Phonon images of crystals

Using the pair of coupled Boltzmann kinetic equations for 2D electron gas and bulk acoustic phonons we derive the explicit formula for the phonon drag voltage induced by a pulsed phonon beam. A point source producing very short bursts of monoenergetic phonons is considered. The time integrated signal of the phonon drag voltage is calculated numerically for 2D electron gas lying in a {001} plane. For the raster scanned source of phonons the pattern of induced voltage is obtained and compared to the suitable experimental pattern and to the calculated quasimomentum focusing image. For several phonon propagation directions the dependency of induced voltage on the phonon energy is studied and compared with the experimental results. The ratio of the strength of piezo-electric coupling to the deformation potential constant and the localization length of 2D electrons are fitted.