具奈米結構半導體材料熱傳導性質之蒙地卡羅模擬研究

Thermal Conductivity of Nanostructured Semiconductors: Analysis and Monte-Carlo Simulation

劉亮君(Liang-Chun Liu)

指導教授 ： 黃美嬌

國立臺灣大學/工學院/機械工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.10741

摘要

歸功於奈米工程的進步，近幾十年來，熱電技術在效益上獲得了極大進展，並進而受到學界及業界的矚目。實驗顯示，奈米結構（例如奈米管及超晶格）可使材料獲得較塊材更低之熱傳導性質，而此低熱傳導性可提高熱電材料效益。其原因為，聲子為半導體材料中之主要熱載子，而奈米結構可阻礙聲子傳遞，進而造成更低之熱傳導性。
本論文研究在奈米尺度下，矽孔隙材料以及具曲度之奈米管的熱傳導特性。首先，對多孔矽材，本文提出一近似模型，用以預測具陣列孔之多孔矽材熱傳導性質。本模型同時考慮聲子之擴散及彈道傳導機制，並適用於塊材及具奈米尺度特徵之材料。而幾何特徵對熱傳導特性的影響，則是藉由與幾何相關之孔隙函數與視角因數而引入。模型預測值接著與蒙地卡羅法模擬而得的熱傳導值做比較。測試例為兩種特徵尺寸（100 nm與500 nm）及數種孔隙率（0.05~0.31）。結果顯示，模型預測和模擬結果相當符合，而其關鍵在於是否對聲子平均自由徑做正確模擬。而對於彎曲之奈米管，本文引界了一新參數—管曲率。模擬結果顯示，除了已知之影響參數（管徑及表面粗糙度）外，管曲率亦會降低矽奈米管之有效熱傳導係數。舉例來說，一曲率半徑為30 nm之粗糙奈米管，其熱傳導係數只達其直管狀態下之百分之八十。

關鍵字

熱電效應 ； 聲子傳遞蒙地卡羅法 ； 擴散極限 ； 彈道極限 ； 幾何效應

並列摘要

Thermoelectrics receives great attention in the past decades because its efficiency barrier has been broken by the recently advanced nanoengineering. Nanostructures such as nanowire and superlattice are shown to have remarkably low thermal conductivity than their bulk counterparts, and this property is particularly favorable to the design of highly efficient thermoelectric (TE) devices. Encouraged by the TE advances since 1990, much experimental and theoretical research toward novel nanostructures of low thermal conductivity is currently undertaken.
This thesis explores the structure-dependent thermal conductivity of nanosized silicon porous materials and curved silicon nanowires. First, an approximate model is proposed to predict the thermal conductivity of porous silicon with aligned pores. This model, by taking both diffusive and ballistic transport mechanisms into consideration, is suitable for bulk as well as nanoscale materials. The effects of geometry are accounted for by introducing the geometry-dependent porosity functions and view factors. We also compared the model predictions with Monte Carlo simulation data under two pore characteristic sizes (100nm and 500nm) and various porosities (0.05~0.31). The agreement between the model predictions and the simulation results is excellent if the phonon mean free path is properly modeled. Next, a new factor, the wire curvature, is introduced for the nanowire case. In addition to the wire thickness and surface roughness, curvature is shown to decrease the effective thermal conductivity in nanoscale. For instance, a rough nanowire of curvature 30 nm has 80% thermal conductivity as compared with its straight counterpart.

並列關鍵字

thermoelectric ； phonon transport ； Monte Carlo method ； diffusive limit ； ballistic limit ； geometric effect

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