Abstract
Through this book, the reader meets many different examples of ‘low dimensional systems’, where the reduced dimensionality arises from spatial confinement —along one or more directions— of different elementary excitations. One is then interested in knowing the effects of confinement on their energy spectrum, and also on their interaction with other excitations and with external electromagnetic fields.
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References
B. Jusserand and M. Cardona, Raman spectroscopy of vibrations in superlattices, in: “Light Scattering in Solids V”, edited by M. Cardona and G. Güntherodt, Springer, Berlin (1989), p. 49. A general review, with emphasis on light scattering experiments.
B. Jusserand and D. Paquet, Confined and propagative vibrations in superlattices, in: “Semiconductor Heterojunctions and Superlattices”, edited by G. Allan et al., Springer, Berlin (1986), p. 108. The focus is on analogies between lattice-dynamical and electronic properties of superlattices in terms of simple models.
J. Menéndez, Phonons in GaAs/Al x Ga 1™x As superlattices, J. Luminesc. 44, 285 (1989). A broad review of theoretical and experimental results, with emphasis on optical modes (including anisotropy related to macroscopic fields) and resonant Raman experiments.
S. Baroni, P. Pavone, P. Giannozzi, S. de Gironcoli, and E. Molinari, Ab initio calculation of phonon spectra in semiconductors: from pure crystals to alloys and superlattices, in “Proc. of the International School of Physics ‘Enrico Fermi’, Course CXVII”, edited by A. Stella and L. Miglio, North-Holland, Amsterdam (1993), p. 243. An introductory explanation of modern theoretical approaches to the vibrational properties of AlGaAs alloys and superlattices. Disorder effects on the phonon spectra are also discussed.
J.A. Kash and J.C. Tsang, Light scattering and other secondary emission studies of dynamic processes in semiconductors, in: “Light Scattering in Solids VI”, edited by M. Cardona and G. Güntherodt, Springer, Berlin (1993), p. 423. Specific sections review time-resolved spectroscopies as probes of the dynamics of non-equilibrium phonon populations. Electron-phonon and phonon-phonon interaction mechanisms are discussed for bulk semiconductors as well as low-dimensional structures.
References
G. E. Stillman and C.M. Wolfe, Electrical characterization of epitaxial layers, Thin Solid Films 31, 69 (1976).
L. Pfeiffer, K.W. West, H.L. Stormer, and K.W. Baldwin, Electron mobilities exceeding 107 cm2/V s in modulation-doped GaAs, Appl. Phys. Lett. 55, 1888 (1989).
See e.g. C. Weisbuch and B. Vinter, “Quantum Semiconductor Structures. Fundamentals and Applications”, Academic Press (1991), Chapter 4.
The use of complex band dispersions is a standard approach since the early studies of surface problems: see e.g. T.E. Feuchtwang, Dynamics of a semi-infinite crystal lattice in a quasiharmonic approximation. II. The normal-mode analysis of a semiinfinite crystal, Phys. Rev. 155, 731 (1967).
See also: N.W. Ashcroft and N.D. Mermin, “Solid State Physics”, Saunders College (1981), p. 368.
P. Giannozzi, S. de Gironcoli, P. Pavone, and S. Baroni, Ab initio calculation of phonon dispersions in semiconductors, Phys. Rev. B43, 7231 (1991).
See e. g.: P. Brüesch, “Phonons: Theory and Experiments II. Experiments and Interpretation of Experimental Results”, Springer, Berlin (1986), and references therein.
See e.g.: P. Brüesch, “Phonons: Theory and Experiments I. Lattice Dynamics and Models of Interatomic Forces”, Springer, Berlin (1986), and references therein.
A. Fasolino, E. Molinari, and K. Kunc, Planar force constant method for lattice dynamics of superstructures, Phys. Rev. B41, 8302 (1990).
K. Kunc, Recent results in semiconductor dynamics by ab initio ‘direct’ approach, in: “Electronic Structure, Dynamics and Quantum Structural Properties of Condensed Matter”, edited by J.T. Devreese and P.E. van Camp, Plenum, New York (1985), p. 221.
See e.g.: C. Colvard, T.A. Gant, M.V. Klein, R. Merlin, R. Fischer, H. Morkoc, and A.C. Gossard, Folded acoustic and quantized optical phonons in (GaAl)As superlattices, Phys. Rev. B31, 2080 (1985).
E. Molinari, S. Baroni, P. Giannozzi, and S. de Gironcoli, Phonon spectra of ultrathin GaAs/AlAs superlattices, in “Light Scattering in Semiconductor Structures and Superlattices”, edited by D.J. Lockwood and J.F. Young, Plenum Press, New York (1991), p. 39.
