Calculation of Confined Phonon Spectrum in Narrow Silicon Nanowires Using the Valence Force Field Method

Abstract

We study the effect of confinement on the phonon properties of ultra-narrow silicon nanowires of side sizes of 1 10nm . We use the modified valence force field method to compute the phononic dispersion, and extract the density of states, the transmission function, the sound velocity, the ballistic thermal conductance and boundary scatteringlimited diffusive thermal conductivity. We find that the phononic dispersion and the ballistic thermal conductance are functions of the geometrical features of the structures, i.e. the transport orientation and confinement dimension. The phonon group velocity and thermal conductance can vary by a factor of two depending on the geometrical features of the channel. The <110> nanowire has the highest group velocity and thermal conductance, whereas the <111> the lowest. The <111> channel is thus the most suitable orientation for thermoelectric devices based on Si nanowires since it also has a large power factor. Our findings could be useful in the thermal transport design of siliconbased devices for thermoelectric and thermal management applications.

Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation

“…These findings agree qualitatively well with diffusive phonon transport calculations that indicate the superiority of the thermal conductivity of the {110}/<110> channel over other geometries, and the low thermal conductance for the {111}/<110> and {112}/<111> channels [24]. They also agree with calculations for Si NWs, which indicate the beneficial <110> transport orientation to heat transport, compared to other orientations [38][39][40]. When it comes to comparing to experimental results, however,unfortunately we could not identify any works in the literature that perform systematic thermal conductivity measurements in such ultra-thin layers (H < 16 nm) and in various confinement and transport orientations.…”

“…H = 2 nm, and even then, they are small. We note that also in the case of Si nanowires, our previous work has demonstrated a similar result, namely that even for nanowires with cross section sizes down to H = 6 nm, the density of states is orientation independent [40]. From this we conclude that the variation in the thermal conductance and transmission does not originate from the difference in the density of states.…”

“…The thermal conductance for channels with {112} surface is shown in Fig. 3-d [38][39][40]. A similar conclusion was found for thin layers of larger sizes [24].…”

Thermal conductivity of silicon nanomeshes: Effects of porosity and roughness

“…The use of bulk phonon dispersion was shown to be a valid approximation for describing phonon transport in nanostructures of feature sizes down to several nanometers at room temperature [27]. The phonon bands could change significantly at the nanoscale, but this is the case for channels with ultra-thin feature sizes [28], which in this work we do not consider. We include the longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches.…”

A coherent phonon pulse model for transient phonon thermal transport

“…(1). In addition, we do not differentiate acoustic and optical phonons since they are no longer relevant in nanostructures due to the phonon dispersion modification [42]. Hence, the displacement of the 2nd atom is not controlled, but solved in the simulation according to the equation of motion.…”