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Photon–Phonon Interaction

Semiconductor Physics

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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. 1.

    This follows from \( P{\int}_{-\infty}^{\infty}\frac{f(x)}{x-a} dx=P{\int}_0^{\infty}\frac{x\left(f(x)-f\left(-x\right)\right)+a\left(f(x)+f\left(-x\right)\right)}{x^2-{a}^2}\kern0.5em dx. \)

  2. 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. 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. 4.

    ωp has the same form as the plasma frequency for electrons (Eq. 4 in chapter “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. 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: \( \alpha \propto {\left({n}_{\mathrm{r}}-1\right)}^2/\left(N\kern0.5em {\lambda}^4\right) \), 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 θΒ, which is the angle between the diffracting planes and the incident or diffracted beam - cf. Fig. 11.

  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; for a study of this effect applying Brillouin scattering see Vacher et al. (2006).

  10. 10.

    Strain coefficients for c-Si are reported by Anastassakis et al. (1990).

  11. 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.

    Fig. 20
    figure 20

    Raman spectra for α-Si:H on c-Si (blue curve) and c-Si (black). The red curve is an ab initio calculated spectrum. TO and LO phonon peaks are obtained from a fit to the measured α-Si:H spectrum. Inset: Measured (blue dots) and calculated (red) TO peak shifts induced by compressive strain; lines are linear regressions (After Strubbe et al. 2015)

    Full size image

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Authors and Affiliations

  1. 138 Moorings Park Rd. O 301, Naples, 34105, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2022). Photon–Phonon Interaction. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_11-4

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  • DOI: https://doi.org/10.1007/978-3-319-06540-3_11-4

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  1. Latest

    Photon–Phonon Interaction
    Published:
    27 May 2022

    DOI: https://doi.org/10.1007/978-3-319-06540-3_11-4

  2. Photon–Phonon Interaction
    Published:
    30 March 2020

    DOI: https://doi.org/10.1007/978-3-319-06540-3_11-3

  3. Photon–Phonon Interaction
    Published:
    28 September 2017

    DOI: https://doi.org/10.1007/978-3-319-06540-3_11-2

  4. Original

    Photon-Phonon Interaction
    Published:
    05 January 2016

    DOI: https://doi.org/10.1007/978-3-319-06540-3_11-1

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