, S. Shionoya, and H. Kawaguchi, “Picosecond time-resolved study of excitons in GaAs–AlAs multiquantum well structures,” Phys. Rev. B 29, 3324 (1984).
    [CrossRef]
  41. J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
    [CrossRef]
  42. J. Hegarty, L. Goldner, and M. D. Sturge, “Localized and delocalized 2D excitons in GaAs–Alx Ga1−x As multiple quantum well structures,” Phys. Rev. B 30, 7346 (1984).Note that the absorption scale for the 102-Å sample (Fig. 1 of this reference) should be multiplied by a factor of 1.8 (see Erratum, Phys. Rev. B, to be published).
    [CrossRef]
  43. Resonant Rayleigh scattering is a linear process and is not to be confused with resonant Rayleigh-type mixing [T. Yajima and H. Souma, “Study of ultra-fast relaxation processes by resonant Rayleigh-type mixing,” Phys. Rev. B 17, 309 (1978)], which is a nonlinear four-wave mixing process closely related to the transient-grating technique.
  44. N. Bloembergen, E. M. Purcell, and R. V. Pound, “Relaxation effects in NMR absorption,” Phys. Rev. 73, 679 (1948);M. L. Spaeth and W. R. Sooy, “Fluorescence and bleaching of organic dyes,” J. Chem.Phys. 48, 2315 (1968);P. M. Selzer, “General techniques and experimental methods,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 4.
    [CrossRef]
  45. R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584 (1970);R. L. Fork, C. V. Shank, C. Hirliman, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1 (1983).
    [CrossRef] [PubMed]
  46. J. Hegarty and M. D. Sturge, “Exciton hole-burning in GaAs–AlGaAs multi-quantum wells,” in Proceedings of the International Conference on Luminescence, W. M. Yen and J. C. Wright, eds. (North-Holland, Amsterdam, 1984), p. 494.
  47. N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
    [CrossRef]
  48. W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
    [CrossRef]
  49. J. Hegarty, “Effect of hole burning on pulse propagation in GaAs quantum wells,” Phys. Rev. B 25, 4324 (1982).
    [CrossRef]
  50. J. M. Ziman, Models of Disorder (Cambridge U. Press, Cambridge, 1979), p. 484.
  51. D. S. Chemla and D. A. B. Miller, “Room-temperature excitonic nonlinear-optical effects in semiconducter quantum-well structures,” J. Opt. Soc. Am. B. 2, 1173–1175 (1985).
    [CrossRef]

1985 (2)

H. Kalt, V. G. Lyssenko, R. Renner, and C. Klingshirn, “Laser-induced gratings and wave mixing in large-gap semiconductors,” J. Opt. Soc. Am. B 2, 1188–1196 (1985).
[CrossRef]

D. S. Chemla and D. A. B. Miller, “Room-temperature excitonic nonlinear-optical effects in semiconducter quantum-well structures,” J. Opt. Soc. Am. B. 2, 1173–1175 (1985).
[CrossRef]

1984 (6)

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

D. Hsu and J. L. Skinner, “On the thermal broadening of zero-phonon impurity lines in absorption and fluorescent spectra,” J. Chem. Phys. 81, 1604 (1984).
[CrossRef]

Y. Masumoto, S. Shionoya, and H. Kawaguchi, “Picosecond time-resolved study of excitons in GaAs–AlAs multiquantum well structures,” Phys. Rev. B 29, 3324 (1984).
[CrossRef]

J. Hegarty, L. Goldner, and M. D. Sturge, “Localized and delocalized 2D excitons in GaAs–Alx Ga1−x As multiple quantum well structures,” Phys. Rev. B 30, 7346 (1984).Note that the absorption scale for the 102-Å sample (Fig. 1 of this reference) should be multiplied by a factor of 1.8 (see Erratum, Phys. Rev. B, to be published).
[CrossRef]

A. E. White, R. C. Dynes, and J. P. Garno, “Low temperature magnetoresistance in 2D Mg films,” Phys. Rev. B 29, 3694 (1984).
[CrossRef]

R. C. Miller, D. A. Kleinman, and A. C. Gossard, “Energy gap discontinuities and effective masses for GaAs–Alx Ga1−x As quantum wells,” Phys. Rev. B 29, 7085 (1984).
[CrossRef]

1983 (2)

P. W. Anderson, “Localization redux,” Physica 117/118B, 30 (1983).

D. E. McCumber and M. D. Sturge, “Linewidth and temperature shift of the R lines in ruby,” J. Appl. Phys. 34, 1682 (1983).
[CrossRef]

1982 (5)

J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
[CrossRef]

E. Cohen and M. D. Sturge, “Fluorescent line narrowing, localized exciton states and spectral diffusion in the mixed semiconductor CdSx Se1−x,” Phys. Rev. B 25, 3828 (1982).
[CrossRef]

J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Degenerate four wave mixing at the 2D exciton resonance of GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132 (1982).
[CrossRef]

