Abstract
Electrons in solids are subject to the crystal potential, as well as to the mutual electronelectron interaction. The resulting quantum-mechanical system represents a many-body problem of great complexity. In weakly-correlated systems like the usual semiconductors, a good starting point is provided by the one-particle picture, in which the crystal eigenstates are approximated by Slater determinants where the electrons occupy the one-particle eigenstates called band levels. This is only an approximate picture, since the electron-electron interaction yields corrections to the excited-state spectrum of the crystal. In particular, two-particle excitations called excitons arise at energies below the band gap, and excitonic corrections are found also at energies above the band gap.
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References
V. M. Agranovich, and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience Publ., London, 1966).
W. Hanke, Adv. Phys. 27, 287 (1978) and references therein.
F. Wooten, Optical Properties of Solids (Academic Press, London,1972).
J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
F. Stern, Solid State Physics, vol. 15, F. Seitz, D. Turnbull, eds, p. 300 (1963).
M. Altarelli, D. L. Dexter, H. M. Nussenzveig, and D. Y. Smith, Phys. Rev. B 6, 4502 (1972).
F. Bassani, and S. Scandolo, Phys. Rev. B 44, 8446 (1991)
S. Scandolo, and F. Bassani, Phys. Rev. B 45, 13257 (1992)
F. Bassani, Electronic Structure and Dielectric Properties of Superlattices, in Optical Properties of Semiconductors, edited by G. Martinez (Kluwer Academic Publ., Amsterdam, 1993), p. 27.
M. Sheik-Bahae et al., IEEE J. Quantum Electron. QE-27, 1296 (1991).
F. Bassani, and G. Pastori Parravicini, Electronic States and Optical Transitions in Solids (Pergamon Press, Oxford, 1975).
D. Greenaway, and G. Harbeke, Optical Properties of Semiconductors (Pergamon Press, Oxford, 1966).
R. S. Knox, Theory of Excitons, in Solid State Physics, suppl. 5, edited by F. Seitz and D. Turnbull (Academic Press, New York, 1963).
J. O. Dimmock, Introduction to the Theory of Exciton States in Semiconductors, in Semiconductors and Semimetals, vol. 3, edited by R. K. Willardson and A. C. Beer (Academic Press, New York, 1967), p. 259.
G. D. Mahan, Many Particle Physics (Plenum Press, New York, N.Y., 1981).
G. Iadonisi, and F. Bassani, Il Nuovo Cimento D 2, 1541 (1983) and references therein.
J. Dresselhaus, J. Phys. Chem. Solids 1, 14 (1956).
J. M. Luttinger, Phys. Rev. 102, 1030 (1956).
A. Baldereschi, and Nunzio O. Lipari, Phys. Rev. B 3, 439 (1971).
R. J. Elliott, Phys. Rev. 108, 1384 (1957).
J. J. Hopfield, J. Phys. Chem. Solids 15, 97 (1960).
G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz, Properties of the Thirty-two Point Groups (MIT, Cambridge, 1963).
E. O. Kane, Energy Band Theory, in Handbook of Semiconductors, edited by W. Paul (North-Holland Amsterdam, 1982), p. 193.
M. Sturge, Phys. Rev. 127, 768 (1962)
D. D. Sell, Phys. Rev. B 6, 3750 (1972)
D. E. Hill, Solid State Commun. 11, 1187 (1972).
H. Mayer, U. Rössler, and M. Ruff, Phys. Rev. B 47, 12929 (1993).
Y. Onodera and Y. Toyozawa, J. Phys. Soc. Jpn. 22, 833 (1967).
O. Schütz, and C. Uihlein, Phys. Status Solidi (b) 63, 545 (1974).
K. Cho, Phys. Rev. B 14, 4463 (1976).
L. C. Andreani, and F. Bassani, Phys. Rev. B 41, 7536 (1990).
M. M. Denisov, and V. P. Makarov, Phys. Status Solidi (b) 56, 9 (1973).
U. Rössler, and H.-R. Trebin, Phys. Rev. B 23, 1961 (1981).
K. Ehara, and K. Cho, Solid State Commun. 44, 453 (1982).
K. Cho, Solid State Commun. 33, 911 (1980).
E. Burstein, F. De Martini (eds.): Polaritons, Proceedings of the First Taormina Conference on the Structure of Matter (Pergamon, New York, 1974).
