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Title: | 全頻聲子蒙地卡羅法開發 Development of a full-spectrum Monte Carlo simulation for phonons |
Authors: | Hao-Bo Huang 黃浩柏 |
Advisor: | 黃美嬌(Mei-Jiau Huang) |
Keyword: | 全頻,能量偏差蒙地卡羅法,擴散-彈道熱傳,介面熱阻,尺寸效應, full-spectrum,deviational energy-based Monte Carlo,ballistic-diffusive transport,interface resistance,size effect, |
Publication Year : | 2019 |
Degree: | 碩士 |
Abstract: | 本論文主要研究目的是建立一全頻蒙地卡羅模擬工具以及探討聲子在矽鍺單晶及單介面材料結構內所受尺寸效應之影響。於本論文中,我們首先驗證模擬工具的正確性,再進行模擬結果及模型理論預測之比較,以釐清其中物理機制。
數值模擬部分使用3D非結構性網格,以能量-基底偏差觀點求解聲子波茲曼傳輸方程式,聲子性質使用在文獻上實驗量測之材料色散關係且假設等向性材料,本質散射機制則使用Holland及Klemens的經驗方程式;利用定溫、絕熱及週期性邊界條件來模擬不同情況之熱傳情形。理論模型則包括單晶材料漫射-彈道熱傳模型及介面熱阻的理論模型,其中異質材料間之介面穿透模型則依據其介面為完全粗糙及完全光滑兩情況分別使用DMM及TMM處理。 對於單晶材料模擬結果,由於聲子發生彈道熱傳,使得邊界上溫度產生不連續溫降(升),且系統內溫度分布近邊界處呈非線性分布,其熱傳行為不再符合傳統傅立葉定律所描述。與理論模型相比,修正線性模型考慮不同頻率聲子對應有各自的局部溫度,其邊界熱阻預測與模擬結果趨勢上較吻合,且此模型所預測傳導熱阻也與模擬結果一致。分析不同尺寸波數聲子對於熱通量的貢獻,發現當尺寸下降時,中高波數聲子對於熱通量的貢獻越來越大;全頻溫度分析則顯示低波數及中高波數聲子分別呈彈道及擴散熱傳行為。 在具單介面的系統中,模擬結果顯示在矽鍺兩端邊界熱阻受尺寸長度影響很小,而介面熱阻隨尺寸長度下降而有逐漸上升的趨勢;與介面熱阻理論解相比,以局部平衡溫度差定義之熱阻雖恆為定值,但尚符合模擬結果。而由全頻熱通量密度,可得熱通量在不同系統長度下,會因兩材料所受本質與介面兩散射機制不同程度影響,其中介面散射又因所使用介面穿透模型不同,使得熱通量隨尺寸下降而有所增減。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/72448 |
DOI: | 10.6342/NTU201901125 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 機械工程學系 |
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ntu-108-1.pdf Restricted Access | 4.7 MB | Adobe PDF |
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