| Summary: | 碩士 === 國立臺灣大學 === 應用力學研究所 === 96 === In recent years, many researches on nanotube, nanowire, and superlattices have been carried out. In this thesis, we study the thermal conductivities of silicon and germanium at different index planes in the nanoscale. The simulation method used molecular dynamics simulation, and the governing equation is Hamiltonian equations of motion in classical Newtonian mechanics. The molecular initial position of a diamond unit cell structure is used for periodic boundary condition and expresses the infinite boundary crystal lattice arrangement by the limited bulk material. The molecular initial velocity is determined by Maxwell-Boltzmann distribution. Because silicon and germanium mainly belongs to three body potential for the covalent bonding and also the needs to consider the intermolecular bonding angle, we choose Tersoff potential to calculate covalent bonding intermolecular force and molecular acceleration. We obtain each molecular new position and the new velocity by the Velocity-Verlet integration method, and obtain the heat flux under the state of equilibrium. Through the different time evolution, we calculate the autocorrelation function from heat flux. Finally, we calculate the thermal conductivity by Green-Kubo formalism. We compare the thermal conductivities of silicon and germanium at different index planes.
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