C. Weisbuch, and R. G. Ulbrich, Resonant Light Scattering Mediated by Excitonic Polaritons in Semiconductors, in Light Scattering in Solids III, edited by M. Cardona and G. Günterodt, Topics in Applied Physics, vol. 51 (Springer, Berlin, 1982), p. 207.
S. I. Pekar, Crystal Optics and Additional Light Waves (Benjamin-Cummings, Menlo Park, Califomia, 1983).
B. Hönerlage, R. Lévy, J. B. Grun, C. Klingshirn, and K. Bohnert, Phys. Rep. 124, 163 (1985).
F. Bassani, and L. C. Andreani, Exciton-Polariton States in Insulators and Semiconductors, in Excited-State Spectroscopy in Solids, edited by U. Grassano and N. Terzi (Academic Press, Amsterdam, 1987), p. 1.
P. Halevi, Exciton-Polaritons and Optical Properties of Direct-Gap Semiconductors, in Spatial Dispersion in Solids and Plasmas, edited by P. Halevi (Elsevier, 1992), p. 340
R. Fuchs, and P. Halevi, Basic Concepts and Formalism of Spatial Dispersion, edited by P. Halevi (Elsevier, 1992), p. 2.
K. Huang, Proc. Roy. Soc. A 208, 352 (1951).
M. Born, and K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, 1954.
S. I. Pekar, J. Exptl. Theoret. Phys. 33, 1022 (1957) [Sov. Phys. JETP 6, 785 (1958)].
J. J. Hopfield, and D. G. Thomas, Phys. Rev. 132, 563 (1963).
A. Stahl, and I. Balslev, Electrodynamics of the Semiconductor Band Edge (Springer, Berlin, 1987).
A. D’andrea, and R. Del Sole, Phys. Rev. B 32, 2337 (1985).
D. Fröhlich, E. Mohler, and P. Wiesner, Phys. Rev. Lett. 26, 554 (1971).
B. Hönerlage, A. Bivas, and Vu Duy Phach, Phys. Rev. Lett. 41, 49 (1978).
J. J. Hopfield, Phys. Rev. 112, 1555 (1958).
V. M. Agranovich, J. Exptl. Theoret. Phys. 37, 430 (1959) [Sov. Phys. JETP 37, 307 (1960)].
U. Fano, Phys. Rev. 103, 1202 (1956).
A. Quattropani, L. C. Andreani, and F. Bassani, Il Nuovo Cimento D 7, 55 (1986).
M. Artoni, and J. Birman, Phys. Rev. B 44, 3736 (1991)
P. Schwendimann, and A. Quattropani, Europhys. Lett. 17, 355 (1992).
See lecture notes by J.-M. Raimond and S. Haroche, this volume.
J.J. Hopfield, Phys. Rev. 182, 945 (1969).
R. Ulbrich, and C. Weisbuch, Phys. Rev. Lett. 38, 865 (1977).
L. Schultheis, J. Kuhl, A. Honold, and C.W. Tu, Phys. Rev. Lett. 57, 1797 (1986).
W.C. Tait, Phys. Rev. B 5, 648 (1972).
V. A. Kiselev, B.S. Razbirin, and I.N. Uraltsev, Phys. Stat. Solidi (b) 72, 161 (1975).
D.D. Sell, S.E. Stokovski, R. Dingle, and J.V. DiLorenzo, Phys. Rev. B 7, 4568 (1973).
R.G. Ulbrich, and G.W. Fehrenbach, Phys. Rev. Lett. 43, 963 (1979).