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Magnetoresistance in Si MOSFETs; evidence for weak localization and correlation,” Phys. Rev. B 26, 773 (1982).
[CrossRef]

J. Hegarty, “Effect of hole burning on pulse propagation in GaAs quantum wells,” Phys. Rev. B 25, 4324 (1982).
[CrossRef]

1981 (2)

R. G. Wheeler, “Magnetoconductance and weak localization in silicon inversion layers,” Phys. Rev. B 24, 4645 (1981).
[CrossRef]

C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs–Alx Ga1−x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
[CrossRef]

1980 (3)

Y. M. Wong and V. M. Kenkre, “Extension of exciton transport theory for transient grating experiments into the intermediate coherence domain,” Phys. Rev. B 22, 3072 (1980).
[CrossRef]

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Nonmetallic conduction in electron inversion layers at low temperatures,” Phys. Rev. Lett. 44, 1153 (1980).
[CrossRef]

B. L. Altshuler, A. G. Aronov, and P. A. Lee, “Interaction effects in disordered Fermi systems in 2D,” Phys. Rev. Lett. 44, 1288 (1980).
[CrossRef]

1979 (1)

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in 2D,” Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

1978 (3)

P. M. Petroff, A. C. Gossard, W. Wiegmann, and A. L. Savage, “Crystal growth kinetics in (GaAs)n–(AlAs)m superlattices deposited by MBE,” J. Crystal Growth 44, 5 (1978).
[CrossRef]

H. J. Eichler, “Forced light scattering at laser-induced gratings—a method for investigation of optically excited solids,” Festkoerperprobleme 18, 241 (1978).

J. R. Salcedo, A. E. Siegman, D. D. Dlott, and M. D. Fayer, “Dynamics of exciton transport in molecular crystals: the picosecond transient grating method,” Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

1975 (2)

N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
[CrossRef]

A. Y. Cho and J. R. Arthur, “Molecular beam epitaxy,” Prog. Solid State Chem. 10, 157 (1975).
[CrossRef]

1974 (3)

R. Dingle, W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin Alx Ga1−x As–Ga As–Alx Ga1−x As heterostructures,” Phys. Rev. Lett. 33, 827 (1974);R. Dingle, “Confined carrier quantum states in ultra-thin semiconductor heterostructures,” Festkoerperprobleme 15, 21 (1975).
[CrossRef]

E. Arnold, “Disorder induced carrier localization in Si surface layers,” Appl. Phys. Lett. 26, 705 (1974);C. J. Adkins, “The Hall effect in inversion layers,” Phil. Mag. 38, 535 (1978).
[CrossRef]

A. J. Grant and E. A. Davis, “Hopping conduction in amorphous semiconductors,” Solid Sate Commun. 15, 563 (1974).
[CrossRef]

1971 (1)

J. P. Woerdman, “Some optical and electrical properties of a laser-generated free-carrier plasma in Si,” Philips Research Rep. Suppl. No. 7 (1971).

1970 (1)

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584 (1970);R. L. Fork, C. V. Shank, C. Hirliman, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1 (1983).
[CrossRef] [PubMed]

1966 (1)

N. F. Mott, “Electrical properties of liquid mercury,” Phil. Mag. 13, 989 (1966);see also M. H. Cohen, H. Fritzsche, and S. R. Ovshinsky, “Simple band model for amorphous semiconducting alloys;” Phys. Rev. Lett. 22, 1065 (1969).
[CrossRef]

1960 (1)

A. F. Ioffe and A. R. Regel, “Noncrystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237 (1960).

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492 (1958).
[CrossRef]

1956 (1)

O. Simpson, “Electronic properties of aromatic hydrocarbons III. Diffusion of excitons,” Proc. R. Soc. London Ser. A 238, 402 (1956).

1949 (1)

N. F. Mott, “The basis of the electron theory of metals, with special reference to the transition metals,” Proc. Phys. Soc. (London) 62, 416 (1949);“On the transition to metallic conduction in semiconductors,” Can. J. Phys. 34, 1356 (1956);“The transition to the metallic state,” Phil. Mag. 6, 287 (1961).
[CrossRef]

1948 (1)

N. Bloembergen, E. M. Purcell, and R. V. Pound, “Relaxation effects in NMR absorption,” Phys. Rev. 73, 679 (1948);M. L. Spaeth and W. R. Sooy, “Fluorescence and bleaching of organic dyes,” J. Chem.Phys. 48, 2315 (1968);P. M. Selzer, “General techniques and experimental methods,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 4.
[CrossRef]

Abrahams, E.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in 2D,” Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

Adkins, C. J.

N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
[CrossRef]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584 (1970);R. L. Fork, C. V. Shank, C. Hirliman, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1 (1983).
[CrossRef] [PubMed]

Altshuler, B. L.

B. L. Altshuler, A. G. Aronov, and P. A. Lee, “Interaction effects in disordered Fermi systems in 2D,” Phys. Rev. Lett. 44, 1288 (1980).
[CrossRef]

Anderson, P. W.

