A Theoretical model for Conjugated Polymer Solar Cells

石油一直是人類所依賴的主要能源，但近一兩年來石油的價格不斷攀升，大幅度的價格變化甚至直接衝擊了全球經濟和民生物價，因此找尋可替代能源的議題越來越顯得重要，而太陽能電池是眾多替代能源中最具有潛力的，因為太陽能電池可直接從太陽捕獲能量並且在使用上無汙染。市面上太陽能電池的種類很多，其中導電高分子太陽能電池是目前最具前瞻性的太陽能電池類型，其發展的時間也是所有種類中最晚的，但導電高分子太陽能電池因為具許多的優點所以特別受人注目，尤其是可攜帶性及易於製造等優點，但是低效率的問題卻一直是導電高分子太陽能電池所面臨的一大挑戰，因此若能有數學模型去描述電池內部的機制，那麼對於導電高分子太陽能電池的研究會是相當有幫助的。 在本論文研究中，我們將建立一個導電高分子太陽能電池的數學模型，利用數值解的方法去求解卜瓦松方程式和質量守恆關係式，藉此將模擬計算出導電高分子太陽能電池的放電表現，而模型中的物理參數分佈將可以幫助我們分析各個操作點時的狀況，以了解整體機制。論文中我們將使用兩組實驗數據去比對模型的計算結果，比對之後發現此模型的計算結果和實驗點之間都有不錯的結果，並進一步證明此模型具有一定的參考價值，之後我們將改變材料的物性參數，希望能找出影響電池效率的關鍵因素，相信這些資訊都能有助於找出解決低效率問題的方法，進而達到改善太陽能電池的效率值。The fossil oil has been the primary source energy which the modern human society relies on. Recently, the price of crude oil increase dramatically and it impacts the global economy and the livelihood of the people. To solve this problem, it is necessary to develop other inexpensive energy sources to reduce our dependence on oil. Therefore searching for alternative energies is an important issue. The solar cell has great potential among the numerous alternative energy sources, because it directly captures the solar energy from the sun and does not release chemical pollutant during operation. There are many types of solar cells on the market. The conjugated polymer solar cell is a new generation of solar cell at the present. Although its development started very recently, it has attracted a significant amount of attention because of a lot of advantages, especially its low cost and the ease of fabrication. However, the low efficiency (currently about 6%) problem has been a big challenge for the conjugated polymer solar cell and makes it impossible for commercialization. If we can have a mathematical model to describe the internal mechanism inside the cell, it would be helpful to find the optimal design of the conjugated polymer solar cells. In this thesis, we developed a numerical model for polymer/fullerene bulk heterojunction solar cell. Using this model, we can simulate the electric performance of solar cell and the result is consistent with experimental current-voltage curve. On the other hand, we can analyze the distribution of physical properties to better understand the distribution and transport of electrons and holes inside the solar cell. Based on the good agreement with experiments, the prediction of solar cell''s efficiency can be calculated by changing the material''s parameters in the model. Our analysis suggests that the key factors for the efficiency are orbital energies of materials. Finally, the mathematic model can also offer an efficiency table for the new material development to solve the low efficiency problem.目錄試委員會審定書 I謝 II文摘要 IVbstract V索引 VIII索引 X. 緒論 1.1 研究背景 1.2 太陽能源介紹 1.3 太陽能電池的種類和簡介 2.4 導電高分子太陽能電池 6. 混摻異質接面型太陽能電池 8.1 混摻異質接面型太陽能電池介紹和工作原理 8.2 太陽能電池的電流-電壓特徵曲線圖介紹 10.3 發展數學模型的目的 12. 數值解模型的建立 13.1 數學模型的原理與方程式 13.1.1 半導體元件基本統御方程式 14.1.2 自由載子的淨產生速率 16.1.3 Braun’s model 19.1.4 統御方程式整理 21.2 電子-電洞對的產生速率 22.3 邊界條件 24.3.1 電位的邊界條件 24.3.2 金屬和有機界面的電荷注入 25.3.3 電流密度的邊界方程式整理 28. 模型的數值方法 31.1 數值方法解邊界值問題 31.1.1 有限差分法和統御方程式的離散化 31.1.2 牛頓法 34.2 Scharfetter-Gummel Approximation 離散化 36.3 離散化統御方程式整理 39.4 模型求解流程 40.5 模型參數 42. 結果與討論 46.1 電流-電壓特徵曲線圖 46.2 電池內部物理參數分佈 49.3 不同照光強度下的電流-電壓特徵曲線圖 55.4 開環電壓和短路電流預測 59.5 電子和電洞的遷移率對於放電效率的影響 61.6 電極工作函數對於放電效率的影響 65.7 高分子材料的能階對於放電效率的影響 68. 結論 70考文獻 72錄 7