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Understanding phonon transport mechanisms in nanostructures is of greatimportance for delicately tailoring thermal properties. Combining phononparticle and wave effects through different strategies, previous studies haveobtained ultra-low thermal conductivity in nanostructures. However, phononparticle and wave effects are coupled together, that is their individualcontributions to phonon transport cannot be figured out. Here, we present howto quantify the particle and wave effects on phonon transport by combiningMonte Carlo and atomic green function methods. We apply it to 1D siliconnanophononic metamaterial with cross-junctions, where it has been thought thatthe wave effect was the main modulator to block phonon transport and theparticle effect was negligibly weak. Surprisingly, we find that the particleeffect is quite significant as well and can contribute as much as 39% to thetotal thermal conductivity reduction. Moreover, the particle effect does notdecrease much as the cross section area (CSA) of the structure decreases andstill keeps quite strong even for CSA as small as 2.23 nm2. Further phonontransmission analysis by reducing the junction leg length also qualitativelydemonstrates the strong particle effect. The results highlight the importanceof mutually controlling particle and wave characteristics, and themethodologies for quantifying phonon particle and wave effect are important forphonon engineering by nanostructuring.

Quantifying phonon particle and wave transport in nanostructures--The  unexpectedly strong particle effect in silicon nanophononic metamaterial with  cross junction