P. W. Anderson, “Localization redux,” Physica 117/118B, 30 (1983).

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in 2D,” Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492 (1958).
[CrossRef]

Antonetti, A.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Arnold, E.

E. Arnold, “Disorder induced carrier localization in Si surface layers,” Appl. Phys. Lett. 26, 705 (1974);C. J. Adkins, “The Hall effect in inversion layers,” Phil. Mag. 38, 535 (1978).
[CrossRef]

Aronov, A. G.

B. L. Altshuler, A. G. Aronov, and P. A. Lee, “Interaction effects in disordered Fermi systems in 2D,” Phys. Rev. Lett. 44, 1288 (1980).
[CrossRef]

Arthur, J. R.

A. Y. Cho and J. R. Arthur, “Molecular beam epitaxy,” Prog. Solid State Chem. 10, 157 (1975).
[CrossRef]

Bishop, D. J.

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Magnetoresistance in Si MOSFETs; evidence for weak localization and correlation,” Phys. Rev. B 26, 773 (1982).
[CrossRef]

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Nonmetallic conduction in electron inversion layers at low temperatures,” Phys. Rev. Lett. 44, 1153 (1980).
[CrossRef]

Bloembergen, N.

N. Bloembergen, E. M. Purcell, and R. V. Pound, “Relaxation effects in NMR absorption,” Phys. Rev. 73, 679 (1948);M. L. Spaeth and W. R. Sooy, “Fluorescence and bleaching of organic dyes,” J. Chem.Phys. 48, 2315 (1968);P. M. Selzer, “General techniques and experimental methods,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 4.
[CrossRef]

Chemla, D. S.

D. S. Chemla and D. A. B. Miller, “Room-temperature excitonic nonlinear-optical effects in semiconducter quantum-well structures,” J. Opt. Soc. Am. B. 2, 1173–1175 (1985).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Cho, A. Y.

A. Y. Cho and J. R. Arthur, “Molecular beam epitaxy,” Prog. Solid State Chem. 10, 157 (1975).
[CrossRef]

Cohen, E.

E. Cohen and M. D. Sturge, “Fluorescent line narrowing, localized exciton states and spectral diffusion in the mixed semiconductor CdSx Se1−x,” Phys. Rev. B 25, 3828 (1982).
[CrossRef]

Dapkus, P. D.

R. D. Dupuis, L. A. Moudy, and P. D. Dapkus, “Preparation and properties of Ga1−x AlxAs–GaAs heterojunctions grown by MOCVD,” in GaAs and Related Compounds, C. N. Wolfe, ed. (Institute of Physics, London, 1979);R. C. Miller, R. D. Dupuis, and P. M. Petroff, “High quality single GaAs quantum wells grown by MOCVD,” Appl. Phys. Lett. 44, 508–510 (1984).
[CrossRef]

Davis, E. A.

A. J. Grant and E. A. Davis, “Hopping conduction in amorphous semiconductors,” Solid Sate Commun. 15, 563 (1974).
[CrossRef]

N. F. Mott and E. A. Davis, Electronic Processes in Noncrystalline Materials, 2nd ed. (Clarendon, Oxford, 1979).

Dingle, R.

C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs–Alx Ga1−x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
[CrossRef]

R. Dingle, W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin Alx Ga1−x As–Ga As–Alx Ga1−x As heterostructures,” Phys. Rev. Lett. 33, 827 (1974);R. Dingle, “Confined carrier quantum states in ultra-thin semiconductor heterostructures,” Festkoerperprobleme 15, 21 (1975).
[CrossRef]

Dlott, D. D.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, and M. D. Fayer, “Dynamics of exciton transport in molecular crystals: the picosecond transient grating method,” Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Downer, M. C.

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Dupuis, R. D.

R. D. Dupuis, L. A. Moudy, and P. D. Dapkus, “Preparation and properties of Ga1−x AlxAs–GaAs heterojunctions grown by MOCVD,” in GaAs and Related Compounds, C. N. Wolfe, ed. (Institute of Physics, London, 1979);R. C. Miller, R. D. Dupuis, and P. M. Petroff, “High quality single GaAs quantum wells grown by MOCVD,” Appl. Phys. Lett. 44, 508–510 (1984).
[CrossRef]

Dynes, R. C.

A. E. White, R. C. Dynes, and J. P. Garno, “Low temperature magnetoresistance in 2D Mg films,” Phys. Rev. B 29, 3694 (1984).
[CrossRef]

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Magnetoresistance in Si MOSFETs; evidence for weak localization and correlation,” Phys. Rev. B 26, 773 (1982).
[CrossRef]

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Nonmetallic conduction in electron inversion layers at low temperatures,” Phys. Rev. Lett. 44, 1153 (1980).
[CrossRef]

Eichler, H. J.

H. J. Eichler, “Forced light scattering at laser-induced gratings—a method for investigation of optically excited solids,” Festkoerperprobleme 18, 241 (1978).

