Impact of thermally dead volume on phonon conduction along silicon nanoladders

Abstract

Thermal conduction in complex periodic nanostructures remains a key area of open questions and research, and a particularly provocative and challenging detail is the impact of nanoscale material volumes that do not lie along the optimal line of sight for conduction. Here, we experimentally study thermal transport in silicon nanoladders, which feature two orthogonal heat conduction paths: unobstructed line-of-sight channels in the axial direction and interconnecting bridges between them. The nanoladders feature an array of rectangular holes in a 10 μm long straight beam with a 970 nm wide and 75 nm thick cross-section. We vary the pitch of these holes from 200 nm to 1100 nm to modulate the contribution of bridges to the net transport of heat in the axial direction. The effective thermal conductivity, corresponding to reduced heat flux, decreases from ∼45 W m-1 K-1 to ∼31 W m-1 K-1 with decreasing pitch. By solving the Boltzmann transport equation using phonon mean free paths taken from ab initio calculations, we model thermal transport in the nanoladders, and experimental results show excellent agreement with the predictions to within ∼11%. A combination of experiments and calculations shows that with decreasing pitch, thermal transport in nanoladders approaches the counterpart in a straight beam equivalent to the line-of-sight channels, indicating that the bridges constitute a thermally dead volume. This study suggests that ballistic effects are dictated by the line-of-sight channels, providing key insights into thermal conduction in nanostructured metamaterials.

On the reduction and rectification of thermal conduction using phononic crystals with pacman-shaped holes

“…The mean free path of phonons in Si ranges from few tens of nanometers to several microns 12,18,19 and the effect of thermal conductivity rectification should be observed only for small size holes when the size of the hole is significantly smaller than phonon mean free paths contributing the most to material thermal conductivity. However, fabrication of smaller holes with a complex shape remains difficult due to a limited resolution of electron beam lithography.…”

Enhanced Thermoelectric Performance of Polycrystalline Si0.8Ge0.2 Alloys through the Addition of Nanoscale Porosity

“…These simulations were performed using the OpenBTE Boltzmann transport solver [ 29 ] making use of materials properties for Si x Ge 1-x computed from first principles. The development and validation of OpenBTE with experimental data has been established in the literature through a series of publications [ 30 , 31 , 32 , 33 ]. The model incorporated the effects from four different phonon scattering processes: three-phonon scattering, elastic mass impurity scattering, scattering from grain boundaries, and scattering from pores.…”

Phonon Transport within Periodic Porous Structures — From Classical Phonon Size Effects to Wave Effects

“…Besides aligned or staggered circular pores, other porous patterns are also studied under the circumstance of incoherent phonon transport. 142,143 When the porous patterns are designed to tune the phonon transmission by pore-edge phonon scattering, asymmetric phonon transmission along the forward and backward directions may lead to thermal rectification effects. 55,144 The high performance of such a thermal rectifier requires strong ballistic transport within the nanoporous pattern and strong specular reflection by pore edges.…”

“…55,142 In general, certain "thermally dead volume" can be introduced in a patterned thin film, where phonons can be trapped and contribute less to heat conduction. Examples can be found in nanoladders with a row of rectangular holes 143 and SiNWs with periodic wings. 149…”