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.
Karl W. Böer: deceased.
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Notes
- 1.
This follows from \( P{\int}_{-\infty}^{\infty}\frac{f(x)}{x-a} dx=P{\int}_0^{\infty}\frac{x\left(f(x)-f\left(-x\right)\right)+a\left(f(x)+f\left(-x\right)\right)}{x^2-{a}^2}\, dx. \)
- 2.
Such an 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.
Sometimes the effective atomic weight is used, related to the mass MH of the hydrogen atom:
$$ {M}_{\mathrm{r}}^{\ast }={M}_{\mathrm{r}}/{M}_{\mathrm{H}}. $$(33) - 4.
ωp has the same form as the plasma frequency for electrons (Eq. 4 in Chap. 12, “Photon–Free-Electron Interaction”), except N is the density and Mr the mass of phonons. Sometimes the definition of ωp includes an additional factor εopt in the denominator.
- 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.
- 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.
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 Chap. 4, “Elasticity and Phonons.”
- 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; for a study of this effect applying Brillouin scattering see Vacher et al. (2006).
- 10.
Strain coefficients for c-Si are reported by Anastassakis et al. (1990).
- 11.
Generally, the strain coefficient is a rank-2 tensor like \( \underline {\boldsymbol{\upvarepsilon}} \). For an isotropic solid such as α-Si:H, only diagonal components exist due to symmetry. Since the TO phonon band of α-Si:H transforms as a scalar rather than a vector as for c-Si, only a single value s remains and the trace of the strain tensor yields the total acting strain.
References
Abstreiter G (1986) Light scattering in novel layered semiconductor structures. In: Grosse P (ed) Festkörperprobleme/Adv Solid State Phys 26:41
Abstreiter G, Merlin R, Pinczuk A (1986) Inelastic light scattering by electronic excitations in semiconductor heterostructures. IEEE J Quantum Electron 22:1771
Anastassakis E, Cantarero A, Cardona M (1990) Piezo-Raman measurements and anharmonic parameters in silicon and diamond. Phys Rev B 41:7529
Baldi G, Giordano VM, Monaco G, Ruta B, (2010) Sound attenuation at terahertz frequencies and the boson peak of vitreous silica. Phys Rev Lett 104:195501
Baldi G, Giordano VM, Ruta B, Monaco G (2016) On the nontrivial wave-vector dependence of the elastic modulus of glasses. Phys Rev B 93:144204
Balkanski M (ed) (1980) Handbook of semiconductors, vol 2. North-Holland, Amsterdam
Balkanski M, Lallemand P (1973) Photonics. Gauthiers-Villard, Paris
Bannov N, Aristov V, Mitin V, Stroscio MA (1995) Electron relaxation times due to the deformation-potential interaction of electrons with confined acoustic phonons in a free-standing quantum well. Phys Rev B 51:9930
Barker AS Jr, Sievers AJ (1975) Optical studies of the vibrational properties of disordered solids. Rev Mod Phys 47(Suppl 2):S1
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
Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford University Press, London
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)
Broser I, Rosenzweig M (1980) Magneto-Brillouin scattering of polaritons in CdS. Solid State Commun 36:1027
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
Callen HB (1949) Electric breakdown in ionic crystals. Phys Rev 76:1394
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
Carles RN, Saint-Cricq N, Renucci MA, Bennucci BJ (1978) In: Balkanski M (ed) Lattice dynamics. Flammarion, Paris, p 195
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
Chang IF, Mitra SS (1971) Long wavelength optical phonons in mixed crystals. Adv Phys 20:359
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
Chiao RY, Townes CH, Stiocheff BP (1964) Stimulated Brillouin scattering and coherent generation of intense hypersonic waves. Phys Rev Lett 12:592
Cochran W (1973) The dynamics of atoms in crystals. Edward Arnold, London
Conwell EM (1967) High-field transport in semiconductors. Academic Press, New York
Dong CH, Shen Z, Zou CL, Zhang YL, Fu W, Guo G-C (2015) Brillouin-scattering-induced transparency and non-reciprocal light storage. Nature Commun 6:6193
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
Fornari B, Pagannone M (1978) Experimental observation of the upper polariton branch in isotropic crystals. Phys Rev B 17:3047
Freeman R, Lemasters R, Kalejaiye T, Wang F, Chen G, Ding J, Wu M, Demidov VE, Demokritov SO, Harutyunyan H, Urazhdin S (2020) Brillouin light scattering of spin waves inaccessible with free-space light. Phys Rev Research 2:033427
Galeener FL, Lucovsky G, Geils RH (1979) Raman and infrared spectra of vitreous As2O3. Phys Rev B 19:4251
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
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
Gillet Y, Kontur S, Giantomassi M, Draxl C, Gonze X (2017) Ab initio approach to second-order resonant Raman scattering including exciton-phonon interaction. Sci Rep 7:7344
Gutman F (1948) The electret. Rev Mod Phys 20:457
Hamaguchi C, Adachi S, Itoh Y (1978) Resonant Brillouin scattering phenomena in some II–VI compounds. Solid State Electron 21:1585
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
Hass M (1967) Lattice reflection. In: Willardson RK, Beer AC (eds) Semiconductors and semimetals, vol 3. Academic Press, New York, p 3
