Acoustic vibrations in free-standing double layer membranes

Abstract

We report on a Brillouin light scattering study of acoustic excitations in free-standing polymethyl methacrylate $(\mathrm{PMMA})∕{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ double layer membranes. For vanishing-wave vector transfer along the membrane, the observed excitations are a series of longitudinal standing wave harmonics whose frequencies depend on PMMA and ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ layer thickness. The associated displacement profiles below $30\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ are largely confined to the softer PMMA layer with mode amplitudes significantly higher at the PMMA surface than at the free surface of the high elastic modulus ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ layer. At higher frequencies, in the vicinity and beyond the resonance associated with the ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ layer, the mode amplitudes become comparable at both free surfaces. Excitations with transverse polarization as well as waves whose amplitudes within the ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ are consistent with flexural and dilatational modes for a single layer are also observed. For certain ranges of wave vector the latter interact and hybridize with the harmonics arising from the PMMA layer.