Phonon-engineered thermal transport in Si wires with constant and periodically modulated cross-sections: A crossover between nano- and microscale regimes

Abstract

The transition between nanoscale and microscale thermal transport regime at room temperature in silicon wires with constant and periodically modulated cross-section is theoretically investigated. Extrapolating the calculated thermal conductivity from the nano- to micrometer range, we find the characteristic dimensions of the wires where a crossover between nanoscale and microscale thermal transport occurs. This crossover is observed in both generic (smooth) and cross-section-modulated wires. In case of smooth silicon wires, we reveal a strong dependence of the crossing point position on the boundary roughness. For silicon wires with weak boundary roughness, the crossover occurs at cross-sections ∼60 nm × 300 nm, while for very rough boundaries it occurs at cross-sections ∼150 nm × 750 nm. In case of the periodically modulated wires, the crossover between nano- and microscale regimes occurs at typical cross-sections ∼120 nm × 120 nm of the narrow segment, and it is almost independent of boundary roughness. A strong distinction from the case of smooth wires is attributed (i) to the different trends at the nanometer scale, wherefrom the extrapolation was performed, and (ii) to the different phonon–boundary scattering due to the specific geometry. For modulated silicon wires, the influence of modulation thickness, modulation length, and cross-sectional area on the phonon thermal conductivity at the room temperature is analyzed. A possibility of thermal transport engineering in cross-section-modulated wires by resizing them is revealed in both nano- and microscale regimes. The presented results pave the way towards a better understanding of thermal transport reduction in Si nanowires with engineered diameter modulations and shed light on the crossover between nano- and microscale regimes of thermal transport.