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Multiscale Nondiusive Heat Transfer in Dielectric Materials

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With the progress of nanotechnologies for microelectronic and thermoelectric devices, a lack of understanding of the heat transfer in nano-/micro-scale creates the bottleneck for the applications. Although Fourier's law is able to describe the heat transfer in macroscale, it breaks down in nano-/micro-scale due to the nondiffusive heat transfer, which is still not well understood. Consequently, the objective for this thesis is to achieve a fundamental understanding of nondiffusive heat transfer.

Phonon is a quantum mechanical description of lattice oscillations, and it is the main heat carrier in insulators and semiconductors. When the system sizes are comparable or even smaller than the mean free path (MFP) of phonons, the heat transfer becomes nondiffusive due to the contribution from ballistic phonon transport. The phonon-mediated heat transfer in nanosystems and their interfaces is very complicated. In this thesis, we mainly focus on three problems: (1) there lacks a criterion to evaluate when Fourier's law breaks down; (2) the size-dependence of thermal interface resistivity is not clearly captured; (3) the ballistic heat transfer has not been directly observed at room temperature.

Accordingly, there are three goals for this thesis: (1) to find the criterion which is able to identify when Fourier's law breaks down; (2) to characterize how interface resistivity changes with the hotspot size; (3) to seek the possibility of a direct observation of ballistic heat transfer at room temperature.

To achieve the first goal, a criterion is proposed based on the nondimensional parameter defined in the Two-Parameter Heat Conduction (TPHC) model, to predict the breakdown of Fourier's law. The physical interpretation of this nondimensional parameter is a product of the nondimensional diffusive phonon MFP and ballistic phonon MFP. To validate this criterion, both Fourier's law and the TPHC model are analytically or numerically solved for multiple experiments on different materials. These experiments include the one-dimensional and two-dimensional transient thermal grating (1D/2D TTG) experiments on silicon and gallium arsenide, and the metallic grating (MG) experiments on sapphire. The comparison results indicate that this criterion is able to identify the breakdown of Fourier's law.

To achieve the second goal, the TPHC model and the enhanced gray Boltzmann transport equation (EG-BTE) are numerically solved on the MG experiments by finite difference method and lattice Boltzmann method, respectively. Current study of the interface resistivity is based on Fourier's law, which fails to decouple the size-dependence of the thermal conductivity (material thermal property defined by Fourier's law) and the interface resistivity. While the TPHC model and EG-BTE are able to exclude the size-dependence of the thermal conductivity, and thus extract a clean size-dependence of the interface resistivity. Based on these two models, a monotonically change of the interface resistivity with the size of interface is captured, which is different from but more reliable than the results by Fourier's law.

To achieve the third goal, we focus on the thermal wave, the direct evidence of ballistic heat transfer. Although ballistic heat transfer is believed to be the cause of nondiffusive heat transfer, so far only the deviation from prediction by Fourier's law is reported as the evidence of nondiffusive heat transfer at room temperature. To study the thermal wave, the EG-BTE is applied on the thermal wave experiments in cryogenic crystal. In these cases, the EG-BTE is numerically solved by an in-house numerical scheme developed called the discrete ordinates method for phonon transport, which is validated by other theoretical study in this thesis. The results are compared with the experiments and indicate a successful reproduction of the thermal wave. Based on the proved capability of describing the thermal wave, the EG-BTE is extensively applied to identify the length and time scale to observe the thermal wave at room temperature.

In conclusion, the criterion proposed in this thesis facilitates the choice of models between the efficient Fourier's law and the accurate nondiffusive models, benefiting the engineering use in multiscale situations. Secondly, the monotonic behavior of interface resistivity offers new insights of the physics of nondiffusive heat transfer across the interface. At last, the prediction of the thermal wave at room temperature provides potential guidance for the design of experiments to directly observe the thermal wave at room temperature, opening up a new gate to study the unique features of the ballistic heat transfer.

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