M. Born and K. Huang, “Dynamical Theory of Crystal Lattices”, Oxford University Press, Oxford (1954).
See also: N.W. Ashcroft and N.D. Mermin, “Solid State Physics”, Saunders College (1981), p. 547 ff.
See e.g. chapter 11.4 in: H. Ibach and H. Lüth, “Solid State Physics”, Springer, Berlin (1981).
See e. g. E. Burstein, A. Hartstein, J. Schönwald, A.A. Maradudin, D.L. Mills, and R.F. Wallis, Surface polaritons. Electromagnetic waves at interfaces, in “Polaritons”, edited by E. Burstein and F. de Martini, Pergamon Press, New York (1974), p. 89.
W. Cochran and R.A. Cowley, J. Chem. Phys. Solids 23, 447 (1962).
S. de Gironcoli, and S. Baroni, Effects of disorder on the vibrational properties of SiGe alloys: Failure of mean field approximations, Phys. Rev. Lett. 69, 1959 (1992)
S. de Gironcoli, and S. Baroni, Effects of local atomic coordination on the vibrational properties of SiGe alloys, in “Proc. XXI International Conference on the Physics of Semiconductors, Beijing, China”, edited by Ping Jiang and Hou-Zhi Zheng, World Scientific, Singapore (1992), p. 109.
S. Baroni, S. de Gironcoli, and P. Giannozzi, Phonon dispersions in Ga x Al l™x As alloys, Phys. Rev. Lett. 65, 84 (1990).
see e.g. “Optical Properties of Mixed Crystals”, edited by R.J. Elliot and I.P. Ipatova, North-Holland, Amsterdam (1988), p. 35; in particular the article by D.W. Taylor.
N. Meskini and K. Kunc, Interpolation, extrapolation, and scaling laws in lattice dynamics of isoelectronic compounds, Technical Report n. 5, Université P. et M. Curie, Paris (1978), unpublished.
R. Schorer, G. Abstreiter, S. de Gironcoli, E. Molinari, H. Kibbel, and H. Presting, Inplane Raman scattering of(001)-Si/Ge superlattices: Theory and experiments, Phys. Rev. B49, 5406 (1994).
J.A. Kash, J.M. Hvam, J.C. Tsang, and T.F. Kuech, Localization and wave-vector conservation for optical phonons in Al x Ga l™x As and thin layers of GaAs, Phys. Rev. B38, 5776 (1988).
B. Jusserand, D. Paquet, and F. Mollot, Dispersive character of optical phonons in GaAlAs alloys from Raman scattering in superlattices, Phys. Rev. Lett. 63, 2397 (1989).
B. Jusserand, F. Mollot, L. Quagliano, G. Le Roux, and R. Planel, Damping of optical phonons in Ga l™x Al x As alloys, Phys. Rev. Lett. 67, 2803 (1991).
see e.g. G.C. Osbourn, Strained-layer superlattices: a brief review, IEEE J. Quantum Electron. QE-22, 1677 (1986).
E. Anastassakis, A. Pinczuk, E. Burstein, F.H. Pollak, and M. Cardona, Effect of static uniaxial stress on the Raman spectrum of silicon, Solid State Commun. 8, 133 (1970).
F. Cerdeira, C.J. Buchenauer, F.H. Pollak, and M. Cardona, Stress-induced shifts of first-order Raman frequencies of diamond-and zinc-blende-type semiconductors, Phys. Rev. B5, 580 (1972).
see e.g. E.M. Anastassakis, Morphic effects in lattice dynamics, in: “Dynamical Properties of Solids, vol. 4”, edited by G.K. Horton and A.A. Maradudin, North-Holland, Amsterdam (1980), p. 157.
A. Qteish and E. Molinari, Interplanar forces and phonon spectra of strained Si and Ge: Ab initio calculations and applications to Si/Ge superlattices, Phys. Rev. B42, 7090 (1990).
S. de Gironcoli, Phonons in Si-Ge systems: An ab-initio interatomic-force-constant approach, Phys. Rev. B46, 8962 (1992).
P.A. Knipp and T.L. Reinecke, Coupling of electrons to interface phonons in semiconductors quantum wells, Phys. Rev. B48, 12338 (1993).
Hanyou Chu and Yia-Chung Chang, Phonon-polariton modes in superlattices: The effect of spatial dispersion, Phys. Rev. B38, 12369 (1988).
E. Molinari and A. Fasolino, Calculated phonon spectra of Si/Ge (001) superlattices: Features for interface characterization, Appl. Phys. Lett. 54, 1220 (1989).