Fayer, M. D.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, and M. D. Fayer, “Dynamics of exciton transport in molecular crystals: the picosecond transient grating method,” Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

M. D. Fayer, “Exciton coherence,” in Spectroscopy and Exciton Dynamics of Condensed Molecular Systems, V. M. Agranovich and R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983).

Fork, R. L.

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Garno, J. P.

A. E. White, R. C. Dynes, and J. P. Garno, “Low temperature magnetoresistance in 2D Mg films,” Phys. Rev. B 29, 3694 (1984).
[CrossRef]

Gibbs, H. M.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Goldner, L.

J. Hegarty, L. Goldner, and M. D. Sturge, “Localized and delocalized 2D excitons in GaAs–Alx Ga1−x As multiple quantum well structures,” Phys. Rev. B 30, 7346 (1984).Note that the absorption scale for the 102-Å sample (Fig. 1 of this reference) should be multiplied by a factor of 1.8 (see Erratum, Phys. Rev. B, to be published).
[CrossRef]

M. D. Sturge, J. Hegarty, and L. Goldner, “Localization of 2D excitons in GaAs–AlGaAs quantum-well layers,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).

Gossard, A. C.

R. C. Miller, D. A. Kleinman, and A. C. Gossard, “Energy gap discontinuities and effective masses for GaAs–Alx Ga1−x As quantum wells,” Phys. Rev. B 29, 7085 (1984).
[CrossRef]

J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Degenerate four wave mixing at the 2D exciton resonance of GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132 (1982).
[CrossRef]

J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
[CrossRef]

C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs–Alx Ga1−x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
[CrossRef]

P. M. Petroff, A. C. Gossard, W. Wiegmann, and A. L. Savage, “Crystal growth kinetics in (GaAs)n–(AlAs)m superlattices deposited by MBE,” J. Crystal Growth 44, 5 (1978).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Grant, A. J.

A. J. Grant and E. A. Davis, “Hopping conduction in amorphous semiconductors,” Solid Sate Commun. 15, 563 (1974).
[CrossRef]

Hegarty, J.

J. Hegarty, L. Goldner, and M. D. Sturge, “Localized and delocalized 2D excitons in GaAs–Alx Ga1−x As multiple quantum well structures,” Phys. Rev. B 30, 7346 (1984).Note that the absorption scale for the 102-Å sample (Fig. 1 of this reference) should be multiplied by a factor of 1.8 (see Erratum, Phys. Rev. B, to be published).
[CrossRef]

J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
[CrossRef]

J. Hegarty, “Effect of hole burning on pulse propagation in GaAs quantum wells,” Phys. Rev. B 25, 4324 (1982).
[CrossRef]

J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Degenerate four wave mixing at the 2D exciton resonance of GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132 (1982).
[CrossRef]

M. D. Sturge, J. Hegarty, and L. Goldner, “Localization of 2D excitons in GaAs–AlGaAs quantum-well layers,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).

J. Hegarty and M. D. Sturge, “Exciton hole-burning in GaAs–AlGaAs multi-quantum wells,” in Proceedings of the International Conference on Luminescence, W. M. Yen and J. C. Wright, eds. (North-Holland, Amsterdam, 1984), p. 494.

Henry, C. H.

R. Dingle, W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin Alx Ga1−x As–Ga As–Alx Ga1−x As heterostructures,” Phys. Rev. Lett. 33, 827 (1974);R. Dingle, “Confined carrier quantum states in ultra-thin semiconductor heterostructures,” Festkoerperprobleme 15, 21 (1975).
[CrossRef]

Holstein, T.

T. Holstein, S. K. Lyo, and R. Orbach, “Excitation transfer in disordered systems,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 2.

Hsu, D.

D. Hsu and J. L. Skinner, “On the thermal broadening of zero-phonon impurity lines in absorption and fluorescent spectra,” J. Chem. Phys. 81, 1604 (1984).
[CrossRef]

Hulin, D.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Imbusch, G. F.

G. F. Imbusch and R. Kopelman, “Optical spectroscopy of electronic centers in solids,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 1.

Ioffe, A. F.

A. F. Ioffe and A. R. Regel, “Noncrystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237 (1960).

Jewell, J. L.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Kalt, H.

Kawaguchi, H.

Y. Masumoto, S. Shionoya, and H. Kawaguchi, “Picosecond time-resolved study of excitons in GaAs–AlAs multiquantum well structures,” Phys. Rev. B 29, 3324 (1984).
[CrossRef]

Kenkre, V. M.

Y. M. Wong and V. M. Kenkre, “Extension of exciton transport theory for transient grating experiments into the intermediate coherence domain,” Phys. Rev. B 22, 3072 (1980).
[CrossRef]

Kleinman, D. A.

R. C. Miller, D. A. Kleinman, and A. C. Gossard, “Energy gap discontinuities and effective masses for GaAs–Alx Ga1−x As quantum wells,” Phys. Rev. B 29, 7085 (1984).
[CrossRef]

Klingshirn, C.

