# Phonons and Thermal Transport in Si/SiO\({}_{2}\) Multishell Nanotubes: Atomistic Study
## 1 Introduction  
Rapid miniaturization of electronic devices and increasing power consumption require an efficient heat management at nanoscale [1, 2]. Thermal properties of nanostructures and different methods of their optimization have been widely investigated both experimentally and theoretically [3, 4, 5, 6, 7, 8]. Phonon engineering, i.e., targeted modification of phonon modes in nanostructures to enhance their thermal [5, 9, 10], electrical [9] and optical properties [11, 12], manifests itself as a powerful tool for the optimization of nanoscale thermal transport [5, 9, 10]. Nanomaterials with high thermal conductivity (TC), such as graphene, are promising candidates as heat spreaders and interconnectors [13, 14, 15, 16], while nanomaterials with low thermal conductivity and high electrical conductivity can be used for thermoelectric applications. The efficiency of the thermoelectric energy conversion, figure of merit \(ZT\), is directly proportional to the electrical conductivity and inversely proportional to the total thermal conductivity: \(ZT=S^{2}\sigma T/\left(\kappa_{ph}+\kappa_{el}\right)\), where \(S\) is the Seebeck coefficient, \(\sigma\) is the electrical conductivity, \(T\) is the absolute temperature, and \(\kappa_{ph}\) and \(\kappa_{el}\) are the phonon and electron thermal conductivities, respectively. Acoustic phonons are the main heat carriers in bulk semiconductors at room temperature (RT) and above. Strong spatial confinement of acoustic phonons in nanostructures significantly changes phonon energy spectra as compared with the bulk case, resulting in a decrease of phonon group velocities [17, 18, 19, 20, 21, 22, 23]. The latter, in combination with an enhancement of phonon boundaryscattering, stipulates a reduction of the lattice TC in nanostructures in comparison with that in bulk materials [9; 17; 18; 20; 22]. A significant reduction of the thermal conductivity leads to an increase of \(ZT\), e.g., in Bi\({}_{2}\)Te\({}_{3}\) quantum-well structures \(ZT\) increases up to 13 times in comparison with the bulk value [24]. The silicon-based nanostructures are also prospective for thermoelectric applications despite the fact that bulk silicon is a poor thermoelectric with \(ZT\sim 0.01\) at RT [25]. [PERSON] et al. [26] and [PERSON] et al. [27] demonstrated that significant increase of \(ZT\) occurs in Si nanowires (NWs) due to suppression of phonon transport. Strong reduction of lattice thermal conductivity in cross-sectional modulated Si nanowires [28; 29; 30] may also lead to improvement of their thermoelectric efficiency as compared with bulk Si. A reduction of RT TC down to 1 Wm\({}^{-1}\)K\({}^{-1}\) was also reported for SiGe nanocomposite materials [31; 3]. It was shown [3] that a rise of the Seebeck coefficient is stronger than a possible increase of the electrical resistivity. Si-based nanotubes (NTs) are even more promising for thermoelectric applications due to a very large surface-to-volume ratio. It was shown in a molecular dynamics study [32] that RT thermal conductivity of Si NTs is as small as about 33 percent of that of Si NW with the same cross section area. In p-type Si NTs, a five-fold enhancement of \(ZT\) (\(ZT=0.34\) at 550 \({}^{\circ}\)C) was experimentally achieved as compared to the bulk counterpart [33]. Considerable advancements were also achieved in the methods of large-scale and low-cost preparation of Si NTs. A template-free preparation by an electrochemical method with in-situ surface modification of Si NTs was reported in Ref. [34]. In Ref. [35], a low-cost fabrication technology of vertically aligned Si NTs via a wet-etching process with controllable NT thickness was demonstrated. Besides thermoelectrics, the applications of Si-based NTs include biosensors, energy storage, photodetectors, optoelectronics and field-effect transistors [36; 37; 38; 39; 35]. Efficient engineering of the acoustic phonon energy spectrum is carried out in self-rolled micro- and nanoarchitectures [40].