| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 107 === In this thesis, a full-spectrum energy-based deviational Monte Carlo simulation tool was successfully developed and employed to investigate the size effect on the thermal properties of Si/Ge crystal at nanoscale. The phonon Boltzmann transport equation was solved based on a bulk dispersion relation and the Holland’s and Klemens’s empirical relations for impurity and Umklapped scatterings respectively. The diffuse mismatch model (DMM) and the The thermal mismatch model (TMM) were adopted to handle the phonon responses when they hit a heterogeneous interface. The simulation tool was first verified by comparing its simulation results with theoretical predictions of classical problems; physical mechanisms were discussed about the observed small differences.
For single crystal materials, due to the ballistic behaviors of phonons, temperature jumps occur at the boundaries and the nonlinear temperature profile is observed near the boundaries/interfaces. These phenomena can no longer be described in accordance with the Fourier’s conduction law. Instead, a modified linear model which assumes phonons of different frequencies possess different local equilibrium temperature predicts well with the variation trend of the boundary thermal resistance but fails to capture the nonlinear characteristic. Spectral heat flux densities are therefore also explored to understand the influence of the ballistic transport. It is found as the size decreases, ballistic phonons of medium- and high-wavenumber increase and so are their contribution to the heat transfer.
When a single heterogeneous (Si/Ge) interface exists in the system, the simulation results show that the thermal boundary resistances of both ends are nearly independent of the system size. The resistance of the interface gradually increases with decreasing size on the other hand. The theoretical predictions by DMM and TMM are size-independent, but are of about the same order in magnitude.
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