Complete Report - University of New South Wales

energy. In a few cases – such as InN – this gap can be larger than the highest acoustic energy
and hence prevent operation of the optical phonon decay mechanism described above, see
Figure 4.5.24.
Figure 4.5.24: Phonon dispersion for InN
[4.5.20] in which E LO >2E LA such that LO
→ 2LA (only) is forbidden. (E LO ; LA ) denote
longitudinal optical and acoustic phonon
energies.)
The current work is investigating achieving a similar effect in less exotic materials possibly
based on silicon, by exploiting the refl ection that occurs at the mini-Brillouin zone boundaries
of nanostructure superlattices. This opens up mini-gaps in the phonon dispersion for those
acoustic phonon energies which satisfy the Bragg condition. Figure 4.5.25 and Figure 4.5.26
show phonon dispersions modelled using a nearest neighbour elastic continuum model
based on Rytov calculations, for quantum well (QW) and quantum dot (QD) superlattices
respectively.
Figure 4.5.25: Acoustic phonon dispersion
and DOS calculated using an elastic
continuum model based on the Rytov
formulation for QW and barrier thicknesses
of 5 lattice spacings and ratio of acoustic
impedances of 4.
Figure 4.5.26: Acoustic phonon dispersion
for multiple QD array showing a folded
dispersion with mini-gaps in all directions
in real and reciprocal space, hence giving
true mini-gaps in the DOS.
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