title: Direct measurements of surface scattering in Si nanosheets using a microscale phonon spectrometer: implications for Casimir-limit predicted by Ziman theory.
abstract: Thermal transport in nanostructures is strongly affected by phonon-surface interactions, which are expected to depend on the phonon's wavelength and the surface roughness. Here we fabricate silicon nanosheets, measure their surface roughness (∼ 1 nm) using atomic force microscopy (AFM), and assess the phonon scattering rate in the sheets with a novel technique: a microscale phonon spectrometer. The spectrometer employs superconducting tunnel junctions (STJs) to produce and detect controllable nonthermal distributions of phonons from ∼ 90 to ∼ 870 GHz. This technique offers spectral resolution nearly 10 times better than a thermal conductance measurement. We compare measured phonon transmission rates to rates predicted by a Monte Carlo model of phonon trajectories, assuming that these trajectories are dominated by phonon-surface interactions and using the Ziman theory to predict phonon-surface scattering rates based on surface topology. Whereas theory predicts a diffuse surface scattering probability of less than 40%, our measurements are consistent with a 100% probability. Our nanosheets therefore exhibit the so-called "Casimir limit" at a much lower frequency than expected if the phonon scattering rates follow the Ziman theory for a 1 nm surface roughness. Such a result holds implications for thermal management in nanoscale electronics and the design of nanostructured thermoelectrics.
authors.affiliation: Department of Materials Science and Engineering, ‡School of Electrical and Computer Engineering, and §Cornell Nanoscale Facility, Cornell University , Ithaca, New York 14853, United States.
authors.forename: Jared B
authors.initials: JB
authors.lastname: Hertzberg
authors.forename: Mahmut
authors.initials: M
authors.lastname: Aksit
authors.forename: Obafemi O
authors.initials: OO
authors.lastname: Otelaja
authors.forename: Derek A
authors.initials: DA
authors.lastname: Stewart
authors.forename: Richard D
authors.initials: RD
authors.lastname: Robinson