Introduction to Nanoscale Thermal Conduction

Abstract

where the thermal flux, Q, is related to the change in temperature, T, along the direction of thermal propagation, z, through the thermal conductivity, κ. The thermal conductivity is a temperature dependent material property that is unique to any givenmaterial. Figure 1 shows the measured thermal conductivity of two metals Au and Pt and two semiconductors Si and Ge (Ho et al., 1972). In these bulk materials, the thermal conductivities span three orders of magnitude over the temperature range from 1 1,000 K. Temperature trends in the thermal conductivities are similar depending on the type of material, i.e., Si and Ge show similar thermal conductivity trends with temperature as do Au and Pt. These similarities arise due to the different thermal energy carriers in the different classes of materials. In metals, heat is primarily carried by electrons, whereas in semiconductors, heat moves via atomic vibrations of the crystalline lattice. The macroscopic average of these carriers’ scattering events, which is related to the thermal conductivity of the material, gives rise to the spatial temperature gradient in Eq. 1. This temperature gradient is established from the energy carriers traversing a certain distance, the mean free path, before scattering and losing their thermal energy. In bulk systems, this mean free path is related to the intrinsic properties of the materials. However, in material systems with engineered length scales on the order of the mean free path, additional scattering events arise due to energy carrier scattering with interfaces, inclusions, grain boundaries, etc. These scattering events can substantially change the thermal conductivity of nanostructured systems as compared to that of the bulk constituents (Cahill et al., 2003). In fact, in any given material in which the physical size is less than the mean free path, the carrier scattering events will only occur at the boundaries of the material. Therefore, there will be no temperature gradient established in the material and Eq. 1 will no longer be valid. Typical carrier room temperature mean free paths in metals and semiconductors are about 10 100 nm, respectively (Tien et al., 1998). Clearly, with the wealth of technology and applications that rely on material systems with characteristic lengths scales in the sub-1.0 μm regime (Wolf, 2006), the need to understand thermal conduction at the nanoscale is immensely important for thermal management and engineering applications. In this chapter, the basic concepts of 13