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Photon–Phonon Interaction

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Semiconductor Physics

Abstract

The interaction of photons with solids comprises ionic and electronic oscillations; this chapter focuses on lattice vibrations. The dielectric polarization is related to the atomic polarizability. The dynamic response of the dielectric function on electromagnetic radiation can be described classically by elementary oscillators, yielding strong interaction of photons and TO phonons with a resulting large Reststrahl absorption in the IR range. The dispersion is described by a phonon-polariton, which is observed in inelastic scattering processes. Brillouin scattering at acoustic phonons and Raman scattering at optical phonons provide direct information about the spectrum and symmetry of vibrations in a semiconductor.

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Notes

  1. 1.

    This follows from \( P{\int}_{-\infty}^{\infty}\frac{f(x)}{x-a} dx=P{\int}_0^{\infty}\frac{x\left(f(x)-f\left(-x\right)\right)+a\left(f(x)+f\left(-x\right)\right)}{x^2-{a}^2}.5em dx. \)

  2. 2.

    Such interdependence can be visualized by considering a row of coupled pendula and forcing one of them to oscillate according to a given driving force. All other pendula will influence the motion, the more so, the closer the forced oscillation is to the resonance frequency of the others.

  3. 3.

    Sometimes the effective atomic weight is used, related to the mass M H of the hydrogen atom:

    $$ {M}_{\mathrm{r}}^{\ast }=1/{M}_{\mathrm{r}}+1/{M}_{\mathrm{H}}. $$
    (33)
  4. 4.

    ω p has the same form as the plasma frequency for electrons (Eq. 4 in chapter “Photon–Free-Electron Interaction”), except N is the density and M r the mass of phonons. Sometimes the definition of ω p includes an additional factor ε opt in the denominator.

  5. 5.

    Rayleigh scattering is a well-known effect in media with large density fluctuations, such as gasses. The elastic scattering proceeds without changes in frequency of the scattered photon. Rayleigh scattering is responsible for the blue light of the sky by scattering the short-wavelength component of the sunlight on density fluctuations of the earth’s atmosphere. The scattering amplitude – and consequently the absorption coefficient α – increases with decreasing wavelength: \( \alpha \propto {\left({n}_{\mathrm{r}}-1\right)}^2/\left(N {\lambda}^4\right) \), where N is the density of air molecules and λ is the wavelength. In solids, the Rayleigh component can usually be neglected, except near critical points where density fluctuations can become rather large, e.g., when electron–hole condensation starts to occur. Frozen-in density fluctuations in glasses, although very small, provide transparency limitations for fiber optics because of such Rayleigh scattering.

  6. 6.

    The scattering angle θ defined in Fig. 10 is twice the Bragg angle θ Β, which is the angle between the diffracting planes and the incident or diffracted beam.

  7. 7.

    The very small difference between the refractive indices at \( h{\nu}_{\mathrm{i}}+\hslash {\omega}_{\mathbf{q}} \) and \( h{\nu}_{\mathrm{i}}-\hslash {\omega}_{\mathbf{q}} \) is neglected in Eq. 74.

  8. 8.

    There is no such folding of the branches parallel to the superlattice layers, i.e., in in-plane directions. Thus, phonons propagating in this direction do not show the additional Raman doublets, as shown in the lower curve in Fig. 18 of chapter “Elasticity and Phonons”.

  9. 9.

    In glasses, one cannot plot Brillouin zones; there is a breakdown of q conservation, i.e., all momenta can contribute during scattering, causing substantial broadening.

