Abstract
So far we have discussed the optical properties of a system of model oscillators and the basics of lattice vibrations in semiconductors. We will now demonstrate that the optical properties of phonons in semiconductors are well explained in the framework of the polariton model of Chap. 8. We will discuss the optical properties related to phonon polaritons like the phonon stop band and how to determine them via Fourier transform infrared spectroscopy. We will further describe the phonon-polartion dispersion and its experimental identification by Raman and Brillouin scattering as well as attenuated total reflection.
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Problems
Problems
12.1
Try to find more reflection spectra like that in Fig. 12.1b in the literature. Deduce \(\hbar \omega _\text {T}\), \(\Delta _\text {LT}\), \(\varepsilon _\text {s}\) and \(\varepsilon _\text {b}\) from these spectra and compare with values in the literature.
12.2
Show that the (eventually only weak) dependence of \(\omega \) on \(\varvec{k}\) is important to explain the experimental fact that the TO and LO phonon modes can be followed through the whole Brillouin zone by neutron scattering. Compare for the explanation with Fig. 8.1 for vanishing and finite damping.
12.3
Why is the phonon spectrum of high \(T_{{\text {c}}}\) superconductors so complex?
12.4
Which trend would you expect for the zone boundary LA and TA phonons when going from ZnO via ZnS and ZnSe to ZnTe. Compare with data in the literature. What do you expect for zone center optical phonons?
12.5
Can you give qualitative arguments for why the optical phonons in CdS\(_{1-x}\)Se\(_{x}\) and Zn\(_{1-y}\)Cd\(_{y}\)S are of the persistent and amalgamation type, respectively? Consider the atomic masses of the oscillating atoms.
12.6
Find out why phonon data for CdS and CdSe obtained by neutron scattering are relatively rare?
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Kalt, H., Klingshirn, C.F. (2019). Phonon Polaritons. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_12
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