Radiation patterns of acoustic phonons emitted by hot electrons in a quantum well

The acoustic phonon radiation patterns and acoustic phonon spectra due to electron-acoustic-phonon interaction in a double barrier quantum well have been investigated by solving both the kinetic equations for electrons and phonons. The acoustic phonon radiation patterns have strongly pronounced maximum in the directions close to the perpendicular to the quantum well direction. The radiation pattern anisotropy is explained in terms of possible electron transitions, electron distribution function, and the Hamiltonian of electron-phonon interaction. It was shown that, the simple assumption that emitted phonons always have a perpendicular wave-vector component of the order of 2 π/a, where a is the width of the quantum well, cannot explain the strong anisotropy of the radiation patterns. More detailed analysis is required and has been carried out. The emitted acoustic phonon spectra have maxima at energies 2 πℏu/a, where u is the sound velocity.