Size Dependence Of Thermal Conductivity For Nanowires

With the rapid development of industry, environmental pollution and energy crisis are becoming more and more serious in the world today. It is extremely urgent to explore new environmentally energy. Thermoelectric material is one kind of important energy conversion material. The figure of merit is an important index to evaluate thermoelectric performance. The excellent thermoelectric efficiency is described by the high thermoelectric figure of merit. It shows that the effective way to increase the figure of merit is to reduce the thermal conductivity. Silicon is the widely used material in the semiconductor industry with a low-cost and mature manufacturing process, so it has been considered as a promising thermoelectric material. The thermoelectric property of bulk silicon is very low because of high thermal conductivity. Fortunately, it is found that nanometer treatment can significantly reduce the thermal conductivity of silicon. Therefore, silicon nanowires(SiNWs) have already attracted considerable attention in recent years.The size(length and diameter) of nanowires plays an important role in the heat transport of phonons. As an efficient way to modulate the thermal conductivity, the size effect has important significance. We solve the Boltzmann transport equation(BTE) under the relaxation time approximation by incorporating the direction-dependent phonon-boundary scattering, and study the size dependence of thermal conductivity for pure Si NWs and Si1-xGex NWs. It is demonstrated that phonon-boundary scattering is critical to the size dependence of thermal conductivity for nanowires. With the increase of specularity parameter, the length dependence is getting stronger and the diameter dependence is getting weaker for thermal conductivity of nanowires. Due to the severe suppression of high-frequency phonons by alloy scattering, the low frequency phonons in Si1-xGex NWs nanowires have a much higher contribution to the thermal conductivity than pure Si NWs. Since the low frequency phonons have long mean free path(MFP) and the specularity parameter at lateral boundaries is very close to 1, the low frequency phonons exhibit more ballistic characteristics. This results in a stronger length-dependent and weaker diameter-dependent thermal conductivity in Si1-xGex NWs compared with pure SiNWs.The research in this paper is helpful not only to understand the phonon transport of low dimensional materials in theory, but also to modulate thermal conductivity of nanowires by phononic engineering in application.