H. Sumi, J. Phys. Soc. Jpn. 41, 526 (1976).
C. Weisbuch, and R.G. Ulbrich, Phys. Rev. Lett. 39, 654 (1977)
C. Weisbuch, and R.G. Ulbrich, J. Lumin. 18/19, 27 (1979).
M. Dagenais, and W.F. Sharfin, Phys. Rev. Lett. 58, 1776 (1987)
F. Vallée, F. Bogani, and C. Flytzanis, Phys. Rev. Lett. 66, 1509 (1991).
W.C. Tait, and R.L. Weiher, Phys. Rev. 166, 769 (1968).
Y. Toyozawa, Prog. Theor. Phys. Suppl. 12, 111 (1959).
U. Heim, and P. Wiesner, Phys. Rev. Lett. 30, 1205 (1973).
W.J. Rappel, L.F. Feiner, and M.F.H. Schuurmans, Phys. Rev. B 38, 7874 (1988).
D.L. Dexter, Theory of the Optical Properties of Imperfections in Nanometals, in Solid State Physics, vol. 6, edited by F. Seitz and D. Turnbull (Academic, New York, 1958).
E.I. Rashba, and G.E. Gurgenishvili, Fiz. Tverd. Tela 4, 1029 (1982) [Sov. Phys.-Solid State 4, 759 (1962)]
C.H. Henry, and K. Nassau, Phys. Rev. B 1, 1628 (1970).
G.W. t’ Hooft, W.A.J.A. van der Poel, L.W. Molenkamp, and C.T. Foxon, Phys. Rev. B 35, 8281 (1987).
V.M. Agranovich, and V.E. Kravtsov, Solid State Commun. 55, 85 (1985)
V.M. Agranovich, Solid State Commun. 78, 747 (1991).
The Dielectric Function of Condensed Systems, edited by L. V. Keldysh, D. A. Kirzhnitz, and A. A. Maradudin (North-Holland, Amsterdam, 1989).
G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructure (Les Editions de Physique, Paris, 1989).
M. Altarelli, Envelope-Function Approach to Electronic States in Heterostructures, in Semiconductor Superlattices and Interfaces, Proceedings of the International School of Physics “E. Fermi”, edited by A. Stella (North-Holland, Amsterdam, 1993), p. 217.
U. Ekenberg, Phys. Rev. B 40, 7714 (1989).
L.C. Andreani, and A. Pasquarello, Phys. Rev. B 42, 8928 (1990).
Lecture notes by G. Bastard, this volume.
R. Grousson, V. Voliotis, P. Lavallard, M.L. Roblin, and R. Planel, Semicond. Sci. Techn. 8, 1217 (1993).
W.T. Masselink, P.J. Pearah, J. Klem, C.K. Peng, H. Morkoç, G.D. Sanders, and Y.-C. Chang, Phys. Rev. B 32, 8027 (1985)
Y. Masumoto, M. Matsuura, S. Tarucha, and H. Okamoto, Phys. Rev. B 32, 4275(1985).
R. Dingle, Confined Carrier Quantum States in Ultrathin Semiconductor Heterostructures, in Festkörperprobleme XV, edited by H. J. Queisser (Vieweg, Braunschweig, 1975), p. 21.
S. Frisk, J.-L. Staehli, L. C. Andreani, A. Bosacchi, and S. Franchi, in Ref. [89], p. 183
B. Rotelli, C. Arena, L. Tarricone, and C. Rigo, in Ref. [90], p. 315.
M. Shinada, and S. Sugano, J. Phys. Soc. Jpn. 21, 1936 (1966).
K.S. Chan, J. Phys. C, 20, 791 (1987).
