Impact of limiting dimension on thermal conductivity of one-dimensional silicon phononic crystals

Abstract

We present experimental and theoretical investigations on the roles of the limiting dimensions, such as the smallest dimension, surface roughness, and density of holes in the reduction of thermal conductivity of one-dimensional phononic nanostructures at temperatures of 4 and 295 K. We discover that the thermal conductivity does not strongly depend on the period of the phononic crystal nanostructures whereas the surface roughness and the smallest dimension of the structure—the neck—play the most important roles in thermal conductivity reduction. Surface roughness is a very important structural parameter in nanostructures with a characteristic length less than 100 nm in silicon. The importance of the roughness increases as the neck size decreases, and the thermal conductivity of the structure can differ by a factor of four, reaching the thermal conductivity of a small nanowire. The experimental data are analyzed using the Callaway–Holland model of Boltzmann equation and Monte Carlo simulation providing deeper insight into the thermal phonon transport in phononic nanostructures.

Phonon and heat transport control using pillar-based phononic crystals

“…On one hand, a stronger reduction was measured in silicon with pores (>50%) [9,18,19], nanodots (>70%) [13,68], polycrystalline grains (>80%) [15,69,70], dopants (>50%) [71,72] or germanium atoms (>70%) [14,71,73]. On the other hand, the 20% reduction by the pillars [63] is comparable to the reduction by holes (20–25%) [21,74] or slits (20–30%) [75] covering the same relative area. This relative comparison shows that pillars could achieve the same reduction in the thermal conductivity without sacrificing the material volume or introducing scattering points inside the bulk of the material.…”

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

“…Also, experiments show that the surface area of holes may play a key role in the reduction of thermal conductivity 12,13 but only above a certain nanoscale limit, below which narrow passages between the holes take over the control of thermal conductivity. 6,12,14,15 However, the exact roles of hole symmetry, surface area, size, and separation in the thermal conductivity reduction remain unclear.…”

2D Phononic Crystals: Progress and Prospects in Hypersound and Thermal Transport Engineering

“…[17,32,83,[94][95][96][97] Similar to thin films, the roughness of the surfaces impacts surface scattering, and therefore thermal conductivity. [98] Further experiments confirmed the importance of geometric parameters such as the filling fraction, surface-tovolume ratio, or the neck size, but also demonstrated that a further tuning of the thermal conductivity is possible with PnCs with random hole positions, by varying the hole overlap, i.e., the number and relative position of the phonon channels. [37] Impurity and phonon-phonon scattering processes are predominant in bulk material at room temperature, whereas the importance of boundary scattering increases as temperature decreases.…”

“…In most cases, this further reduction in thermal conductivity is due to an increase in surface scattering that can be summarized by two parameters, namely, the surface‐to‐volume ratio and the spacing between holes (neck size), i.e., the smallest width of the channels allowing phonon transport . Similar to thin films, the roughness of the surfaces impacts surface scattering, and therefore thermal conductivity . Further experiments confirmed the importance of geometric parameters such as the filling fraction, surface‐to‐volume ratio, or the neck size, but also demonstrated that a further tuning of the thermal conductivity is possible with PnCs with random hole positions, by varying the hole overlap, i.e., the number and relative position of the phonon channels …”