隨著經濟發展，能源的產生及使用成為了一個日漸重要的課題。其中，熱電材料是一個極具前瞻性的能源材料。「輕薄短小」為目前科技發展趨勢，對熱電材料來說，縮小尺度也可以增加其熱電轉換效率。本研究由計算量子力學出發，模擬奈米尺度熱電材料的熱傳情形，並透過計算分析得到材料的熱電相關性質，進而算出熱電優值（Figure of Merit, ZT），並依此數值評估一個熱電材料的優劣與否，之後再透過改變元素配比、摻雜以及改變結構的方式達到熱電優值的最佳化。
　　模擬材料方面，由於現今熱電晶片大多使用稀土元素，本研究利用矽、鍺等較豐富的元素建構無機奈米線，先透過模擬塊材矽與實驗數據比對，確認計算方法的準確及適用性後，再開始計算奈米線。透過建立分子模型，以Kohn-Sham定理、平面波基底(Plane Wave Basis)、自洽場方法做幾何結構最佳化。接著以二、三階密度泛函微擾理論(Density Functional Perturbation Theory, DFPT)計算出奈米線的聲子頻散圖和聲子態密度圖等熱性相關圖表，再分析得到聲子群速度、熱容量、鬆弛時間後推得聲子熱傳導係數。電性方面，我們以密度泛函理論求得材料的能帶結構以及電子態密度圖，接著帶入一維波茲曼傳輸方程式(Boltzmann Transport Equation, BTE)，搭配人工摻雜的概念求得電子傳導率、電子熱傳導率以及席貝克係數。最後，依據以上第一原理計算結果，計算出矽鍺奈米線之熱電優值。
　　研究結論為無論奈米線是何種結構，低頻聲子主宰著材料熱傳；矽鍺核殼結構的奈米線則最能有效阻絕聲子的傳輸，因而擁有最低的聲子熱傳導率，並且在相同直徑的情況下，奈米線的熱傳導率隨著鍺殼厚度的增加而下降。

As the economic develops, the production and usage of the energy has become an increasing important issue. Thermoelectric materials are one of the most promising energy material. At the same time, light and low dimension are the ways that technology develops nowadays. For thermoelectric materials, the reduction of the scale can also lead to higher conversion efficiency. We use computational quantum mechanics to simulate thermoelectric materials in nanoscale, and obtain their thermal and electrical properties, and then finally calculate the figure of merit to find out whether it is a good thermoelectric material. In the end, we aim to optimize the figure of merit by changing the composition, structure and doping.
As a result of the commercial materials nowadays are rare and expensive, we choose silicon and germanium to set up our model. The study uses Kohn-Sham equation, plane wave basis and self-consistent field to optimize the model. After that, density functional perturbation theory (DFPT) is employed to calculate the phonon dispersion relation and phonon density of states, which can be further analyzed to achieve the group velocity, heat capacity, phonon relaxation time and finally the thermal conductivity. Next, we use density functional theory (DFT) to calculate the band structure and the density of states. Implementing the above parameters into the Boltzmann Transport Equation (BTE) and artificial doping, the electrical properties can be calculated.
In conclusion, no matter what the structure the nanowire is, low frequency phonons dominate the heat transfer, while the silicon core germanium shell nanowire leads to the lowest thermal conductivity, and the thermal conductivity decreases with the increasing thickness of the germanium shell at the same nanowire diameter.

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