多孔材料在工程上一直具有相當重要的應用，其中低熱傳導係數特性使其應用在許多絕熱的情形，例如作為CMOS絕緣層的多孔矽。隨著微奈米技術的發展，也相繼提出多孔矽材料的新興應用，如低維度熱電材料、熱整流等，然而在孔洞間距過小時，此時熱傳輸的過程因受到尺寸效應及量子效應影響而不再符合巨觀熱傳導理論，當特徵長度小於熱載子的平均自由路徑時，此時是以彈道傳輸的方式而非巨觀的擴散傳輸。微觀熱傳理論透過將熱載子視為粒子，在固體中以聲子散射來討論微觀熱傳，可利用波茲曼方程式來描述聲子運動行為。
本文使用聲子波茲曼方程式來分析微觀尺度下的熱傳行為，以有限元素法與離散座標法來求解，探討多孔矽的熱傳現象。首先以二維薄膜與單位孔洞的模型與文獻結果作驗證，而因孔洞結構與塊材之間存在一過渡區域，其為受孔洞結構影響的區域，分析得到在不同結構厚度、塊材長度及材料參數下，皆不影響此過渡區長度。接著以對稱孔洞模型與多孔理論模型比較，並分析整齊排列與交錯排列的差異，與理論模型結果比較得到熱傳導係數的誤差小於20 %且隨著孔隙率變化具有相似的趨勢。
最後探討非對稱多孔矽之熱傳性質，分析在孔隙率與孔徑相同的條件下，以不同間距的疏密排列形成非對稱的結構，發現在疏密程度增加時，熱傳導係數會降低，此時理論模型已無法適用。由其熱傳率分布可發現，當孔與孔的間隔小於50 nm時，聲子散射的路徑會受到鄰近孔洞的影響，造成較低的區域熱通量，使熱傳導係數降低。研究發現利用等效熱阻串聯的方式來計算非對稱多孔結構之熱傳導係數在非對稱性小的結構是適用的，但當呈現較大的非對稱性時將不適用。

Porous silicon has tremendous applications in different engineering fields, especially its low thermal conductivity property which can be used as insulated materials. Besides, such low thermal conductivity also has potential applications in thermoelectric materials and thermal rectification. When it comes to small size scale, that is, when the characteristic length is smaller than the mean free path of the heat carrier, the description of conventional heat conduction is no longer applied due to the size effects and the quantum effects. Heat conduction in solids can be considered as the propagation of quantized energy due to lattice vibration called phonons. The transport behavior of phonons can be described using the Boltzmann Transport equation.

In our study, the phonon Boltzmann transport equation is solved using Finite Element Method and Discrete Ordinates Method to simulate the thermal behavior of nano porous silicon films. First, we study the two dimensional thin film and unit cell structure of silicon and discover a transition zone between the porous structure and the bulk material where the heat transport is affected by the pores. The numerical results show that the length of transition zone is independent of porous structure length and bulk material length. Then, we consider symmetric porous silicon with aligned and staggered pores. The simulated thermal conductivities are compared with the results from theoretical models for different porosities. The deviations are less than 20% .

Finally, we discuss the thermal properties of asymmetric porous silicon with different porous density distributions. Consider that the porosity and pore diameter are constants, the numerical results show that as the porous density increases, the thermal conductivity will decline. As the separation between pores becomes smaller than 50 nm, pores will have increasingly impact on the propagation of phonon scattering. Using the thermal circuit concept, the thermal conductivities of asymmetric porous materials can be modeled by thermal resistance in series connection, but the results will have large deviation for large asymmetric cases.

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