Knox, W. H.

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Kopelman, R.

G. F. Imbusch and R. Kopelman, “Optical spectroscopy of electronic centers in solids,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 1.

R. Kopelman, “Energy transport in mixed molecular crystals,” in Spectroscopy and Excitation Dynamics of Condensed Molecular Systems, V. M. Agranovich and R. M. Hochstrasser, eds. (North-Holland, Amsterdam, 1983).

Lee, P. A.

B. L. Altshuler, A. G. Aronov, and P. A. Lee, “Interaction effects in disordered Fermi systems in 2D,” Phys. Rev. Lett. 44, 1288 (1980).
[CrossRef]

Licciardello, D. C.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in 2D,” Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

Lyo, S. K.

T. Holstein, S. K. Lyo, and R. Orbach, “Excitation transfer in disordered systems,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 2.

Lyssenko, V. G.

Masumoto, Y.

Y. Masumoto, S. Shionoya, and H. Kawaguchi, “Picosecond time-resolved study of excitons in GaAs–AlAs multiquantum well structures,” Phys. Rev. B 29, 3324 (1984).
[CrossRef]

McCumber, D. E.

D. E. McCumber and M. D. Sturge, “Linewidth and temperature shift of the R lines in ruby,” J. Appl. Phys. 34, 1682 (1983).
[CrossRef]

Migus, A.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Miller, D. A. B.

D. S. Chemla and D. A. B. Miller, “Room-temperature excitonic nonlinear-optical effects in semiconducter quantum-well structures,” J. Opt. Soc. Am. B. 2, 1173–1175 (1985).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Miller, R. C.

R. C. Miller, D. A. Kleinman, and A. C. Gossard, “Energy gap discontinuities and effective masses for GaAs–Alx Ga1−x As quantum wells,” Phys. Rev. B 29, 7085 (1984).
[CrossRef]

R. C. Miller, AT&T Bell Laboratories Murray Hill, New Jersey 07974 (personal communication, 1984).

Mott, N. F.

N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
[CrossRef]

N. F. Mott, “Electrical properties of liquid mercury,” Phil. Mag. 13, 989 (1966);see also M. H. Cohen, H. Fritzsche, and S. R. Ovshinsky, “Simple band model for amorphous semiconducting alloys;” Phys. Rev. Lett. 22, 1065 (1969).
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N. F. Mott, “The basis of the electron theory of metals, with special reference to the transition metals,” Proc. Phys. Soc. (London) 62, 416 (1949);“On the transition to metallic conduction in semiconductors,” Can. J. Phys. 34, 1356 (1956);“The transition to the metallic state,” Phil. Mag. 6, 287 (1961).
[CrossRef]

N. F. Mott and E. A. Davis, Electronic Processes in Noncrystalline Materials, 2nd ed. (Clarendon, Oxford, 1979).

Moudy, L. A.

R. D. Dupuis, L. A. Moudy, and P. D. Dapkus, “Preparation and properties of Ga1−x AlxAs–GaAs heterojunctions grown by MOCVD,” in GaAs and Related Compounds, C. N. Wolfe, ed. (Institute of Physics, London, 1979);R. C. Miller, R. D. Dupuis, and P. M. Petroff, “High quality single GaAs quantum wells grown by MOCVD,” Appl. Phys. Lett. 44, 508–510 (1984).
[CrossRef]

Mysyrowicz, A.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Orbach, R.

T. Holstein, S. K. Lyo, and R. Orbach, “Excitation transfer in disordered systems,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 2.

Pepper, M.

N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
[CrossRef]

Petroff, P. M.

P. M. Petroff, A. C. Gossard, W. Wiegmann, and A. L. Savage, “Crystal growth kinetics in (GaAs)n–(AlAs)m superlattices deposited by MBE,” J. Crystal Growth 44, 5 (1978).
[CrossRef]

Peyghambarian, N.

N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A. Migus, D. Hulin, and A. Mysyrowicz, “Blue shift of the exciton resonance due to exciton–exciton interactions in a multiple-quantum-well structure,” Phys. Rev. Lett. 53, 2433 (1984).
[CrossRef]

Pollitt, S.

N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
[CrossRef]

Pound, R. V.

N. Bloembergen, E. M. Purcell, and R. V. Pound, “Relaxation effects in NMR absorption,” Phys. Rev. 73, 679 (1948);M. L. Spaeth and W. R. Sooy, “Fluorescence and bleaching of organic dyes,” J. Chem.Phys. 48, 2315 (1968);P. M. Selzer, “General techniques and experimental methods,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 4.
[CrossRef]

Purcell, E. M.

N. Bloembergen, E. M. Purcell, and R. V. Pound, “Relaxation effects in NMR absorption,” Phys. Rev. 73, 679 (1948);M. L. Spaeth and W. R. Sooy, “Fluorescence and bleaching of organic dyes,” J. Chem.Phys. 48, 2315 (1968);P. M. Selzer, “General techniques and experimental methods,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 4.
[CrossRef]

Ramakrishnan, T. V.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in 2D,” Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

Regel, A. R.

