Confinement and transverse standing acoustic resonances in free-standing membranes

Abstract

Brillouin light scattering (BLS) reveal standing wave acoustic resonances in unsupported 100 and 200 nm thick, SiN membranes. In contrast to supported thin films where discrete high frequency (GHz) longitudinal standing wave excitations were recently reported, transverse standing resonances are observed by light scattering in an unsupported laminar structure. Due to the boundary conditions imposed by the free upper and lower surfaces, the standing wave resonances are quantized in frequency. The resonances provide for a direct, nondestructive, measure of all principal elastic constants ${(C}_{11}{,C}_{44})$ that completely characterize the mechanical properties of the membrane. In addition, the two lowest order Lamb waves (dilational and flexural modes) of the membrane are observed. The results are compared to BLS performed on nitride films atop a Si underlayer when it is found that all standing resonances transform to leaky modes leading to featureless light scattering spectra.