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

Abstract

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

Study on Phonon Localization in Silicon Film by Molecular Dynamics

“…When the number of selected small block the more disorderly the arrangement of small blocks, and the smaller the DP reason is that amorphous surfaces are rougher than crystalline surfaces, an surface produces phonon scattering, which ultimately reduces the mean free nons. According to phonon wave interference theory [50], concave or perfo each scattering point constitute a finite discontinuity in the host material, lea distribution of phonon frequencies due to their induced interference with ph The calculation results are discrete frequency points. To better display the results, the frequency points are connected by dotted lines.…”

“…The main reason is that amorphous surfaces are rougher than crystalline surfaces, and the rough surface produces phonon scattering, which ultimately reduces the mean free path of phonons. According to phonon wave interference theory [50], concave or perforation make each scattering point constitute a finite discontinuity in the host material, leading to a redistribution of phonon frequencies due to their induced interference with phonon waves, which in turn, affects the PDOS and, thus, the MPR.…”