  We report an unambiguous phonon resonance effect originating from germanium
nanoparticles embedded in silicon matrix. Our approach features the combination
of phonon wave-packet method with atomistic dynamics and finite element method
rooted in continuum theory. We find that multimodal phonon resonance, caused by
destructive interference of coherent lattice waves propagating through and
around the nanoparticle, gives rise to sharp and significant transmittance
dips, blocking the lower-end frequency range of phonon transport that is hardly
diminished by other nanostructures. The resonance is sensitive to the phonon
coherent length, where the finiteness of the wave packet width weakens the
transmittance dip even when coherent length is longer than the particle
diameter. Further strengthening of transmittance dips are possible by arraying
multiple nanoparticles that gives rise to the collective vibrational mode.
Finally, it is demonstrated that these resonance effects can significantly
reduce thermal conductance in the lower-end frequency range.
