In this paper we investigate theoretically the influence of piezoelectric coupling on phonon dispersion relations. Specifically we solve dispersion relations for a fully coupled zinc-blende freestanding quantum well for different orientations of the crystal unit cell. It is shown that the phonon mode density in GaAs can change by a factor of approximately 2–3 at q_xa=1 for different crystal-growth directions relative to the slab thickness direction. In particular, it is found that optical and acoustic phonon modes are always piezoelectrically coupled, independent of the crystal-growth direction, and will be jointly excited by electrical stimulus. We demonstrate this for an electrically excited freestanding slab for two cases of high-symmetry crystal-growth directions and finally show the impact of the Drude model for permittivity on the phonon dispersion. In particular, it is verified that the piezoelectric effect leads to a drastically enhanced coupling of acoustic and optical phonon modes and increase in the local phonon density of states near the plasma frequency where the permittivity approaches zero.
|Tidsskrift||Physical Review B|
|Status||Udgivet - 30. jan. 2017|