Surface scattering analysis of phonon transport in the quantum limit using an elastic model

Details Surface scattering analysis of phonon transport in the quantum limit using an elastic model Surface scattering analysis of phonon transport in the quantum limit using an elastic model

Publishing date

2002-04-21

URL

arxiv.org/abs/cond-mat/0204450v1

Journals

Phys. Rev. B 66, 144302 (2002)

Science

Physics

Field

Condensed Matter

SubField

Mesoscale and Nanoscale Physics

Additional info

27 pages, 13 figures

Type

Scientific paper

Digital Object Identifier

10.1103/PhysRevB.66.144302

Abstract

We have investigated the effect on phonon energy transport in mesoscopic systems and the reduction in the thermal conductance in the quantum limit due to phonon scattering by surface roughness using full 3-dimensional elasticity theory for an elastic beam with a rectangular cross-section. At low frequencies we find power laws for the scattering coefficients that are strongly mode dependent, and different from the $\omega^{2}$ dependence, deriving from Rayleigh scattering of scalar waves, that is often assumed. The scattering gives contributions to the reduction in thermal conductance with the same power laws. At higher frequencies the scattering coefficients becomes large at the onset frequency of each mode due to the flat dispersion here. We use our results to attempt a quantitative understanding of the suppression of the thermal conductance from the universal value observed in experiment.

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