M. Gurioli, J. Martinez-Pastor, M. Colocci, A. Bosacchi, S. Franchi, and L.C. Andreani, Phys. Rev. B 47, 15755 (1993).
P. Lefebvre, Ph. Christol, and H. Mathieu, in Ref. [90], p. 377
P. Lefebvre, Phys. Rev. B 48, 17308 (1993).
C. Weisbuch, and B. Vinter, Quantum Semiconductor Structures (Academic Press, 1991).
Lecture notes by J.-Y. Duboz, this volume.
L.C. West, and S.J. Eglash, Appl. Phys. Lett. 46, 1156 (1985).
J. Khurgin, Appl. Phys. Lett. 62, 1390 (1993).
P. Von Allmen, PhD Thesis, Ecole Polytechnique Fédérale, Lausanne, 1992 (unpublished).
Y.-C. Chang, and R.B. James, Phys. Rev. B 39, 12672 (1989).
See e.g. Optics of Excitons in Confined Systems, edited by A. D’Andrea, R. Del Sole, R. Girlanda, and A. Quattropani (Institute of Physics, 1992).
J. de Phys. IV, vol. 3, Coll. C5, 1993 (Suppl. JP II, no. 10), Proceedings of the Third International Conference on Optics of Excitons in Confined Systems, Montpellier, 1993.
K. Cho, and M. Kawata, J. Phys. Soc. Jpn. 54, 4431 (1985).
A. D’Andrea, and R. Del Sole, Phys. Rev. B 41, 1413 (1990).
R.C. Miller, D.A. Kleinman, W.T. Tsang, and A.C. Gossard, Phys. Rev. B 24, 1134 (1981).
G. Bastard, E.E. Mendez, L.L. Chang, and E. Esaki, Phys. Rev. B 26, 1974 (1982).
R.L. Greene, K.K. Bajaj, and D.E. Phelps, Phys. Rev. B 29, 1807 (1984).
L.C. Andreani, A. D’Andrea, and R. Del Sole, Phys. Lett. A 168, 451 (1992).
P. Lefebvre, P. Christol, and H. Mathieu, Phys. Rev. B 46, 13 603 (1992) and references therein.
M. Kumagai, and T. Takagahara, Phys. Rev. B 40, 12359 (1991).
Y. Merle d’Aubigné, H. Mariette, N. Magnea, H. Tuffigo, R.T. Cox, G. Lentz, Le Si Dang, J.-L. Pautrat, and A. Wasiela, J. Cryst. Growth 101, 650 (1990).
G.E. W. Bauer, and T. Ando, Phys. Rev. B 38, 6015 (1988).
L.C. Andreani, F. Bassani, and A. Pasquarello, in Symmetry in Nature, Quaderni della Scuola Normale Superiore (Pisa, 1989), p. 19.
R. Cingolani, and K. Ploog, Adv. Phys. 40, 535 (1991).
S. Jorda, U. Rössler, and D. Broido, in Ref. [89], p. 49.
B.S. Wang, and J.L. Birman, Phys. Rev. B 43, 12 458 (1991).
M. Berz, L.C. Andreani, E.F. Steigmeier, and F.K. Reinhart, Solid State Commun. 80, 553 (1991).
D. Fröhlich, P. Köhler, E. Meneses-Pacheco, G. Khitrova, and G. Weimann, in Ref. [89], p. 33.
M. Nakayama, Solid State Commun. 55, 1053 (1985)
M. Nakayama, and M. Matsuura, Surf. Sci. 170, 641 (1986).
V.M. Agranovich, and O.A. Dubovskii, JETP Lett. 3, 223 (1966).
V.M. Agranovich, and S. Mukamel, Phys. Lett. A 147, 155 (1990) and references therein.
