Frequency dependence in phonon surface scattering is a debated topic in fundamental phonon physics. Recent experiments and theory suggest such a phenomenon, but an independent agreement between the two remains elusive. We report low-temperature dependence of thermal conductivity in silicon nanowires fabricated using a two-step, metal-assisted chemical etch. By reducing etch rates down to 0.5 nm/s from the typical >100 nm/s, we report controllable roughening of nanowire surfaces and selectively focus on moderate roughness scales rather than the extreme scales investigated previously. This critically enables direct comparison with perturbation-based spectral scattering theory. Using experimentally characterized surface roughness, we show that a multiple scattering theory provides excellent agreement and explanation of the observed low-temperature dependence of rough surface nanowires. The theory does not employ any fitting parameters. A 5-10 nm roughness correlation length is typical in metal-assisted chemical etching and resonantly scatters dominant phonons in silicon, leading to the observed ~T(1.6-2.4) behavior. Our work provides fundamental and quantitative insight into spectral phonon scattering from rough surfaces. This advances applications of nanowires in thermoelectric energy conversion.

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.

The specularity of phonons at crystal surfaces is of direct importance to thermal transport in nanostructures and to dissipation in nanomechanical resonators. Wave scattering theory provides a framework for estimating wavelength dependent specularity, but experimental validation remains elusive. Widely available thermal conductivity data presents poor validation since the involvement of infinitude of phonon wavelengths in thermal transport presents an underconstrained test for specularity theory. Here, we report phonon specularity by measuring the lifetimes of individual coherent longitudinal acoustic phonon modes excited in ultrathin (36-205 nm) suspended silicon membranes at room temperature over the frequency range ∼ 20-118 GHz. Phonon surface scattering dominates intrinsic Akhiezer damping at frequencies 60 GHz, enabling measurements of phonon boundary scattering time over wavelengths ∼72-140 nm. We obtain detailed statistics of the surface roughness at the top and bottom surfaces of membranes using HRTEM imaging. We find that the specularity of the excited modes are in good agreement with solutions of wave scattering only when the TEM statistics are corrected for projection errors. The often cited Ziman formula for phonon specularity also appears in good agreement with the data, contradicting previous results. This work helps to advance the fundamental understanding of phonon scattering at the surfaces of nanostructures.

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Recent experimental work suggests that individual silicon nanowires with rough surfaces possess a thermoelectric figure of merit as high as 0.6 near room temperature. This paper addresses the possibility of using an array of such nanowires in a thermoelectric junction for generation. Employing a model of frequency dependent phonon boundary scattering, we estimate the effective thermal conductivity of the array and investigate heat flow through the junction. We show that charge transport is largely unaffected by the roughness scales considered. Enhancing the area for heat exchange at an individual 200 μm × 200 μm p-n junction yields significant temperature differences across the junction leading to power >0.6 mW and efficiency >1.5% for a junction with effective thermal conductivity <5 W/mK, when the source and sink are at 450 K and 300 K, respectively. We show that relatively short nanowires of ∼50 μm length are sufficient for obtaining peak power and reasonable efficiency. This substantially reduces the challenge of engineering low resistivity electrical contacts that critically affect power and efficiency. This paper provides insight into how fundamental transport in relation to bulk heat transfer and charge transport, affects the performance of thermoelectric junctions based on nanostructured materials.