References

  • Abstreiter G (1986) Light scattering in novel layered semiconductor structures. In: Grosse P (ed) Festkörperprobleme/Adv Solid State Phys 26:41

    Google Scholar 

  • Abstreiter G, Merlin R, Pinczuk A (1986) Inelastic light scattering by electronic excitations in semiconductor heterostructures. IEEE J Quantum Electron 22:1771

    Article  ADS  Google Scholar 

  • Balkanski M (ed) (1980) Handbook of semiconductors, vol 2. North-Holland, Amsterdam

    Google Scholar 

  • Balkanski M, Lallemand P (1973) Photonics. Gauthiers-Villard, Paris

    Google Scholar 

  • Barker AS Jr, Sievers AJ (1975) Optical studies of the vibrational properties of disordered solids. Rev Mod Phys 47(Suppl 2):S1

    Article  Google Scholar 

  • Birman JL (1974) Infra-Red and Raman Optical Processes of Insulating Crystals; Infra-Red and Raman Optical Processes of Insulating Crystals. Vol. 25/2b, Springer, Berlin Heidelberg

    Google Scholar 

  • Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford University Press, London

    MATH  Google Scholar 

  • Brillouin L (1922) Diffusion de la lumiere et des rayonnes X par un corps transparent homogene; influence de l’agitation thermique. Ann Phys (Leipzig) 17:88 (Diffusion of light and X-rays through transparent homogeneous bulk; influence of thermic motion, in French)

    Article  ADS  Google Scholar 

  • Broser I, Rosenzweig M (1980) Magneto-Brillouin scattering of polaritons in CdS. Solid State Commun 36:1027

    Article  ADS  Google Scholar 

  • Burstein E, Chen CY, Lundquist S (1979) Light scattering in solids. In: Birman J, Cummins HZ, Rebane KK (eds) 2nd joint USA-USSR symposium on light scattering in condensed matter. Plenum Press, New York, p 479

    Google Scholar 

  • Callen HB (1949) Electric breakdown in ionic crystals. Phys Rev 76:1394

    Article  ADS  MATH  Google Scholar 

  • Cardona M (1969) Optical constants of insulators: dispersion relations. In: Nudelman S, Mitra MM (eds) Optical properties of solids. Plenum Press, New York, pp 137–151

    Google Scholar 

  • Carles RN, Saint-Cricq N, Renucci MA, Bennucci BJ (1978) In: Balkanski M (ed) Lattice dynamics. Flammarion, Paris, p 195

    Google Scholar 

  • Chang IF, Mitra SS (1968) Application of a modified random-element-isodisplacement model to long-wavelength optic phonons of mixed crystals. Phys Rev 172:924

    Article  ADS  Google Scholar 

  • Chang IF, Mitra SS (1971) Long wavelength optical phonons in mixed crystals. Adv Phys 20:359

    Article  ADS  Google Scholar 

  • Charfi F, Zuoaghi M, Llinares C, Balkanski M, Hirlimann C, Joullie A (1977) Small wave vector modes in Al1-xGaxSb. In: Balkanski M (ed) Lattice dynamics. Flammarion, Paris, p 438

    Google Scholar 

  • Chiao RY, Townes CH, Stiocheff BP (1964) Stimulated Brillouin scattering and coherent generation of intense hypersonic waves. Phys Rev Lett 12:592

    Article  ADS  Google Scholar 

  • Cochran W (1973) The dynamics of atoms in crystals. Edward Arnold, London

    Google Scholar 

  • Conwell EM (1967) High-field transport in semiconductors. Academic Press, New York

    Google Scholar 

  • Fasolino A, Molinari E (1990) Calculations of phonon spectra in III-V and Si-Ge superlattices: a tool for structural characterization. Surf Sci 228:112

    Article  ADS  Google Scholar 

  • Fornari B, Pagannone M (1978) Experimental observation of the upper polariton branch in isotropic crystals. Phys Rev B 17:3047

    Article  ADS  Google Scholar 

  • Galeener FL, Lucovsky G, Geils RH (1979) Raman and infrared spectra of vitreous As2O3. Phys Rev B 19:4251

    Google Scholar 

  • Galeener FL, Leadbetter AJ, Stringfellow MW (1983) Comparison of the neutron, Raman, and infrared vibrational spectra of vitreous SiO2, GeO2, and BeF2. Phys Rev B 27:1052

