Tuning the thermal conductivity of a silicon membrane using nanopillars: From crystalline to amorphous pillars

Tuning thermal transport in nanostructures is essential for many applications, such as thermal management and thermoelectrics. Nanophononic metamaterials (NPMs) have shown great potential for reducing thermal conductivity. In this work, the thermal conductivity of NPMs with crystalline $\mathrm{Si}$ ($c$-$\mathrm{Si}$) pillar, crystalline $\mathrm{Ge}$ ($c$-$\mathrm{Ge}$) pillar, and amorphous $\mathrm{Si}$ ($a$-$\mathrm{Si}$) pillar are systematically investigated by a molecular dynamics method. An analysis of phonon dispersion and spectral energy density shows that phonon dispersions of a $\mathrm{Si}$ membrane are flattened due to local resonant hybridization induced by both crystalline and amorphous pillars. In addition, an $a$-$\mathrm{Si}$ pillar can cause a larger reduction in thermal conductivity compared with a $c$-$\mathrm{Si}$ pillar. Specifically, when the atomic mass of the atoms in the pillars increases, the thermal conductivity of NPMs with a crystalline pillar increases because of the weakened phonon hybridization. However, the thermal conductivity of NPMs with an amorphous pillar is almost unchanged. The analyses of the reduction of thermal conductivity show that both resonant hybridization and scattering mechanisms are important in NPMs with a crystalline pillar, while the scattering mechanism dominates in NPMs with an amorphous pillar and NPMs with a short crystalline pillar. The results of this work can provide meaningful insights into controlling thermal transport in NPMs by choosing the materials and atomic mass of pillars for specific applications.