Spectral analysis of coherent and incoherent phonon transport in silicon nanomeshes

In this paper, we investigate the spectral thermal transport properties of silicon nanomeshes (SNMs) with large and small holes arranged periodically, aperiodically in the $x$ direction (ap-x), and fully aperiodically (ap-xy). Our simulations reveal a significant reduction in thermal conductivity $(\ensuremath{\kappa})$ of small-hole SNMs due to ap-x aperiodicity, in contrast with large-hole SNMs. Spectral phonon analysis indicates that low-frequency phonons in small-hole SNMs are notably suppressed by ap-x aperiodicity, like one-dimensional superlattices. Spectral energy density analysis shows the existence of well-defined coherent phonon modes in small-hole SNMs in the 0--3 THz range; spectral thermal conductivity analysis shows that these modes transport ballistically in the SNM. In contrast, ap-x aperiodicity has negligible impact on large-hole SNMs, attributed to hindered coherent phonon formation. Surprisingly, low-frequency phonons in small-hole SNMs demonstrate enhanced heat transfer capabilities compared with large-hole counterparts, highlighting coherent phonon behavior. Finally, while the heat flux splitting and shape factors effectively categorize $\ensuremath{\kappa}$ for large-hole SNMs, their utility is limited for small-hole SNMs, emphasizing the importance of coherent phonon considerations in thermal transport analysis.