The effect of echoes interference on phonon attenuation in a nanophononic membrane

Nanophononic materials are characterized by a periodic nanostructuration, which may lead to coherent scattering of phonons, enabling interference and resulting in modified phonon dispersions. We have used the extreme ultraviolet transient grating technique to measure phonon frequencies and lifetimes in a low-roughness nanoporous phononic membrane of SiN at wavelengths between 50 and 100 nm, comparable to the nanostructure lengthscale. Surprisingly, phonon frequencies are only slightly modified upon nanostructuration, while phonon lifetime is strongly reduced. Finite element calculations indicate that this is due to coherent phonon interference, which becomes dominant for wavelengths between ~ half and twice the inter-pores distance. Despite this, vibrational energy transport is ensured through an energy flow among the coherent modes created by reflections. This interference of phonon echos from periodic interfaces is likely another aspect of the mutual coherence effects recently highlighted in amorphous and complex crystalline materials and, in this context, could be used to tailor transport properties of nanostructured materials.