4.2.3 Remarks

Finally, it is worth mentioning that this chapter focused on the influence of bandstructure on the anisotropic behavior of the thermal transport properties of ultra-thin silicon layers and ultra narrow silicon nanowires. The accurate phonon bandstructures is employed, but a rather simplified ballistic transport formalism is utilized, which ignores the effects of phonon scattering. The intent, here, is to provide a qualitative indication of the anisotropic behavior of phonon transport in thin layers. Employing atomistic phonon bandstructures and a fully diffusive transport formalism that accounts for the energy, momentum, and bandstructure dependence of each scattering event will be the topic of the subsequent chapter.

Our results, however, point out that a factor of two in phonon transport can be achieved once the channel geometry is optimized. These results agree qualitatively well with diffusive phonon transport calculations that indicate the superiority of the thermal conductivity of the $\{110\}/\textless110\textgreater$ channel over other geometries, and the low thermal conductance for the $\{111\}/\textless110\textgreater$ and $\{112\}/\textless111\textgreater$ channel [112]. They also agree with calculations for silicon nanowires, which indicate the beneficial $\textless 110\textgreater$ transport orientation to heat transport, compared to other orientations [111,107,113]. 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 ( $H<16~\mathrm{nm}$ ) and in various confinement and transport orientations. Most experimental works on thermal conductivity consider relatively thick layers of thicknesses in the range of several 10 to several 100 of nanometers and primarily on $\{100\}$ layers. In thicker layers the phonon modes are almost bulk-like and one cannot observe the anisotropic phonon confinement effects that lead to bandstructure modifications and conductance variations. In addition, the influence of various scattering mechanisms make the thermal conductivity of thicker layers more isotropic, and hide the results of bandstructure anisotropy (that ballistic simulations fully capture).

Our findings, however, are useful in understanding phonon transport in ultra-thin silicon layers, and with regards to applications, could provide guidance in either maximizing thermal conductivity as in the case of thermal management, or minimizing it as in the case of thermoelectrics. For example, for electronic applications, we mention that for $p$ -type nanoelectronic channels, transport in the $\{110\}/\textless110\textgreater$ orientation is beneficial compared to other orientations [114,115]. This is also the case for the power factor of thermoelectric devices [116]. In the former case, however, for electronic devices large thermal conductivity is necessary in order to remove the heat from the device, otherwise the mobility is degraded. The large thermal conductivity of the $\{110\}/\textless110\textgreater$ channel, therefore, could be advantageous for $p$ -type electronic devices. In the latter case, for thermoelectric devices channels with low thermal conductivity are needed in order to reduce losses and increase thermoelectric efficiency. The large thermal conductivity of the $\{110\}/\textless110\textgreater$ channel, therefore, could counteract the benefit of its larger power factor, and this channel might not be the optimal for thermoelectric $p$ -type silicon devices.