奈米複合材料聲子傳輸現象蒙地卡羅模擬法之研發

Development of a Monte-Carlo Simulator for Phonon Transport in Nanocomposites

蔡東峻(Tung-Chun 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(2009年)

https://doi.org/10.6342/NTU.2009.01563

摘要

本論文成功開發出一個模擬半導體奈米結構聲子傳輸現象之數值工具，該工具乃使用蒙地卡羅法(MC)求解聲子波茲曼傳輸方程式。在本質散射部份採用單一鬆弛時間近似法，而聲子性質的部份則使用灰介質假設，並利用實驗量測之色散關係來計算其平均性質。同時亦建立及設計了適當的材料界面物理模型和數值邊界條件，並利用存在於系統中的對稱性條件來減少計算量。
在論文中主要模擬矽/鍺超晶格薄膜和碲化鉛(PbTe)超晶格薄膜中的聲子傳輸現象，探討界面粗糙度、週期長度以及夾層厚度比對熱傳導的影響，並比較分析其與理論分析結果的異同。研究結果證實超晶格薄膜的熱傳導係數主要受界面粗糙度和界面密度(單位體積的界面面積)的影響，界面愈粗糙或界面密度愈大則熱傳導係數愈小，尤其是垂直熱流方向之界面，其影響程度比平行熱流方向之界面高出甚多。研究也發現當熱流方向平行膜平面時，會存在一具有最小熱傳導係數之夾層厚度比，此最小值緣自界面散射的影響，此影響使夾層的等效熱傳導係數不再等於其本質熱傳導係數，而是隨膜厚而改變。此外，比較理論分析中使用的假設與模擬工具的差異程度，可以解釋何以在超晶格薄膜垂直平面方向方面的熱傳傳導係數理論預測結果與模擬結果較為吻合，而在平行平面方向吻合性就較差。

關鍵字

蒙地卡羅法 ； 聲子傳輸 ； 灰介質假設 ； 界面粗糙度 ； 超晶格薄膜 ； 熱傳導係數

並列摘要

A Monte-Carlo simulator is developed for phonon transport in nanostructured semiconductors, which solves the phonon Boltzmann transport equation under the single mode relaxation time (SMRT) approximation and the gray medium approximation. Physical models for phonon transmission/reflection at heterogeneous interfaces and numerical boundary conditions are properly designed. Most of all, we take advantage of the geometric symmetry that exists in a system to reduce the computational amount.
In use of this MC solver, we investigate the phonon transport phenomena within Si/Ge and PbTe/PbTe superlattice thin films. The influences of the interface roughness, the superlattice period, and the layer thickness ratio on the phonon thermal conductivity are explored. The investigation results verify the thermal conductivity of superlattice thin films is strongly affected by the interface roughness and the interface density (interfacial area per volume). Especially, the influences of the interfaces perpendicular to the heat flow direction are much stronger than the parallel ones. Moreover, a minimum in-plane thermal conductivity is observed when the layer thickness ratio is varied with the superlattice period fixed. It arises from the influences of interface scattering on the layer thermal conductivity. Finally, it is found the analytic predictions and simulation results of the cross-plane thermal conductivity agree very well, but those of the in-plane thermal conductivity do not. It is explained by the discrepancies between the physical models in the analysis and in the simulation.

並列關鍵字

Monte-Carlo simulation ； phonon transport ； gray medium approximation ； interface roughness ； superlattice thin film ； thermal conductivity

參考文獻

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