Lifetime of high-order thickness resonances of thin silicon membranes

Femtosecond laser pulses are used to excite and probe high-order longitudinal thickness resonances at a frequency of ∼270 GHz in suspended Si membranes with thickness ranging from 0.4 to 15 μm. The measured acoustic lifetime scales linearly with the membrane thickness and is shown to be controlled by the surface specularity which correlates with roughness characterized by atomic force microscopy. Observed Q-factor values up to 2400 at room temperature result from the existence of a local maximum of the material Q in the sub-THz range. However, surface specularity would need to be improved over measured values of ∼0.5 in order to achieve high Q values in nanoscale devices. The results support the validity of the diffuse boundary scattering model in analyzing thermal transport in thin Si membranes.