單介面系統全頻聲子熱傳之研究

A Full-spectrum Investigation into the Phonon Flow in Single-interface Systems

蔡沛耕(Pei-Keng Tsai)

指導教授 ： 黃美嬌

國立臺灣大學/工學院/機械工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202100528

摘要

本論文利用全頻聲子蒙地卡羅法研究單介面結構的穩態微觀熱傳性質，包括由矽/矽組成的同質結構及由矽/鍺組成的異質結構。藉由改變材料長度，系統性地探討不同尺寸下彈道-擴散熱傳效應、非彈性散射與介面穿透率對溫度分布與熱通量的影響。研究發現彈道熱傳使材料與邊界熱槽溫度不連續，介面穿透率導致小尺寸的矽與鍺展現迥異於單一材料的全頻熱通量，而非彈性散射讓全頻熱通量頻譜更為平滑，並稀釋介面穿透率的影響。介面熱阻在同質結構中隨尺寸先降後升，在異質結構中則隨尺寸單調下降。
同步我們提出一個適用於單介面結構的理論模型-全頻線性模型，以彈道熱傳描述邊界熱通量，再利用塊材聲子分布推導材料內部與介面之熱通量，在假設熱通量詳細守恆的情況下，求得全頻熱通量密度與全頻溫度。此模型可用以描述聲子彈道-擴散熱傳現象，並在系統尺寸極大時趨近塊材理論之結果、尺寸極小時與彈道熱傳的熱通量吻合；不同於模擬結果，此模型預測介面熱阻與尺寸無關。同質介面的全頻熱通量與模擬結果吻合，異質介面的預測值則與完全彈性散射的模擬結果吻合。在預測溫度分布方面，同質介面獲得較佳的結果，準確度隨尺寸提升，而異質介面中矽區的溫度分布較準確，鍺只有在大尺寸時誤差較小。
模擬與模型結果都指出在相同邊界條件下，尺寸越大的系統熱傳越依賴較低頻的聲子，系統中含有鍺也會對小尺寸矽的熱通量產生選擇性抑制作用，本研究成果有助於設計多尺寸結構以達成低熱傳導係數之目標。

關鍵字

彈道-擴散熱傳 ； 聲子蒙地卡羅法 ； 全頻 ； 矽鍺 ； 線性模型 ； 尺寸效應

並列摘要

In this thesis, a full-spectrum phonon Monte Carlo simulation method is utilized to investigate the nanoscale, steady thermal properties in single-interface structure. A homogeneous structure made of Si/Si and a heterogeneous structure made of Si/Ge are covered. By changing the materials’ length, we look into the effect of ballistic-diffusive heat transfer, inelastic scattering and interfacial transmissivity on the temperature distribution and heat flux of the system. Ballistic effect causes temperature jump between the system and the boundary thermal reservoirs. The interfacial transmissivity leaves Si/Ge structure a distinguished spectral heat flux from the homogeneous case. Inelastic scattering however, reduces the effect of transmissivity and makes the spectral heat flux smoother. The simulated interfacial resistance drops before rising with the system length in homogeneous structures, while monotonically decreases in heterogeneous structures.
We also propose a theoretical model to account for the single-interface system. The model incorporates the concept of detailed energy balance and spectral temperature that characterizes phonons of different frequencies. This model is consistent with both diffusive heat transfer in large-scale limit and ballistic heat flux in small-scale limit. Different from simulation result, the model interfacial resistance is constant for all system length. The predicted spectral heat flux of the homogeneous structure coincides with the simulation result, while in the heterogeneous case, the model predictions only meet the results of simulations that only include elastic scatterings. The model predicts temperature distributions better in Si/Si than in Si/Ge, and it becomes more accurate for longer system.
Both simulation and model point out that heat transfer within larger systems relies on phonons with lower frequency, and how Ge suppresses the heat flux in Si depending on the system length. This research helps to develop multiscale structures to achieve lower heat conductivity.

並列關鍵字

ballistic-diffusive heat conduction ； phonon Monte Carlo ； full-spectrum ； silicon ； germanium ； linear model ； size effect

參考文獻

1. N. Jaziri, et al., A comprehensive review of Thermoelectric Generators: Technologies and common applications. Energy Reports, 2019.

2. H. S. Kim, et al., Relationship between thermoelectric figure of merit and energy conversion efficiency. Proceedings of the National Academy of Sciences. 112(27): p. 8205, 2015.

3. J. Ravichandran, et al., Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices. Nature Materials. 13(2): p. 168-172, 2014.

4. J. Maire, et al., Thermal conductivity reduction in silicon fishbone nanowires. Scientific Reports. 8(1): p. 4452, 2018.

5. T. Oyake, et al., Ultimate Confinement of Phonon Propagation in Silicon Nanocrystalline Structure. Physical Review Letters. 120(4): p. 045901, 2018.