R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
K. Cho, J. Phys. Soc. Jpn. 55, 4113 (1986).
H. Ishihara, and K. Cho, Phys. Rev. B 41, 1424 (1990).
T. Mita, and N. Nagasawa, Solid State Commun. 44, 1003 (1982).
Y. Chen, F. Bassani, J. Massies, C. Deparis, and G. Neu, Europhys. Lett. 14, 483 (1991).
H. Tuffigo, R.T. Cox, N. Magnea, Y. Merle d’Aubigné, and A. Million, Phys. Rev. 37, 4310 (1988)
H. Tuffigo, PhD Thesis, Université J. Fourier-Grenoble I, 1990 (unpublished).
J. Kusano, Y. Segawa, M. Mihara, Y. Aoyagi, and S. Namba, Solid State Commun. 72, 215 (1989).
A. Tredicucci, Y. Chen, F. Bassani, J. Massies, C. Deparis, and G. Neu, Phys. Rev. B 47, 10348 (1993).
R.N. Philp, and D.R. Tilley, Phys. Rev. B 44, 8170 (1991).
F. Tassone, F. Bassani, and L.C. Andreani, Nuovo Cimento D 12, 1673 (1990).
S. Jorda, U. Rössler, and D. Broido, Phys. Rev. B 48, 1669 (1993).
M. Kohl, D. Heitmann, P. Grambow, and K. Ploog, Phys. Rev. B 37, 10927 (1988); 42, 2941 (1990).
K. Ogawa, T. Katsuyama, and H. Nakamura, Phys. Rev. Lett. 64, 796 (1990).
L.C. Andreani, F. Tassone, and F. Bassani, Solid State Commun. 77, 641 (1991).
E.L. Ivchenko, Fiz. Tverd. Tela 33, 2388 (1991) [Sov. Phys. Solid State 33, 1344 (1991)].
F. Tassone, F. Bassani, and L.C. Andreani, Phys. Rev. B 45, 6023 (1992).
E.L. Ivchenko, and A.V. Kavokin, Fiz. Tverd. Tela 34, 1815 (1992) [Sov. Phys. Solid State 34, 968 (1992)].
R.H. Dicke, Phys. Rev. 93, 99 (1954).
Ya. Aaviksoo, Ya. Lippmaa, and T. Reinot, Opt. Spectrosc. (USSR) 62, 419 (1987).
A. Sumi, J. Phys. Soc. Jpn. 50, 2985 (1981).
J. Knoester, Phys. Rev. Lett. 68, 654 (1992).
E. Hanamura, Phys. Rev. B 38, 1228 (1988).
D.S. Citrin, Solid State Commun. 84, 281 (1992)
D.S. Citrin, Phys. Rev. B 47, 3832 (1993).
B. Deveaud, F. Clérot, N. Roy, K. Satzke, B. Sermage, and D.S. Katzer, Phys. Rev. Lett. 67, 2355 (1991).
B. Sermage, B. Deveaud, K. Satzke, F. Clérot, C. Dumas, N. Roy, D.S. Katzer, F. Mollot, R. Planel, M. Berz, and J.L. Oudar, Superl. Microstr. 13, 271 (1993).
J. Hegarty, L. Goldner, and M.D. Sturge, Phys. Rev. B 30, 7346 (1984).
See also lecture notes by D. S. Citrin, this volume.
M. Colocci, M. Gurioli, and J. Martinez-Pastor, in Ref. [90], p. 3.
J. Feldmann, G. Peter, E.O. Göbel, P. Dawson, K. Moore, C. Foxon, and R.J. Elliott, Phys. Rev. Lett. 59, 2337 (1987).
J. Martinez-Pastor, A. Vinattieri, L. Carraresi, M. Colocci, Ph. Roussignol, and G. Weimann, Phys. Rev. B 47, 10456(1993).
R. Eccleston, B.F. Feuerbacher, J. Kuhl, W.W. Rühle, and K. Ploog, Phys. Rev. B 45, 11403 (1992).
F.C. Spano, J.R. Kuklinski, and S. Mukamel, Phys. Rev. Lett. 65, 211 (1990).
D.S. Citrin, Phys. Rev. Lett. 69, 3393 (1992).
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Claudio Andreani, L. (1995). Optical Transitions, Excitons, and Polaritons in Bulk and Low-Dimensional Semiconductor Structures. 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_3
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