A. F. Ioffe and A. R. Regel, “Noncrystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237 (1960).

Renner, R.

Salcedo, J. R.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, and M. D. Fayer, “Dynamics of exciton transport in molecular crystals: the picosecond transient grating method,” Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Savage, A. L.

P. M. Petroff, A. C. Gossard, W. Wiegmann, and A. L. Savage, “Crystal growth kinetics in (GaAs)n–(AlAs)m superlattices deposited by MBE,” J. Crystal Growth 44, 5 (1978).
[CrossRef]

Shank, C. V.

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584 (1970);R. L. Fork, C. V. Shank, C. Hirliman, R. Yen, and W. J. Tomlinson, “Femtosecond white-light continuum pulses,” Opt. Lett. 8, 1 (1983).
[CrossRef] [PubMed]

Shionoya, S.

Y. Masumoto, S. Shionoya, and H. Kawaguchi, “Picosecond time-resolved study of excitons in GaAs–AlAs multiquantum well structures,” Phys. Rev. B 29, 3324 (1984).
[CrossRef]

Siegman, A. E.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, and M. D. Fayer, “Dynamics of exciton transport in molecular crystals: the picosecond transient grating method,” Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Simpson, O.

O. Simpson, “Electronic properties of aromatic hydrocarbons III. Diffusion of excitons,” Proc. R. Soc. London Ser. A 238, 402 (1956).

Skinner, J. L.

D. Hsu and J. L. Skinner, “On the thermal broadening of zero-phonon impurity lines in absorption and fluorescent spectra,” J. Chem. Phys. 81, 1604 (1984).
[CrossRef]

Sturge, M. D.

J. Hegarty, L. Goldner, and M. D. Sturge, “Localized and delocalized 2D excitons in GaAs–Alx Ga1−x As multiple quantum well structures,” Phys. Rev. B 30, 7346 (1984).Note that the absorption scale for the 102-Å sample (Fig. 1 of this reference) should be multiplied by a factor of 1.8 (see Erratum, Phys. Rev. B, to be published).
[CrossRef]

D. E. McCumber and M. D. Sturge, “Linewidth and temperature shift of the R lines in ruby,” J. Appl. Phys. 34, 1682 (1983).
[CrossRef]

J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
[CrossRef]

J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Degenerate four wave mixing at the 2D exciton resonance of GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132 (1982).
[CrossRef]

E. Cohen and M. D. Sturge, “Fluorescent line narrowing, localized exciton states and spectral diffusion in the mixed semiconductor CdSx Se1−x,” Phys. Rev. B 25, 3828 (1982).
[CrossRef]

M. D. Sturge, J. Hegarty, and L. Goldner, “Localization of 2D excitons in GaAs–AlGaAs quantum-well layers,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).

J. Hegarty and M. D. Sturge, “Exciton hole-burning in GaAs–AlGaAs multi-quantum wells,” in Proceedings of the International Conference on Luminescence, W. M. Yen and J. C. Wright, eds. (North-Holland, Amsterdam, 1984), p. 494.

Takagahara, T.

T. Takagahara, “Theoretical study of population dynamics of 2D excitons in GaAs–AlAs quantum well structures,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).

Tsui, D. C.

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Magnetoresistance in Si MOSFETs; evidence for weak localization and correlation,” Phys. Rev. B 26, 773 (1982).
[CrossRef]

D. J. Bishop, R. C. Dynes, and D. C. Tsui, “Nonmetallic conduction in electron inversion layers at low temperatures,” Phys. Rev. Lett. 44, 1153 (1980).
[CrossRef]

Wallis, R. H.

N. F. Mott, M. Pepper, S. Pollitt, R. H. Wallis, and C. J. Adkins, “The Anderson transition,” Proc. R. Soc. London Ser. A 345, 169 (1975).
[CrossRef]

Weisbuch, C.

J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
[CrossRef]

C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs–Alx Ga1−x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
[CrossRef]

Wheeler, R. G.

R. G. Wheeler, “Magnetoconductance and weak localization in silicon inversion layers,” Phys. Rev. B 24, 4645 (1981).
[CrossRef]

White, A. E.

A. E. White, R. C. Dynes, and J. P. Garno, “Low temperature magnetoresistance in 2D Mg films,” Phys. Rev. B 29, 3694 (1984).
[CrossRef]

Wiegmann, W.

