Coherent Phonon-Grain Boundary Scattering in Silicon Inverse Opals

Abstract

We report measurements and modeling of thermal conductivity in periodic three-dimensional dielectric nanostructures, silicon inverse opals. Such structures represent a three-dimensional "phononic crystal" but affect heat flow instead of acoustics. Employing the Stober method, we fabricate high quality silica opal templates that on filling with amorphous silicon, etching and recrystallizing produce silicon inverse opals. The periodicities and shell thicknesses are in the range 420-900 and 18-38 nm, respectively. The thermal conductivity of inverse opal films are relatively low, ~0.6-1.4 W/mK at 300 K and arise due to macroscopic bending of heat flow lines in the structure. The corresponding material thermal conductivity is in the range 5-12 W/mK and has an anomalous ~T(1.8) dependence at low temperatures, distinct from the typical ~T(3) behavior of bulk polycrystalline silicon. Using phonon scattering theory, we show such dependence arising from coherent phonon reflections in the intergrain region. This is consistent with an unconfirmed theory proposed in 1955. The low thermal conductivity is significant for applications in photonics where they imply significant temperature rise at relatively low absorption and in thermoelectrics, where they suggest the possibility of enhancement in the figure of merit for polysilicon with optimal doping.

A bottom-up fabrication method for the production of visible light active photonic crystals

“…The slightly attenuated/diminished PL emission in this case may be attributed to the effect of the diffuse scattering resulting from the presence of disorder (dislocations, point defects and line defects) inherent to the SIO structure, to possible absorption losses due to the ncSis, as well as to a possible interference from the roughened interfaces of the ncSi-SIO structure, which happens to be higher at the higher energy region of the stopband. 70 Overall, the observation of much of the ncSi PL emission spectrum despite the presence of various loss mechanisms underlines the efficacy of 3D patterning by the method presented here. The method described here is significant considering its ability to integrate functional materials into complex 3D structures by a simple process.…”

Thermal transport in 2- and 3-dimensional periodic “holey” nanostructures

“…Copyright 2013 American Chemical Society. 32 Phonons scatter with a grain boundary due to change in orientation of crystal planes as well as disorder in the inter-grain region. In order to explain this scattering process, Klemens 66 adopted a perturbative approach, which introduces a perturbation in wave velocity ∆v, caused by either a tilt boundary or an inter-grain region.…”

“…30 However, recent measurements show that the scattering process due to grain boundary is a rather complicated mechanism. 31,32 Different approaches have been proposed to fit the corresponding measurement values. Here we adopt a scattering rate that explains the low temperature behavior of thermal conductivity of silicon inverse opals: 32…”

“…Copyright 2013 American Chemical Society. 32 suggested that it was possible to obtain thermal conductivity close to the amorphous limit with truly nanoscale features. More recent theory, 9,10 following the publication of data on nanostructures, has revisited the Boltzmann transport simulations while considering frequency dependent scattering rates.…”

“…For instance, carbon inverse opal, as a battery electrode, shows superior transport properties and mechanical integrity. 50 Ma et al 32 fabricated 3D periodic silicon nanostructure in the form of inverse opals. 21 The opal template is comprised of silica spheres made from the Stober method.…”