Abstract
In this chapter we treat the properties of phonons in scenarios where the periodicity of the crystalline lattice is perturbed. This is the case for crystals with a random distribution of atoms on lattice sites (alloys) or for local deviations from periodicity (defects). We also consider the situation of reduced periodicity in layered structures like superlattices and quantum wells. Finally we address confinement of phonons in quantum dots.
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Problems
13.1
(a) Derive a simple formula to estimate the average sound velocity in a superlattice from two materials A and B with thicknesses \(d_\text {A}\), \(d_\text {B}\) and speeds of sound \(v_\text {A}\), \(v_\text {B}\), respectively. (b) Try to estimate the average speed of sound and the respective speeds for CdS and ZnSe from the data of Fig. 13.7a.
13.2
Sketch the qualitative atomic displacement of the first few (small wave vector in growth direction) confined optical phonon modes in an (GaAs)\(_{n}\)(AlAs)\(_{n}\) superlattice. What do you expect for the movement of the atoms right at the interface between the layers?
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Kalt, H., Klingshirn, C.F. (2019). Phonons in Solids of Perturbed Lattice Periodicity. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_13
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DOI: https://doi.org/10.1007/978-3-030-24152-0_13
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