Hayes W, Loudon R (1978) Scattering of light by crystals. Wiley, New York
Henry CH, Hopfield JJ (1965) Raman scattering by polaritons. Phys Rev Lett 15:964
Jackson JD (1999) Classical electrodynamis, 2nd edn. Wiley, New York
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
Jonscher AK (1983) Dielectric relaxation in solids. Chelsea Dielectric Press, London
Jones RR, Hooper DC, Zhang L, Wolverson D, Valev VK (2019) Raman techniques: Fundamentals and frontiers. Nanoscale Res Lett 14:231
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
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
Jusserand B, Poddubny AN, Poshakinskiy AV, Fainstein A, Lemaitre A (2015) Polariton resonances for ultrastrong coupling cavity optomechanics in GaAs/AlAs multiple quantum wells. Phys Rev Lett 115:267402
Kargar F, Debnath B, Joona-Pekko K, Säynätjoki A, Lipsanen H, Nika DL, Lake RK, Balandin AA (2016) Direct observation of confined acoustic phonon polarization branches in freestanding semiconductor nanowires. Nature Commun 7:13400
Kramers HA (1929) Die Dispersion und Absorption von Röntgenstrahlen. Phys Z 30:522 (The dispersion and absorption of X-rays, in German)
Kronig R d L (1926) On the theory of dispersion of X-rays. J Opt Soc Am 12:547
Kontos AG, Anastassakis E, Chrysanthakopoulos N, Calamiotou M, Pohl UW (1999) Strain profiles in overcritical (001) ZnSe/GaAs heteroepitaxial layers. J Appl Phys 86:412
Lifshits E, Pitaevski LP, Landau LD (1985) Electrodynamics of continuous media. Elsevier, Amsterdam
Lines ME, Glass AM (1979) Principles and applications of ferroelectrics and related materials. Oxford University Press, London
Loudon R (1964) The Raman effect in crystals. Adv Phys 13:423
Lyddane RH, Sachs RG, Teller E (1959) On the polar vibrations of alkali halides. Phys Rev 59:673
Martin RM, Damen TC (1971) Breakdown of selection rules in resonance Raman scattering. Phys Rev Lett 26:86
Merklein M, Stiller B, Eggleton BJ (2018) Brillouin-based light storage and delay techniques. J Opt 20:083003
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
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
Pandey RN, Sharma TP, Dayal B (1977) Electronic polarisabilities of ions in group III-V crystals. J Phys Chem Solids 38:329
Pant R, Byrnes A, Poulton CG, Li E, Choi DY, Madden S, Luther-Davies B, Eggleton BJ (2012) Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering. Opt Lett 37:969
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
Pine AS (1972) Resonance Brillouin scattering in cadmium sulfide. Phys Rev B 5:3003
Pine AS (1983) Brillouin scattering in semiconductors. In: Cardona M (ed) Light scattering in solids I. Springer, Berlin, pp 253–273
Pokatilov E P, Nika DL, Askerov AS, Balandin AA (2007) Size-quantized oscillations of the electron mobility limited by the optical and confined acoustic phonons in the nanoscale heterostructures. J Appl Phys 102:54304
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)
Poulet H, Mathieu JP (1970) Spectres des Vibration et Symétrie des Cristeaux. Gordon & Breach, London (Vibration spectra and symmetry of crystals, in French)
Ruf T (1998) Phonon scattering in semiconductors, quantum wells and superlattices. Springer, Berlin
Rytov SM (1956) Electromagnetic properties of a finely stratified medium. Sov Phys -JETP 2:466
Santos AM, Alves HWL, Ataide CA, Guilhon I, Marques M, Teles LK (2019) Rigorous statistical thermodynamical model for lattice dynamics in alloys. Phys Rev B 100:144205
Shanker J, Agrawal GG, Dutt N (1986) Electronic polarizabilities and photoelastic behaviour of ionic crystals. Phys Status Solidi B 138:9
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
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
Spitzer WG, Fan HY (1957) Determination of optical constants and carrier effective mass of semiconductors. Phys Rev 106:882
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
Strubbe DA, Johlin EC, Kirkpatrick TR, Buonassisi T, Grossman JC (2015) Stress effects on the Raman spectrum of an amorphous material: Theory and experiment on α-Si:H. Phys Rev B 92:241202
Szigeti B (1949) Polarizability and dielectric constant of ionic crystals. Trans Faraday Soc 45:155
Ulbrich RG, Weisbuch C (1978) Resonant Brillouin scattering in semiconductors. In: Treusch J (ed) Festkörperprobleme/Adv Solid State Phys 18:217. Vieweg, Braunschweig
Vacher R, Ayrinhac S, Foret M, Rufflé B, Courtens E (2006) Finite size effects in Brillouin scattering from silica glass. Phys Rev B 74:012203
Weinstein BA, Cardona M (1973) Resonant first- and second-order Raman scattering in GaP. Phys Rev B 8:2795
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
Wynne JJ (1974) Spectroscopy of third-order optical nonlinear susceptibilities I. Comments Solid State Phys 6:31
Yu PY (1979) Resonant Brillouin scattering of exciton polaritons. Comments Solid State Phys 9:37
Yu PY, Cardona M (1999) Fundamentals of semiconductors: physics and materials properties, 2nd edn. Springer, Berlin
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Böer, K.W., Pohl, U.W. (2023). Photon–Phonon Interaction. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-18286-0_11
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