Coherent and incoherent thermal transport in nanomeshes

Coherent thermal transport in nanopatterned structures is a topic of considerable interest, but whether it occurs in certain structures remains unclear due to a poor understanding of which phonons conduct heat. Here, we perform fully three-dimensional, frequency-dependent simulations of thermal transport in nanomeshes by solving the Boltzmann transport equation with an efficient Monte Carlo method. From the spectral information in our simulations, we show that thermal transport in nanostructures that can be created with available lithographic techniques is dominated by incoherent boundary scattering at room temperature. Our result provides important insights into the conditions required for coherent thermal transport to occur in artificial structures.

Figure 1

Thermal conductivity of the NM as a function of temperature. The thermal conductivity of the NM reported by Yu et al. [14] (black diamonds) is significantly lower than our simulation result with square and circular pore geometries.

Figure 2

Thermal conductivity accumulation (k-accumulation) versus phonon frequency for a NM that reflects phonons with frequency less than 2 THz specularly and the rest diffusely. Even under these conservative assumptions, the reported measurements cannot be explained even by completely neglecting the contribution of these low frequency phonons that could undergo coherent interference.

Figure 3

Thermal conductivity as a function of temperature for different nanostructures in the experiments of Yu et al. [14] and our simulations for (a) a 2-nm disordered layer thickness and (b) a $3.5$-nm disordered layer thickness. The disordered layer is added to both the nanowire array (NWA) and the nanomesh (NM) in our simulations. In these two figures, the red dashed line, pink circles, and pink squares are the MC solutions for the NWA, NM with circular holes, and NM with square holes, respectively. The black diamonds, green triangles, and blue inverted triangles represent the reported thermal conductivity for the NM, the recalculated thermal conductivity for the NM, and the recalculated thermal conductivity for the NWA, respectively, from Yu et al.'s experiments [14].

Figure 4

Fraction of backscattered phonons for the NWA and the NM with circular and square holes for different disordered layer thicknesses. NMs have a larger fraction of backscattered phonons than the NWA, explaining their lower thermal conductivity.