An extensive and detailed description of heat conduction at the micro- and nano-scale is presented. During the last two decades this phenomenon has become very attractive to study because of the shrinking in size of thermoelectric technologies and electronic devices. These newer technologies are at the micro- and nano-scale. Due to the small size, a power dissipation problem has presented itself in these applications. The proper thermal performance is related with the performance of the technology. Because of these facts a description of the thermal transport in different materials at these scales is required. This problem is important because understanding the energy transport will allow engineers to design faster electronic devices and more efficient thermoelectric applications.
For macro-scale it is known that diffusive behavior is presented in heat conduction; here models that show different behavior than diffusive such as wave-like are presented. One extra tool to understand heat conduction is to calculate the thermal conductivity. Equilibrium molecular dynamics combined with the Green-Kubo formula can be used to calculate the thermal conductivity of materials such as germanium and carbon. The foundation of this calculation is extracting the heat current from the results, and implementing it into the Green-Kubo formula. This work considers all formulations from the literature that calculate the heat current for the Tersoff potential, the interatomic potential most applicable to semiconductor materials. The formulations for the heat current are described, and results for germanium and carbon are presented. The formulations are compared with respect to how well they capture the physics of the Tersoff potential and how well the calculated value of the thermal conductivity reflects the experimentally-measured value.
The second part of this work deals with heat transport in low dimensions at the nano-scale. The energy transport in a two dimensional graphene sheet is studied and compared to that in a one dimensional chain. The equations of motion for each individual atom of the sheet are solved numerically to generate the distribution of kinetic energy in the structure. The distribution of kinetic energy in the sheet shows two different characteristics of the transport. The components of frequency of the kinetic energy in the graphene structure are identified. The components allow the identification under which potential more low frequency carriers are expected. The presence of chaos in the graphene sheet using the anharmonic potential is identified. Finally, conclusions and recommendations for the study of heat conduction at the nano-scale are presented.