J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Degenerate four wave mixing at the 2D exciton resonance of GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132 (1982).
[CrossRef]

J. Hegarty, M. D. Sturge, C. Weisbuch, A. C. Gossard, and W. Wiegmann, “Resonant Rayleigh scattering in an inhomogeneous medium: a new probe of the homogeneous linewidth,” Phys. Rev. Lett. 49, 930 (1982).
[CrossRef]

C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs–Alx Ga1−x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
[CrossRef]

P. M. Petroff, A. C. Gossard, W. Wiegmann, and A. L. Savage, “Crystal growth kinetics in (GaAs)n–(AlAs)m superlattices deposited by MBE,” J. Crystal Growth 44, 5 (1978).
[CrossRef]

R. Dingle, W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin Alx Ga1−x As–Ga As–Alx Ga1−x As heterostructures,” Phys. Rev. Lett. 33, 827 (1974);R. Dingle, “Confined carrier quantum states in ultra-thin semiconductor heterostructures,” Festkoerperprobleme 15, 21 (1975).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank, A. C. Gossard, and W. Wiegmann, “Femtosecond dynamics of nonequilibrium correlated electron-hole pair distributions in room-temperature GaAs multiple quantum well structures,” in Ultrafast Phenomena IV, D. H. Auston and K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984).
[CrossRef]

Woerdman, J. P.

J. P. Woerdman, “Some optical and electrical properties of a laser-generated free-carrier plasma in Si,” Philips Research Rep. Suppl. No. 7 (1971).

Wong, Y. M.

Y. M. Wong and V. M. Kenkre, “Extension of exciton transport theory for transient grating experiments into the intermediate coherence domain,” Phys. Rev. B 22, 3072 (1980).
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Ziman, J. M.

J. M. Ziman, Models of Disorder (Cambridge U. Press, Cambridge, 1979), p. 484.

Appl. Phys. Lett. (2)

E. Arnold, “Disorder induced carrier localization in Si surface layers,” Appl. Phys. Lett. 26, 705 (1974);C. J. Adkins, “The Hall effect in inversion layers,” Phil. Mag. 38, 535 (1978).
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J. Hegarty, M. D. Sturge, A. C. Gossard, and W. Wiegmann, “Degenerate four wave mixing at the 2D exciton resonance of GaAs multiquantum well structures,” Appl. Phys. Lett. 40, 132 (1982).
[CrossRef]

Festkoerperprobleme (1)

H. J. Eichler, “Forced light scattering at laser-induced gratings—a method for investigation of optically excited solids,” Festkoerperprobleme 18, 241 (1978).

J. Appl. Phys. (1)

D. E. McCumber and M. D. Sturge, “Linewidth and temperature shift of the R lines in ruby,” J. Appl. Phys. 34, 1682 (1983).
[CrossRef]

J. Chem. Phys. (1)

D. Hsu and J. L. Skinner, “On the thermal broadening of zero-phonon impurity lines in absorption and fluorescent spectra,” J. Chem. Phys. 81, 1604 (1984).
[CrossRef]

J. Crystal Growth (1)

P. M. Petroff, A. C. Gossard, W. Wiegmann, and A. L. Savage, “Crystal growth kinetics in (GaAs)n–(AlAs)m superlattices deposited by MBE,” J. Crystal Growth 44, 5 (1978).
[CrossRef]

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T. Holstein, S. K. Lyo, and R. Orbach, “Excitation transfer in disordered systems,” in Laser Spectroscopy of Solids, W. M. Yen and P. M. Selzer, eds. (Springer-Verlag, Berlin, 1981), Chap. 2.

R. D. Dupuis, L. A. Moudy, and P. D. Dapkus, “Preparation and properties of Ga1−x AlxAs–GaAs heterojunctions grown by MOCVD,” in GaAs and Related Compounds, C. N. Wolfe, ed. (Institute of Physics, London, 1979);R. C. Miller, R. D. Dupuis, and P. M. Petroff, “High quality single GaAs quantum wells grown by MOCVD,” Appl. Phys. Lett. 44, 508–510 (1984).
[CrossRef]

N. F. Mott and E. A. Davis, Electronic Processes in Noncrystalline Materials, 2nd ed. (Clarendon, Oxford, 1979).

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J. Hegarty and M. D. Sturge, “Exciton hole-burning in GaAs–AlGaAs multi-quantum wells,” in Proceedings of the International Conference on Luminescence, W. M. Yen and J. C. Wright, eds. (North-Holland, Amsterdam, 1984), p. 494.

Resonant Rayleigh scattering is a linear process and is not to be confused with resonant Rayleigh-type mixing [T. Yajima and H. Souma, “Study of ultra-fast relaxation processes by resonant Rayleigh-type mixing,” Phys. Rev. B 17, 309 (1978)], which is a nonlinear four-wave mixing process closely related to the transient-grating technique.

T. Takagahara, “Theoretical study of population dynamics of 2D excitons in GaAs–AlAs quantum well structures,” in Proceedings of the Seventeenth International Conference on the Physics of Semiconductors, D. Chadi, ed. (Springer-Verlag, New York, to be published).

