Theoretical Thermal Conductivity of Periodic Two-Dimensional Nanocomposites
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Theoretical Thermal Conductivity of Periodic Two-Dimensional Nanocomposites Ronggui Yang and Gang Chen* Mechanical Engineering Department, Massachusetts Institute Technology Cambridge, MA 02139, U.S.A. ABSTRACT A phonon Boltzmann transport model is established to study the lattice thermal conductivity of nanocomposites with nanowires embedded in a host semiconductor material. Special attention has been paid to cell-cell interaction using periodic boundary conditions. The simulation shows that the temperature profiles in nanocomposites are very different from those in conventional composites, due to ballistic phonon transport at nanoscale. The thermal conductivity of periodic 2-D nanocomposites is a strong function of the size of the embedded wires and the volumetric fraction of the constituent materials. At constant volumetric fraction the smaller the wire diameter, the smaller is the thermal conductivity of periodic two-dimensional nanocomposites. For fixed silicon wire dimension, the lower the atomic percentage of germanium, the lower the thermal conductivity of the nanocomposites. The results of this study can be used to direct the development of high efficiency thermoelectric materials. INTRODUCTION Significant advances have been made for increasing the nondimensional thermoelectric figure of merit ZT by using nanostructures to improve or maintain the electron performance and concurrently reduce phonon thermal conductivity [1]. The two most prominent examples are Bi2Te3/Sb2Te3 superlattices and PbTe/PbSeTe quantum dot superlattices [2,3]. Recently, there is increasing interest in using complex nanostructures, for example nanocomposites, with the conjecture that the major contribution of ZT increase in the two reported material systems [2,3] is due to the thermal conductivity reduction. Another advantage of nanocomposites is the possibility to scale-up for large-scale production of thermoelectric devices in bulk form taking advantage of nanocale effects explored in superlattices and nanowires. So far, there are not many studies on the thermal conductivity of nanocomposites despite their importance in both thermoelectrics and thermal management of electronics. On one hand, the few theoretical models for thermal conductivity of composites taking into the account of the interface thermal resistance [4-7] cannot be valid at nanoscale due to the ballistic phonon transport. On the other hand, most studies of thermal transport in low dimensional structures or nanostructures have focused on thin films, semiconductor superlattices and nanowires. The motivation of this work is to develop a microscopic framework for thermal conductivity prediction of nanocomposites. The framework will be developed as a phonon particle transport model based on the previous studies [8-11]. Those studies have demonstrated that the thermal conductivity reduction in nanostructures is due to diffuse interface scattering. Therefore the classical size effect particle transport model is expected to be applicable to a wide range of nanostruct
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