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.
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References
P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492(1958).
N. F. Mott and E. A. Davis. Electronic Processes in Noncrystalline Materials, 2nd éd. (Clarendon, Oxford, 1979).
P. W. Anderson, “Localization redux,” Physica 117/118B, 30 (1983).
A. F. Ioffe and A. R. Regel, “Noncrystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237 (1960).
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).
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).
R. G. Wheeler. “Magnetoconductance and weak localization in silicon inversion layers,” Phys. Rev. B 24, 4645 (1981).
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).
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).
B. L. Altshuler, A. G. Aronov, and P. A. Lee, “Interaction effects in disordered Fermi systems in 2D,” Phys. Rev. Lett. 44, 1288 (1980).
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).
A. E. White, R. C. Dynes, and J. P. Garno, “Low temperature magnetoresistance in 2D Mg films,” Phys. Rev. B 29, 3694 (1984).
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).
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).
A. Y. Cho and J. R. Arthur, “Molecular beam epitaxy,” Prog. Solid State Chem. 10, 157 (1975).
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).
R. Dingle, W. Wiegmann, and C. H. Henry, “Quantum states of confined carriers in very thin AlxGa1-x As-Ga As-AlxGa1-x As heterostructures,” Phys. Rev. Lett. 33, 827 (1974)
R. Dingle, “Confined carrier quantum states in ultra-thin semiconductor heterostructures,” Festkoerperprobleme 15, 21 (1975).
R. C. Miller, D. A. Kleinman, and A. C. Gossard, “Energy gap discontinuities and effective masses for GaAs-AlxGa1-x As quantum wells,” Phys. Rev. B 29, 7085 (1984).
R. C. Miller, AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (personal communication, 1984).
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).
C. Weisbuch, R. Dingle, A. C. Gossard, and W. Wiegmann, “Optical characterization of interface disorder in GaAs-AlxGa1-x As multi-quantum well structures,” Solid State Commun. 38, 709 (1981).
O. Simpson, “Electronic properties of aromatic hydrocarbons III. Diffusion of excitons,” Proc. R. Soc. London Ser. A 238, 402 (1956).
J. P. Woerdman, “Some optical and electrical properties of a laser-generated free-carrier plasma in Si,” Philips Research Rep. Suppl. No. 7 (1971).
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).
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).
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).
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).
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).
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).
W. M. Yen and P. M. Selzer, eds., Laser Spectroscopy of Solids (Springer-Verlag, Berlin. 1981).
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).
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.
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.
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)
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).
A. J. Grant and E. A. Davis, “Hopping conduction in amorphous semiconductors,” Solid Sate Commun. 15, 563 (1974).
D. E. McCumber and M. D. Sturge, “Linewidth and temperature shift of the R lines in ruby,” J. Appl. Phys. 34, 1682 (1983).
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).
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).
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).
J. Hegarty, L. Goldner, and M. D. Sturge, “Localized and delo-calized 2D excitons in GaAs-AlxGa1-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).
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.
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.
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).
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.
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).
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).
J. Hegarty. “Effect of hole burning on pulse propagation in GaAs quantum wells,” Phys. Rev. B 25, 4324 (1982).
J. M. Ziman. Models of Disorder (Cambridge U. Press, Cambridge, 1979), p. 484.
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).
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Hegarty, J., Sturge, M.D. (1995). Studies of exciton localization in quantum-well structures by nonlinear-optical techniques. In: Burstein, E., Weisbuch, C. (eds) Confined Electrons and Photons. NATO ASI Series, vol 340. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1963-8_37
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