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Figures (13)

Fig. 1
Fig. 1

Schematic density of states ρ(E) in the conduction band of a disordered semiconductor. Localized states are shaded. Em is the mobility edge. (After Mott and Davies.2)

Fig. 2
Fig. 2

(a) Section through a MQW structure (schematic). The wider-band-gap material (barrier layer) is shaded. (b) Energy-band profile of one layer of this structure. The barrier layer is assumed to be sufficiently wide that tunneling through it can be neglected (this is the case in all the structures considered in this paper). Optical transitions allowed by the Δn = 0 selection rule are indicated by vertical lines.

Fig. 3
Fig. 3

Photoluminescence excitation spectrum (which mirrors the absorption spectrum) at 7 K of a GaAs–AlxGa1–xAs MQW structure with x = 0.3, Lz = 145 Å (Ref. 19). The sharp lines are excitonic transitions associated with the subbands indicated (HH, heavy hole; LH, light hole). The line marked F is a forbidden transition with Δn = 2. The underlying absorption is due to the creation of free-electron-hole pairs and reflects the steplike structure of the 2D density of states.

Fig. 4
Fig. 4

Solid line, energy Ex of the heavy-hole exciton in GaAs–AlxGa1−xAs quantum wells as a function of GaAs layer width, for x = 0.3 (see Ref. 19). The observed energies in good-quality material fall on this curve, within experimental error. Dashed line, inhomogeneous linewidth resulting from layer-width fluctuations calculated as in the text (Weisbuch et al.21). Points, measured linewidth of the heavy-hole-exciton absorption line in MQW samples grown by MBE under optimal conditions (Ref. 21).

Fig. 5
Fig. 5

Schematic of two possible arrangements of the transient-grating experiment. In both cases P1 and P2 represent the pump pulses, PR the probe pulse, and D the diffracted pulse. (a) Pump pulses entering sample from same side. Grating in plane of sample; sin θ = n−1 sin ϕ; Λ = λ/2 sin ϕ. (b) Pump pulses entering sample from opposite sides. Grating normal to sample; cos θ = n−1 sin ϕ; Λ ≃ λ/2n for large n.

Fig. 6
Fig. 6

Exciton diffusion constant, obtained from Eq. (3), as a function of exciton energy, for GaAs quantum wells with Lz = 205 Å at 5 K. Exciton density ∼1010 cm−2 per layer. The solid line is the absorption spectrum. Note that the light- and the heavy-hole excitons are not fully resolved in this sample.

Fig. 7
Fig. 7

Dashed curve, absorption at the heavy-hole exciton for a MQW sample with Lz = 51 Å. Solid curve, Γh obtained from Rayleigh scattering at 5 K. Open squares, activation energy for Γh (T) at different exciting energies. The dashed–dotted line has the slope –1 predicted by expression (4). The vertical arrow shows the position of the luminescence peak.

Fig. 8
Fig. 8

Absorption coefficient α (lower trace) of the heavy-hole-exciton line at 5 K for Lz = 102 Å, and the change in transmission ΔT/T = −Δα at zero delay (upper trace), for three different pump frequencies (shown by the arrows). Pump intensity I = 5 ×10−7 J cm−2 per pulse; probe intensity 10−2I. One unit of the vertical scale for ΔT/T is approximately 0.15.

Fig. 9
Fig. 9

Plot of (1 − T)−1 ln[T(I)/T(0)] against I [Eq. (7)] at two points in the heavy-hole-exciton line for Lz = 51 Å. The peak of the line in this sample is at 1.6127 eV.

Fig. 10
Fig. 10

Upper trace, absorption coefficient for the heavy-hole-exciton line, Lz = 51 Å. Lower trace, homogeneous linewidth Γh(T): Solid line, from Rayleigh scattering; filled circles, from saturation [Eq. (7)]. Open circles, the recovery (spectral-diffusion) rates obtained at low intensity in the pump–probe experiment (see Fig. 13).

Fig. 11
Fig. 11

Dependence of the change in transmission ΔT on delay of the probe after the pump pulse, for pump and probe 2 meV above the peak of the absorption line of the heavy-hole exciton. Lz = 51 Å, T = 5K, I0 = 10−7 J cm−2 per pulse. The solid line is an exponential fit to the long-lived induced absorption, with the fluorescent decay time of 800 psec.

Fig. 12
Fig. 12

Semilog plot of the data of Fig. 11, with the long-lived induced absorption subtracted.

Fig. 13
Fig. 13

Semilog plot of the change in transmission ΔT for pump and probe 3.5 meV below the peak of the absorption line. Conditions are otherwise as in Fig. 11. The lines are exponential fits to the long-lived component, with a decay time of 240 psec.

Equations (7)

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W / M > 5 .
D = l 2 / τ s = k l / m ,
ω = 2 / τ + 8 π 2 D / Λ 2 ,
Γ h ( act ) exp ( Δ E / k T ) ,
Γ h ( hop ) exp [ B / T n / ( d + 1 ) ] ,
α ( i ) = i ( z ) 1 d i / d z = α ( 0 ) / [ 1 + i ( z ) / I s ] ,
( 1 T ) 1 ln [ T ( I ) / T ( 0 ) ] = I / I s .

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