染料敏化太陽能電池之數學模型建立

Abstract

我們提出了染料敏化太陽能電池光和電的數學模型。在光模型部分，主要是主動層內奈米顆粒結構與鉑電極粗糙面的一維非同調光問題，以修正的傳遞矩陣方法來解決，其最大特點是引用隨機相位把非同調傳播問題以同調方法來模擬粗糙面或缺陷所造成影響，在電模型部分，主要是以電子、碘離子、碘三負離子的連續性方程做出發，在復合機制上，根據Shockley-Read-Hall 理論及 Marcus-Gerischer理論，假設主動層的二氧化鈦能隙內有一個隨能階呈指數分布的陷阱態函數，以及電解液有一個隨能階呈高斯分布的狀態函數，利用此來描述電子轉移之過程。 此外，我們也討論了主動層厚度對整體電池表現的影響，結果顯示隨著厚度增加開路電壓會有所減少，而轉換效率最大值所相應的厚度，必須看奈米顆粒上染料附著濃度的高低來決定，最後我們將電流電壓曲線，以及開路電壓與光照強度關係和實驗值做一個比較，其中此模型印證了在高強光下主要復合機制為透過二氧化鈦和電解液之間的電子轉移，在弱光下主要是透過透明電極和電解液之間的電子轉移，而此復合機制轉換的分界點取決於阻擋層的性質。 總結以上，此模型解決了光學上染料敏化太陽能電池多層結構中主動層為奈米顆粒與鉑電極粗糙面所遇到的問題，並在電的模型中，呈現詳細的數值結果印證該模型之可行性，並對該模型中所用到的重要物理參數逐一討論。

We present a way to account optical and electrical modeling of dye-sensitized solar cells (DSSCs).The optical model is based on one-dimensional partially coherence system, in which nanoporous active layer and rough Pt electrodes was successfully modeled by transfer-matrix method. The novel feature is that the transition from incoherent to coherent is achieved by introducing a random phase to simulate the ef-fect of defects or roughness surface. The electrical model is based on continuity and transport equations for electrons, iodide and triiodide ions. In recombination mecha-nism, exponential distribution of trap states in TiO2 and Gaussian distributions of en-ergy levels in the electrolyte within active layer are assumed in modeling, according to Shockley-Read-Hall statistics and Marcus-Gerischer electron transfer theory. These theory are used to describe the process of electron transfer . In addition, the effect of the active layer thickness on the DSSC performance is also presented. It was found that the open-circuit voltage decreased with increasing electrode thickness. The optimal electrode thickness for the highest power conversion efficiency was decided by higher or lower dye loading on nano-particle. Finally, Our simulation results are compared with the published experimental data like cur-rent-voltage characteristics and light intensity dependence of open circuit. In particular, the relation between open-voltage and light intensities indicate that the recombination occurred mainly through TiO2 /electrolyte interface under high illumination intensities and recombination via TCO/electrolyte interface is dominant under low illumination intensities. However, the demarcation of two different recombination mechanism is depend on characteristic of blocking layer. In summary, a method for calculating the optical response of multilayer systems is presented, which can deal with nanoporous active layer and rough Pt electrodes of DSSC structure. Also, the electrical model is described in detail, and numerical results are presented, which demonstrate the feasibility of the model. The influence of the most important material parameters on the cell performance are illustrated.