The control of thermal conductivity through coherent and incoherent phonon scattering in 2-dimensional phononic crystals by incorporating elements of self-similarity

In this letter, we report the theoretical study on phonon transport in monocrystalline silicon thin-films having unfilled or metal-filled circular holes (i.e., phononic crystals, PnCs) and show that the thermal conductivity, κ" role="presentation">κ, at 1 K can be maximally reduced by using a multiscale structure, which allows us control over the porosity of the structure. The circular scatterers are placed in the square (SQ) and hexagonal (HX) pattern with a fixed 100 nm interhole spacing, and the pit diameter is varied between 10 and 90 nm. Each of the corresponding silicon PnCs shows reduced κ" role="presentation">κ compared to the unpatterned film. The SQ-PnC having tungsten-filled pits shows the greatest reduction in κ" role="presentation">κ when we consider only the effects of coherent scattering. Furthermore, we have computed κ" role="presentation">κ for the PnC where the unit cell, of 100 nm and 500 nm sizes, comprises the Sierpinski gasket (SG) with circular holes of different diameters (depending on the fractal order) in the same cell. It is observed that the κ" role="presentation">κ for the 2nd (100 nm cell) and 3rd order (500 nm cell) SG-PnC is comparable to the SQ- and HX-PnC with a pit diameter of 90 nm. When we add the effect of the diffuse boundary scattering in κ" role="presentation">κ, there is a lowering in κ" role="presentation">κ compared to that when only the coherent effects are considered. The additional κ" role="presentation">κ-reduction due to boundary scattering for the SQ-PnC and HX-PnC (both with 90 nm diam) as well as the 2nd and 3rd order SG-PnCs is 47%, 40%, 80%, and 60%, respectively