Surface induced phonon decay rates in thin film nano-structures

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Nano-scale structure significantly impacts phonon transport and related phonon relaxation rates, with order of magnitude effects on the thermal conductivity of dielectric thin films and quantum wires, and even larger effects on the lifetimes of ultrasonic phonons of micro- (nano-) oscillators. In both cases, efforts to explain the data have been hampered by our lack of knowledge of the effects of confined dimensionality on phonon-phonon scattering rates. Using a phonon Boltzmann equation with appropriate boundary conditions on the free surfaces to take surface roughness into account, we have obtained an expression yielding phonon lifetimes in 2-D dielectric nanostructures(thin films) resulting from phonon-phonon scattering in conjunction with phonon-surface scattering. We present these theoretical results and, in the limit in which surface induced losses dominate, obtain explicit predictions for the phonon lifetimes. The predicted temperature dependence of the ultrason! ic loss does not explain the observed saturation of the loss at low temperatures(τ(T) → const), but does give results of the order of magnitude of measured ultrasonic lifetimes.