    Article  ADS  Google Scholar 

  • Geurts J, Gnoth D, Finders J, Kohl A, Heime K (1995) Interfaces of InGaAs/InP multi quantum wells studied by Raman spectroscopy. Phys Status Solidi (a) 152:211

    Article  ADS  Google Scholar 

  • Gutman F (1948) The electret. Rev Mod Phys 20:457

    Article  ADS  Google Scholar 

  • Hamaguchi C, Adachi S, Itoh Y (1978) Resonant Brillouin scattering phenomena in some II–VI compounds. Solid State Electron 21:1585

    Article  ADS  Google Scholar 

  • Hasegawa T, Hotate K (1999) Measurement of Brillouin gain spectrum distribution along an optical fiber by direct frequency modulation of a laser diode. Proc SPIE 3860:306

    Article  ADS  Google Scholar 

  • Hass M (1967) Lattice reflection. In: Willardson RK, Beer AC (eds) Semiconductors and semimetals, vol 3. Academic Press, New York, p 3

    Google Scholar 

  • Hayes W, Loudon R (1978) Scattering of light by crystals. Wiley, New York

    Google Scholar 

  • Henry CH, Hopfield JJ (1965) Raman scattering by polaritons. Phys Rev Lett 15:964

    Article  ADS  Google Scholar 

  • Jackson JD (1999) Classical electrodynamis, 2nd edn. Wiley, New York

    Google Scholar 

  • Jahne E (1976) Long-wavelength optical phonons in mixed crystals: I. A system of two coupled modes. Phys Status Solidi B 74:275. And: Long-wavelength optical phonons in mixed crystals. II. The persistence of common gaps. Phys Status Solidi B 75:221

    Google Scholar 

  • Jonscher AK (1983) Dielectric relaxation in solids. Chelsea Dielectric Press, London

    Google Scholar 

  • Jusserand B, Paquet D, Kervarec J, Regreny A (1984) Raman scattering study of acoustical and optical folded modes in GaAs/GaAlAs superlattices. J Physique Colloq 45:145

    Google Scholar 

  • Jusserand B, Alexandre F, Paquet D, Le Roux G (1985) Raman scattering characterization of interface broadening in GaAs/ AlAs short period superlattices grown by molecular beam epitaxy. Appl Phys Lett 47:301

    Article  ADS  Google Scholar 

  • Kramers HA (1929) Die Dispersion und Absorption von Röntgenstrahlen. Phys Z 30:522 (The dispersion and absorption of X-rays, in German)

    MATH  Google Scholar 

  • Kronig R d L (1926) On the theory of dispersion of X-rays. J Opt Soc Am 12:547

    Article  ADS  Google Scholar 

  • Lifshits E, Pitaevski LP, Landau LD (1985) Electrodynamics of continuous media. Elsevier, Amsterdam

    Google Scholar 

  • Lines ME, Glass AM (1979) Principles and applications of ferroelectrics and related materials. Oxford University Press, London

    Google Scholar 

  • Loudon R (1964) The Raman effect in crystals. Adv Phys 13:423

    Article  ADS  Google Scholar 

  • Lyddane RH, Sachs RG, Teller E (1959) On the polar vibrations of alkali halides. Phys Rev 59:673

    Article  ADS  MATH  Google Scholar 

  • Martin RM, Damen TC (1971) Breakdown of selection rules in resonance Raman scattering. Phys Rev Lett 26:86

    Article  ADS  Google Scholar 

  • Mitra SS (1969) Infrared and Raman spectra due to lattice vibrations. In: Nudelman S, Mitra MM (eds) Optical properties of solids. Plenum Press, New York, pp 333–451

    Google Scholar 

  • Mitra SS (1985) Optical properties of nonmetallic solids for photon energies below the fundamental band gap. In: Palik ED (ed) Handbook of optical constants of solids. Academic Press, New York, pp 213–270