G. Scamarcio, V. Spagnolo, E. Molinari, L. Tapfer, L. Sorba, G. Bratina, and A. Franciosi, Phonons in Si/GaAs superlattices, Phys. Rev. B46, 7296 (1992).
A. Fasolino, E. Molinari, and J.C. Maan, Resonant quasiconfined optical phonons in semiconductor superlattices, Phys. Rev. B39, 3923 (1989).
A. Fasolino, E Molinari, and J.C. Maan, Calculated superlattice and interface phonons of InAs/GaSb superlattices, Phys. Rev. B33, 8889 (1986).
A. Pinczuk and E Burstein, Fundamentals of inelastic light scattering in semiconductors and insulators, in: “Light Scattering in Solids”, edited by M. Cardona, Springer, Berlin (1975), p. 23.
B. Jusserand, D. Paquet, J. Kervarec, and A. Regreny, Raman scattering study of acoustical and optical folded modes in GaAslGaAlAs superlattices, Journal de Physique (Colloque) 4, C5–145 (1984).
E Molinari, S. Baroni, P. Giannozzi, and S. de Gironcoli, Effects of disorder on the Raman spectra of GaAs/AlAs superlattices, Phys. Rev. B45, 4280 (1992).
D.J. Mowbray, M. Cardona, and K. Ploog, Confined LO phonons in GaAs/AlAs superlattices, Phys. Rev. B43, 1598 (1991).
E Merzbacher, “Quantum Mechanics”, Wiley, New York (1961), p. 107.
See e.g. C. Weisbuch and B. Vinter, “Quantum Semiconductor Structures. Fundamentals and Applications”, Academic Press (1991), Chapter 4, pp. 37 ff.
G. Bastard, “Wave Mechanics Applied to Semiconductor Heterostructures”, Les Editions de 1a Physique, Les Ulis (1990).
R. Schorer, G. Abstreiter, S. de Gironcoli, E Molinari, H. Kibbel, and E Kasper, Vibrational properties of Si/Ge superlattices: Theory and in-plane Raman scattering experiments, Solid State Electronics 37, 757 (1994).
B.V. Shanabrook, B.R. Bennet, and R.J. Wagner, Planar vibrational modes in superlattices, Phys. Rev. B48, 17172 (1993).
see e.g. D.W. Taylor, Dynamics of impurities in crystals, in: “Dynamical Properties of Solids, vol. 2”, edited by G.K. Horton and A.A. Maradudin, North-Holland, Amsterdam (1975), p. 287.
E Molinari and A. Fasolino, Phonons of ideal (001) superlattices: Application to Si/Ge, in: “Spectroscopy of Semiconductor Microstructures”, edited by G. Fasol, A. Fasolino, and P. Lugli, Plenum, New York (1989), p. 195.
S. de Gironcoli, E. Molinari, R. Schorer, and G. Abstreiter, Interface mode in Si/Ge superlattices: Theory and experiments, Phys. Rev. B48, 8959 (1993).
H. Rücker, E. Molinari, and P. Lugli, Microscopic calculation of the electron-phonon interaction in quantum wells, Phys. Rev. B45, 6747 (1992).
E Molinari, C. Bungaro, F. Rossi, L. Rota, and P. Lugli, Phonons in GaAs/AlAs nanostructures: from two-dimensional to one-dimensional systems, in “Phonons in Semiconductor Nanostructures”, edited by J.P. Leburton, J. Pascual, and C. Sotomayor Torres, NATO ASI Series E: Applied Sciences — Vol. 236, Kluwer, Dordrecht (1993).
A.K. Sood, J. Menéndez, M. Cardona, and K. Ploog, Resonance Raman scattering by confined LO and TO phonons in GaAs-AlAs superlattices, Phys. Rev. Lett. 54, 2111 (1985)
A.K. Sood, J. Menéndez, M. Cardona, and K. Ploog, Interface vibrational modes in GaAs-AlAs superlattices, Phys. Rev. Lett. 54, 2115 (1985).
G. Scamarcio, M. Haines, G. Abstreiter, E. Molinari, S. Baroni, A. Fischer, and K. Ploog, Micro-Raman scattering in ultrathin-layer superlattices: Evidence of zone-center anisotropy of optical phonons, Phys. Rev. B47, 1483 (1993).
for a recent collection of papers on the subject see: “Phonons in Semiconductor Nanostructures”, edited by J.P. Leburton, J. Pascual, and C. Sotomayor Torres, NATO ASI Series E: Applied Sciences — Vol. 236, Kluwer, Dordrecht (1993).
