Temperature-dependent thermal conductivity of epitaxial silicon nano-crystalline (SiNC) structures composed of nanometer-sized grains separated by ultra-thin silicon-oxide (SiO2) films is measured by the time domain thermoreflectance technique in the range from 50 to 300 K. Thermal conductivity of SiNC structures with grain size of 3 nm and 5 nm is anomalously low at the entire temperature range, significantly below the values of bulk amorphous Si and SiO2. Phonon gas kinetics model, with intrinsic transport properties obtained by first-principles-based anharmonic lattice dynamics and phonon transmittance across ultra-thin SiO2 films obtained by atomistic Greens function, reproduces the measured thermal conductivity without any fitting parameters. The analysis reveals that mean free paths of acoustic phonons in the SiNC structures are equivalent or even below half the phonon wavelength, i.e. the minimum thermal conductivity scenario. The result demonstrates that the nanostructures with extremely small length scales and controlled interface can give rise to ultimate classical confinement of thermal phonon propagation.
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