    Chapter  Google Scholar 

  • Pandey RN, Sharma TP, Dayal B (1977) Electronic polarisabilities of ions in group III-V crystals. J Phys Chem Solids 38:329

    Article  ADS  Google Scholar 

  • Pauling L (1927) The theoretical prediction of the physical properties of many-electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space. Proc Roy Soc Lond A 114:181

    Article  ADS  Google Scholar 

  • Pine AS (1972) Resonance Brillouin scattering in cadmium sulfide. Phys Rev B 5:3003

    Article  ADS  Google Scholar 

  • Pine AS (1983) Brillouin scattering in semiconductors. In: Cardona M (ed) Light scattering in solids I. Springer, Berlin, pp 253–273

    Chapter  Google Scholar 

  • Poulet H (1955) Sur certaines anomalies de l’effet Raman dans les cristaux. Ann Phys (Paris) 10:908. (On certain anomalies of the Raman effect in crystals, in French)

    ADS  Google Scholar 

  • Poulet H, Mathieu JP (1970) Spectres des Vibration et Symétrie des Cristeaux. Gordon & Breach, London (Vibration spectra and symmetry of crystals, in French)

    Google Scholar 

  • Ruf T (1998) Phonon scattering in semiconductors, quantum wells and superlattices. Springer, Berlin

    MATH  Google Scholar 

  • Rytov SM (1956) Electromagnetic properties of a finely stratified medium. Sov Phys -JETP 2:466

    MathSciNet  MATH  Google Scholar 

  • Shanker J, Agrawal GG, Dutt N (1986) Electronic polarizabilities and photoelastic behaviour of ionic crystals. Phys Status Solidi B 138:9

    Article  ADS  Google Scholar 

  • Siegle H, Kaczmarczyk G, Filippidis L, Litvinchuk AP, Hoffmann A, Thomsen C (1997) Zone-boundary phonons in hexagonal and cubic GaN. Phys Rev B 55:7000

    Article  ADS  Google Scholar 

  • Smith DY (1985) Dispersion theory, sum rules, and their application to the analysis of optical data. In: Palik ED (ed) Handbook of optical constants of solids. Academic Press, New York, pp 35–68

    Chapter  Google Scholar 

  • Spitzer WG, Fan HY (1957) Determination of optical constants and carrier effective mass of semiconductors. Phys Rev 106:882

    Article  ADS  Google Scholar 

  • Stern F (1963) Elementary theory of the optical properties of solids. In: Seitz F, Turnbull D (eds) Solid state physics, vol 15. Academic Press, New York, p 299

    Google Scholar 

  • Szigeti B (1949) Polarizability and dielectric constant of ionic crystals. Trans Faraday Soc 45:155

    Article  Google Scholar 

  • Ulbrich RG, Weisbuch C (1978) Resonant Brillouin scattering in semiconductors. In: Treusch J (ed) Festkörperprobleme/Adv Solid State Phys 18:217. Vieweg, Braunschweig

    Google Scholar 

  • Weinstein BA, Cardona M (1973) Resonant first- and second-order Raman scattering in GaP. Phys Rev B 8:2795

    Article  ADS  Google Scholar 

  • Windl W, Karch K, Pavone P, Schütt O, Strauch D (1995) Full ab initio calculation of second-order Raman spectra of semiconductors. Int J Quantum Chem 56:787

    Article  Google Scholar 

  • Wynne JJ (1974) Spectroscopy of third-order optical nonlinear susceptibilities I. Comments Solid State Phys 6:31

    Google Scholar 

  • Yu PY (1979) Resonant Brillouin scattering of exciton polaritons. Comments Solid State Phys 9:37

    Google Scholar 

  • Yu PY, Cardona M (1999) Fundamentals of semiconductors: physics and materials properties, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

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Böer, K.W., Pohl, U.W. (2018). Photon–Phonon Interaction. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-69150-3_11

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