Amplification of localized acoustic waves by the electron drift in a quantum well

Abstract

We have investigated acoustic waves in a heterostructure with a layer embedded into a semiconductor providing acoustic waves localization near the layer and electron confinement inside the layer. For layer thicknesses smaller than wavelengths we have obtained and analyzed the dispersion relation for the localized waves. For electrons into the layer we have supposed that parallel transport is semiclassical, while perpendicular electron motion is quantized. For two-dimensional confined electrons interacting with the acoustic waves we have solved the Boltzmann equation in a parallel electric field. The solutions have been found for electron-phonon interaction via deformation potential. The dispersion relation for coupled charge density and acoustic waves has been analyzed. We have established conditions of amplification of localized acoustic waves under the electron drift for two extreme cases: i) the only lowest two-dimensional subband is populated, ii) a large number of the subbands are populated. We have found that the amplification coefficient of the acoustic waves in THz-rigion is of the order of 100 cm⁻¹. We have discussed the results and compared them with acoustic waves amplification in bulk like semiconductors.