V. Narayanamurti, H.L. Störnier, M.A. Chin, A.C. Gossard, and W. Wiegmann, Selective transmission of high frequency phonons by a superlattice: The “dielectric” phonon filter, Phys. Rev. Lett. 43, 2012 (1979). Note that the analogy with optical filters was very clear already in this letter. The denomination ‘dielectric phonon filter’ was chosen ‘because of the close analogy with optical dielectric filters’.
M.S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Acoustic band structure of periodic elastic composites, Phys. Rev. Lett. 71, 2022 (1993).
B.A. Auld, “Acoustic Fields and Waves in Solids”, Wiley, New York (1973).
E. Yablonovich, Photonic bandagaps and semiconductor quantum electronics, this volume.
For cylindrical wires see e.g. P.E. Selbmann and R. Enderlein, Scattering of carriers from confined and interface phonons of a quantum wire, Superlatt. and Microstr. 12, 219 (1992).
P.A. Knipp and T.L. Reinecke, Electron-phonon scattering rates in quantum wires, Phys. Rev. B48, 5700 (1993).
R. Englman and R. Ruppin, Optical lattice vibration infinite ionic crystals, J. Phys. C 1, 614 (1968).
see e.g. P.A. Knipp and T.L. Reinecke, Classical interface modes of quantum dots, Phys. Rev. B46, 10310 (1992), and references therein.
P. Vogl, The electron-phonon interaction in semiconductors, in “Physics of Nonlinear Transport in Semiconductors”, edited by D.K. Ferry, J.R. Barker, and C. Jacoboni, Plenum, New York (1980), and references therein.
B.K. Ridley, “Quantum Processes in Semiconductors”, Clarendon, Oxford (1988).
See, e.g., J. Shah, Hot carriers in quasi-2D polar semiconductors, IEEE J. Quantum Electron. QE-22, 1728 (1986).
L. Rota, F. Rossi, P. Lugli, E. Molinari, S.M. Goodnick, and W. Porod, Monte Carlo simulation of a ‘true’ quantum wire, in “Advanced semiconductor epitaxial growth processes and lateral and vertical fabrication”, edited by R.J. Malik et al., SPIE Vol. 1676 (1992), p. 161.
U. Bockelmann and G. Bastard, Phonon scattering and energy relaxation in two-, one-and zero-dimensional electron gases, Phys. Rev. B42, 8947 (1990).
N. Mori and T. Ando, Electron—optical-phonon interaction in single and double heterostructures, Phys. Rev. B40, 6175 (1989).
L.F. Register, Microscopic basis for a sum rule for polar-optical-phonon scattering of carriers in heterostructures, Phys. Rev. B45, 8756 (1992).
K. Huang and B. Zhu, Dielectric continuum model and Frölich interaction in superlattices, Phys. Rev. B38, 13377 (1988).
J. Shah, A. Pinczuk, A.C. Gossard, and W. Wiegmann, Energy-loss rates for hot electrons and holes in GaAs quantum wells, Phys. Rev. Lett. 54, 2045 (1985).
K. Leo, W.W. Rühle, and K. Ploog, Hot-carrier energy-loss rates in GaAs/Al x Ga l™x As quantum wells, Phys. Rev. B38, 1947 (1988).
J.F. Ryan and M. Tatham, Picosecond optical studies of 2D-electron 2D-phonon dynamics, Solid State Electron. 32, 1429 (1989), and references therein.
R. Cingolani, H. Lage, L. Tapfer, H. Kalt, D. Heitmann, and K. Ploog, Quantum confined one-dimensional electron-hole plasma in semiconductor quantum-wires, Phys. Rev. Lett. 67, 891 (1991).
M. Oestreich, W.W. Rüble, H. Lage, D. Heitmann, and K. Ploog, Reduced excitonexciton scattering in quantum wires, Phys. Rev. Lett. 70, 1682 (1993).
G. Mayer, F.E. Prins, G. Lehr, H. Schweizer, H. Leier, B.E. Maile, J. Straka, A. Forchel, and G. Weimann, Carrier relaxation in intermixed GaAs/AlGaAs quantum wires, Phys. Rev. Lett. B47, 4060 (1993).
U. Bockelmann, Inelastic scattering and thermalization in low dimensional III-V semiconductor structures, this volume.
H. Benisty, C.M. Sotomayor Torres, and C. Weisbuch, Intrinsic mechanism for the poor luminescence properties of quantum box systems, Phys. Rev. B44, 10945 (1991).
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Molinari, E. (1995). Phonons and Electron-Phonon Interaction in Low-Dimensional 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_5
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