Acoustic Phonon Spectrum and Thermal Transport in Nanoporous Alumina Arrays

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We report results of a combined investigation of thermal conductivity and acoustic phonon spectra in nanoporous alumina membranes with the pore diameter decreasing from D=180 nm to 25 nm. The samples with the hexagonally arranged pores were selected to have the same porosity of 13%. The Brillouin-Mandelstam spectroscopy measurements revealed bulk-like phonon spectrum in the samples with D=180-nm pores and spectral features, which were attributed to spatial confinement, in the samples with 25-nm and 40-nm pores. The velocity of the longitudinal acoustic phonons was reduced in the samples with smaller pores. Analysis of the experimental data and calculated phonon dispersion suggests that both phonon-boundary scattering and phonon spatial confinement affect heat conduction in membranes with the feature sizes D<40 nm.