Acoustic phonon modes in asymmetric AlxGa1−xN/GaN/AlyGa1−yN quantum wells

Using an elastic continuum model, the dispersion relations and phonon modes of propagating, confined, half space and interface acoustic phonons in asymmetric AlxGa1−xN/GaN/Al1−yGayN quantum wells (QWs) have been solved theoretically with the varieties of Al components x and y. Contrary to the previous conclusions, some regulations for the existence of the above different acoustic phonons are revealed as well as the transition conditions among these modes are also discussed. With increase of wave vectors, the dispersion relations split into several groups. Because the classification of these groups is related to the eigen frequencies of bulk materials forming QWs, phonon modes in these groups will be confined or propagating in different layers of QWs. Furthermore, the gradients of the dispersion relations' asymptotes are the velocities of longitudinal and the transverse acoustic phonons propagating in bulk materials in turns. The properties of the dispersion relations and their phonon modes are also analyzed in depth based on the cut-off conditions. By the changing of Al components x and y, the bottom of these groups will be modified to adjust eigen frequencies of AlxGa1−xN or Al1−yGayN layers. But the propagation properties of acoustic phonon modes will remain unchanged in each section.