本研究的目的是希望藉由探討有機導電高分子（organic conducting polymers, CPs）聚3, 4-二氧乙基噻吩（poly-3,4-Ethylenedioxythiophene, PEDOT）及其衍生物之結構，尋找提高其熱電優質方法，以替代目前熱電材料。當前普遍採用的熱電材料，多數為貴重稀有金屬（例如：鉍鍗化合物Bi2Te3），雖其轉換效率在常溫較高，但使用稀有金屬材料卻有高成本、高污染、回收不易的風險，且來源受某些國家控制；因此在這裡選擇使用低成本合成、地球含量豐富且具較低熱傳導率之聚噻吩導電高分子來作為熱電材料的研究對象，希望能達到替代稀有材料、降低材料成本、提升熱電性能等目標，並藉此提高台灣本土材料的供應優勢及競爭潛力。
影響熱電材料效能的因素包括：電子傳導率（electrical conductivity）、席貝克係數（Seebeck coefficient）及熱傳導係數（thermal conductivity）等，這些性質皆隨著材料的電子態密度分布（density of state, DOS）與聲子頻散關係（phonon dispersion relation）而改變。本研究將使用第一原理的密度泛函理論（density functional theory, DFT），並配合平面波與周期性邊界條件建立與模擬聚3, 4-二氧乙基噻吩分子結構，再以密度泛函微擾理論（density functional perturbation theory, DFPT）計算取得聲子頻散關係等性質參數。
進行完第一部分的模擬計算後，將獲得的各項參數代入波茲曼傳輸方程式（Boltzmann transport equation），推導出熱電材料之電子傳導率、熱傳導係數、席貝克係數等，最後便可得到用以評斷熱電材料運作效能的熱電優值ZT （figure of merit）。結果顯現，將導電高分子聚3, 4-二氧乙基噻吩及其衍生物(如PEDOT ─ OCH3、PEDOT ─ CH3、PEDOT ─ Br等)各種性質進行比較與探討，結論為取代基Br之聚噻吩衍生物具有較佳的熱電性能，ZT值上亦相對有最好表現，因此，此衍生物可做為未來設計新熱電材料之參考，亦為本研究團隊在全世界高變競爭中，由電子軌域構造首創之新型材料構思。

This study focuses on investigating the structure of organic conducting polymers ─ poly-3,4-Ethylenedioxythiophene (PEDOT) and compare the resulting figure of merit (ZT) against the PEDOT derivatives, such as PEDOT ─ OCH3, PEDOT ─ CH3, PEDOT ─ Br, and so on. This initiative will provide the opportunity to replace rare and expensive materials. By using PEDOT, the supply of materials can be guaranteed without shortages, a reduction of material costs and the enhancement of the thermoelectric performance is potentially achievable.
Some factors which influence the efficiency of thermoelectric materials include; the electrical conductivity, Seebeck coefficient, and thermal conductivity, among others. All of these properties are dependent on the density of states (DOS) of electrons and phonon dispersion relations. In addition, these properties will also vary with different materials. In this research, we use the method of density functional theory (DFT) with plane wave and periodic boundary condition to build and simulate the PEDOT molecular structures. Following the geometry optimizations, we then proceed to determine the phonon dispersion relations and the phonon density of states from the density functional perturbation theory (DFPT).
After the previously mentioned simulation results have been obtained, these calculated properties are input into the Boltzmann transport equation to obtain key properties such as the of Figure of Merit (ZT). Afterwards, the ZT values obtained from the different PEDOT derivatives are compared. A greater ZT indicates a greater thermoelectric efficiency. From the results, it can be seen that the derivative, PEDOT ─ Br may display a better performance than the PEDOT counterparts and can serve as the design reference for new thermoelectric materials of thermoelectric devices. This thesis initialized the new design method to propose new materials via molecular orbital design.

摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VIII
參數定義 IX
第一章 緒論 1
1.1前言 1
1.2 熱電材料原理簡介 6
1.2.1 Seebeck effect 6
1.2.2 Peltier effect 6
1.2.3 Thomson effect 7
1.2.4 熱電優值係數（Figure of Merit） 7
1.3有機導電高分子簡介 8
1.4有機導電高分子熱電材料文獻回顧 12
1.5研究動機與目的 14
第二章 固態物理理論與波茲曼傳輸方程式 16
2.1 前言 16
2.2 密度泛函理論 17
2.2.1 Hohenberg-Kohn定理 17
2.2.2 Kohn-Sham系統 19
2.2.3交換相關泛函 20
2.2.4 平面波與週期性結構系統 22
2.2.5 贗勢與超軟贗勢 22
2.2.6自洽場計算 24
2.3線性微擾近似法 26
2.3.1動力矩陣計算 27
2.3.2微擾自洽場計算 30
2.3.3離散傅立葉轉換 30
2.3.4聲子熱傳導係數 32
2.4 一維波茲曼傳輸方程式 33
2.4.1波茲曼傳輸方程式 33
2.4.2 電子相關參數 38
第三章　系統模型建構與模擬方法 41
3.1 模擬計算流程 41
3.2 模擬模型建立 42
3.2.1 聚3, 4-二氧乙基噻吩 42
3.2.2 聚3, 4-二氧乙基噻吩衍生物-推拉電子基 44
3.3 計算參數設定 47
第四章 模擬計算結果與討論 49
4.1導電高分子模擬參數設定最佳化 49
4.2聚3, 4-二氧乙基噻吩衍生物之模擬 54
4.2.1 電性分析 54
4.2.2 熱性分析 58
4.2.3熱電參數分析 60
第五章 結論與未來工作 63
5.1結論 63
5.2未來工作 64
參考文獻 66

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