尺寸效應對矽鍺材料熱傳現象影響之研究

An Investigation of the Size Effect on the Heat Transfer in Silicon and Germanium

康庭瑜(Ting-Yu Kang)

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(2010年)

https://doi.org/10.6342/NTU.2010.00894

摘要

本論文以蒙地卡羅法(MC)模擬工具研究半導體材料奈米結構之聲子傳輸現象。在求解聲子波茲曼方程式過程中，本質散射部份採用單一鬆弛時間近似法，而聲子性質方面則使用灰介質假設，並以實驗量測之色散關係來計算其平均性質；配合適當的材料介面物理模型與數值邊界條件，並利用存在於系統中的對稱條件來減少計算量。研究方向主要分為兩方面：一是針對矽-鍺奈米線複合材料，探討邊界與異質介面對熱傳之影響；二是探討尺寸效應對擴散熱阻的影響。
對於矽-鍺奈米線複合材料，研究發現若邊界或異質介面為完全粗糙，則介面密度主宰複合材料的熱傳能力，介面密度愈高，熱傳能力愈差；對於光滑介面，則同時受到不同材料之本質散射與介面密度的影響，因此存在一個臨界介面密度，在該臨界介面密度下熱傳導係數達到最小。另外，研究結果建議以較低導熱性材料作為連續熱傳主體，而較高導熱性材料作為內嵌奈米線，可得到較低的等效熱傳導係數。
在尺寸效應對擴散熱阻影響之的研究中，熱乃自一狹窄加熱線沿膜厚方向傳入一相對寬廣的矽薄膜材料，出口邊界乃給定一自由流及一定常熱對流熱傳係數。研究首先比較等向且固定熱傳導係數下之理論解析解與模擬解之差異，從中驗證程式的準確性與瞭解薄膜材料熱傳導係數的不等向性及溫度相依性對溫度分布之影響。接著比較塊材與奈米材料模擬解之異同，研究發現：由於奈米材料尺寸小於聲子平均自由路徑，聲子發生內部散射的機率較小，易向各方向傳達，因此在相同幾何比例下，奈米材料之擴散熱阻會高於塊材。本研究彰顯出擴散熱阻在奈米應用中的重要性。

關鍵字

蒙地卡羅法 ； 熱傳導係數 ； 奈米複合材料 ； 介面密度 ； 尺寸效應 ； 擴散熱阻 ； 熱對流傳導係數

並列摘要

The phonon transport phenomenon in solids was simulated via a Monte-Carlo(MC) simulator , which solves the phonon Boltzmann transport equation under the single mode relaxation time approximation and the gray medium approximation. Physical models for heterogeneous interfaces and numerical boundary conditions are properly designed and implemented. Most of all, we take advantage of the geometric symmetry that exists in a system to reduce the computational amount. We focus our work on investigating the effect of the heterogeneous interfaces and boundaries on the thermal conductivity of Si/Ge nanocomposites and the size effect on the spreading thermal resistance.
For Si/Ge nanocomposites, the investigation results indicate the thermal conductivity significantly reduces with increasing interface density when the interfaces are totally diffuse. When the interfaces are smooth, the thermal conductivities are dominated not only by the interface density but also the intrinsic properties of the components of composites. A critical density ratio is thus resulted with a corresponding minimum thermal conductivity. Furthermore, the investigation results also show that a lower thermal conductivity can be expected by using lower thermal conductivity material in matrix and the higher in wire.
For the size effect on the spreading thermal resistance, the simulated system is a silicon film heated by a narrow heating wire placed on the top surface of the film and cooled by the ambient atmosphere with a constant temperature and convection heat transfer coefficient on the bottom surface. Comparisons were made between the simulation results at micro-scale and the analytical solutions of the thermal diffusion equation as well as between films at micro- and nano- scales. The former verifies the importance of the anisotropy and temperature dependence of the film thermal conductivity. The latter shows an increased spreading-resistance fraction of the total film thermal resistance when the system is scaled down due to the ballistic behaviors of phonons. This paper reveals the importance of spreading resistance in applications at nanoscale.

並列關鍵字

Monte-Carlo simulation ； thermal conductivity ； nanocomposite ； interface density ； size effect ； spreading resistance ； convection heat transfer coefficient

參考文獻

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[4] M. G. Holland, 1963, Phonon Scattering in Semiconductor Form Thermal Conductivity Studies, Physical Review, 134, A471.