Confinement and amplification of acoustic waves in cubic heterostructures

Abstract

We present the theory of acoustic phonon confinement in elastically anisotropic ͑cubic͒ quantum-well ͑QW͒ heterostructures grown in a direction of high symmetry. A general criterion for phonon confinement is derived. For Si/Si 0.5 Ge 0.5 /Si, Si/Ge/Si and AlAs/GaAs/AlAs QW heterostructures, dispersion curves are obtained, and displacement fields corresponding to the confined phonons are studied in detail. It is found that the confinement of acoustic phonons in these QW layers is strong in the subterahertz and terahertz frequency ranges. The resulting description of phonon confinement is applied to analyze the amplification of confined modes by the drift of the two-dimensional carriers as a function of the phonon frequency, the temperature, and the parameters of heterostructure. The calculation shows that the amplification coefficient of the confined phonons can exceed 10 3 cm Ϫ1 for Si/Ge-based structures and 10 2 cm Ϫ1 for AlAs/GaAs-based structures.Consider the heterostructure shown in Fig. 1, where electrons are confined in a QW layer A embedded in a semiconductor material B. The thickness of layer A is 2d. Both materials A and B are supposed to be of cubic symmetry. We assume that the structure is grown in the ͓001͔ direction, and that the propagation direction of the acoustic wave is ͓100͔.

Relaxation of a two-dimensional electron gas in semiconductor thin films at low temperatures: Role of acoustic phonon confinement

“…The quantization of the acoustic-phonon spectrum in such structures manifests itself in optical, 6 electrical, 7 and recent heat-transport 8 measurements. The effect of extreme confinement of acoustic phonons on Peierls transition 9 and on electron-phonon scattering [10][11][12] in free-standing quantum wires has been investigated theoretically. Previous results [10][11][12] demonstrated the profound effect of different mechanical boundary conditions on electron-phonon scattering rates.…”

Electron-acoustic Phonon Interaction in AlAs/GaAlAs Resonance Tunneling Nanostructures

“…However, in the case of acoustic phonons, this direction remains poorly studied. The spectra and components of the displacement field for acoustic phonons were mainly studied for single-well nanosystems [7][8][9] placed in an external non-stressed medium, which simplified the application of boundary conditions for the components of the displacement field and the stress tensor.…”