本論文使用時間獨立密度泛函理論(time-independent density functional theory, TI-DFT)與時間相依密度泛函理論(time-dependent density functional theory, TD-DFT)計算方法，模擬計算高分子發光二極體（polymer light-emitting diodes, PLED）當中的高分子材料聚噻吩(polythiophene, PT)的光電特性，並且用實驗驗證此理論計算方法的合理性。
首先建構噻吩(thiophene, T)之單體(monomer, T1)分子，利用此參數計算各單體分子及其衍生物之最佳化結構，振動頻率、單點能量等資訊，進而獲得最高佔據分子軌道 (HOMO) 能量，最低未佔據分子軌道 (LUMO) 能量、能隙(band gap)、分子軌域(molecular orbital）與吸收光譜(absorption spectrum)以及進行激發態計算而得到放射光譜(emission spectrum)的性質。
量子模擬計算當中增加單體數量由一個(T1)至十個(T10)，十五個(T15)，二十個單體(T20)，二十五個單體(T25)，三十個單體(T30)，除了可以利用計算得到各別的能隙，且隨著單體的增加，LUMO能量逐漸降低，而HOMO能量逐漸增加。再藉由外插法獲得高分子聚噻吩之能隙趨近於2 eV與文獻的實驗數值吻合。
本論文實驗部分藉由紫外-可見光光譜量測、光激發螢光光譜(photoluminescence, PL)量測驗證高分子聚噻吩吸收光譜、放射光譜的波長數值與能隙值也可以藉此做推算。除此之外能隙值也可以用電化學當中的循環伏安法(cyclic voltammetry, CV)得到。而紫外光電子能譜儀(ultraviolet photoelectron spectroscopy，UPS)的實驗結果可以證實最高佔據分子軌道 (HOMO)實際數值。藉由實驗結果可以證實適用此類高分子材料的計算模擬參數，PLED發光材料若需要不同顏色的放光需求就可以藉由調整聚噻吩的取代基來達成。

This thesis uses time-independent density functional theory (TI-DFT) and time-dependent density functional theory (TD-DFT) to calculate the photoelectric characteristics of polymer light-emitting diode (PLED) materials. The fundamental polythiophenes (PTs) are simulated and the rationality of this theoretical calculation method is verified by experiments.
The monomer (T1) molecule of thiophene (T) is constructed first to calculate the optimal structure and its properties, such as vibration frequency, single point energy and other information of each monomer and its derivatives. Extended properties such as the highest occupied molecule orbital (HOMO) energy, lowest unoccupied molecular orbital (LUMO) energy, band gap, molecular orbital, absorption spectrum, and the emission spectrum at excited state are also calculated and analyzed.
In the simulation process, the number of the monomer is increased from one (T1) to ten (T10), fifteen (T15), twenty (T20), twenty-five (T25), and thirty monomers (T30). From the predicted energy gap, we found that as the monomer increases, the LUMO energy gradually decreases and the HOMO energy gradually increases. The energy gap of the polymer polythiophene obtained by the extrapolation method is close to 2 eV, which is consistent with the experimental values in the literature.
The wavelengths of the absorption and emission spectra of the polymer polythiophene are experimentally verified by the ultraviolet-visible (UV/Visible) light spectrum and photoluminescence (PL) measurements. The band gap value is doubly validated from the cyclic voltammetry (CV) and the actual value of the highest occupied molecular orbital (HOMO) is verified from the ultraviolet photoelectron spectroscopy (UPS). If PLED luminescent materials require different colors of light emission, it can be achieved by adjusting the substituents of the polythiophene.

目錄
摘要 II
Abstract III
誌謝 V
目錄 VI
圖目錄 IX
表目錄 XI
符號表 XII
第一章 緒論 1
1.1研究背景 1
1.2有機發光二極體分類與原理 3
1.2.1有機發光二極體分類 3
1.2.2 有機光電元件發光原理 6
1.3文獻回顧 8
1.3.1 PLED材料理論計算文獻回顧 8
1.3.2 PLED材料實驗文獻回顧 10
1.4研究動機與目的 12
1.5研究流程 14
第二章 計算量子力學理論 15
2.1 前言 15
2.2 密度泛函理論 17
2.2.1 Hohenberg-Kohn 理論 17
2.2.2 Kohn-Sham 系統 19
2.2.3 交換相關能 20
2.2.4 BLYP 22
2.2.5 基底函數(Basis function) 22
2.2.6自洽場 25
2.3 與時間相關泛函密度理論(TD-DFT) 28
2.3.1 擴展Roung-Gross定理 28
2.3.2 與時間相關Kohn-Sham方程式 30
2.3.3 線性響應定理(Linear Response TD-DFT) 32
第三章 實驗儀器原理 35
3.1 紫外光-可見光光譜儀(UV/Vis spectrum) 35
3.2電化學循環伏安法量測(cyclic voltammetry，CV) 39
3.3光激發螢光光譜儀(photoluminescence，PL) 43
3.4紫外光光電子能譜儀(UPS) 46
第四章 模型建構與模擬計算方法 50
4.1模擬流程 50
4.2 PLED發光材料模擬模型建立 52
4.3密度泛函理論模擬 54
4.3.1模擬設定 54
4.3.2 PLED模擬計算方法部分: 56
第五章 結果與討論 61
5.1 PLED發光材料最佳化之分子結構 61
5.2能隙(Band gap)與電子雲分布(Molecular orbital) 62
5.2.1 PLED材料模擬結果: 62
5.2.2聚噻吩衍生物分子能隙探討 65
5.3吸收光譜 67
5.3.1 PLED材料吸收光譜計算模擬結果: 67
5.3.2 PLED材料吸收光譜實驗結果: 73
5.3.3計算聚噻吩衍生物之紫外/可見光吸收光譜 74
5.4放射光譜 76
5.4.1 PLED材料計算放射光譜模擬結果: 76
5.4.2 PLED材料光激發螢光光譜實驗結果: 78
5.4.3計算聚噻吩衍生物之放射光譜(Emission Spectrum) 79
5.5電化學循環伏安法 81
5.6紫外光電子能譜儀 82
第六章 結論與未來發展 84
6.1結論 84
6.2未來發展 86
參考文獻 87

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