ACOUSTIC INTERFERENCE IN RANDOM SUPERLATTICES

We study theoretically the interference effects and the resulting transmission of acoustic phonons in random superlattices, i.e., multilayered systems in which two kinds of building blocks A and B are stacked at random. We derive (i) the recursion relations satisfied by the superlattice structure factors, and (ii) an analytic expression for the ensemble-averaged intensity of phonons reflected from layer interfaces of an infinite system. We predict a number of sharp features in the intensity versus frequency, which appear rather regularly. Furthermore, numerical calculations for both the double- and single-layer random superlattices indeed exhibit distinctive dip structures in phonon transmission spectra which are in good agreement with the analytical results. We also find that the single-layer random superlattices show an effective phonon-filtering action as the system size is increased, i.e., they prevent the transmission of phonons except for those satisfying resonance conditions. © 1990 The American Physical Society.