  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 Green's
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.
