使用傳遞矩陣法模擬含有光柵的層狀結構

Modified Transfer Matrix Method for the Modeling of Layer Structure with Grating

高楨樹(Chen-Shu Kao)

指導教授 ： 邱奕鵬

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.03338

摘要

在近幾年，發光二極體 (LED) 以及 有機發光二極體 (OLED) 是非常廣泛被研究的發光元件。由於製程上的方便，通常這兩種元件會被做成層狀的，也就是發光區的部份，他們橫向的寬度會遠大於縱向的厚度。一般在研究這些發光元件時，主要用來模擬光傳播行為的數值方法有兩種：第一種是有限時域差分法 (Finite-Difference Time-Domain)，此種方法可以允許結構有較大的變化彈性，但是由於需要的計算量較大，會花費大量的執行時間，通常用於模擬結構中含有較為複雜的子結構時，i.e.包含光柵(Grating)或其他特殊結構；第二種是傳遞矩陣法 (Transfer Matrix Method)，跟有限時域差分法相反，此方法需要的計算量較小；然而，傳統的傳遞矩陣法只能用來模擬層狀的結構，在處理一些有特殊結構的層狀發光元件上比較困難。
在本篇論文中，我們利用古典電磁學的理論來分析並模擬光在層狀結構中的光學特性。一般層狀的發光元件，光源可以用一個週期性震盪的電偶極來表示。光源發出的光以平面波的形式展開，在層狀結構中各個介面利用傳遞矩陣法來匹配邊界條件，即可得到各層中電場強度的解析解。在含有光柵的層狀結構中，我們嘗試結合嚴格耦合波分析 (Rigorous Couple - Wave Analysis) 與傳統的傳遞矩陣法，使得傳遞矩陣法能夠模擬光柵的結構。換句話說，傳統的傳遞矩陣法在匹配邊界條件時，只會利用菲涅爾 (Fresnel) 方程式去匹配零階的模態；利用嚴格耦合波分析或是其他分析光柵的數值方法，可以幫助傳統的傳遞矩陣法匹配其他高階的模態；如此一來，傳遞矩陣法就能算出有包含光柵的層狀結構各層高階模態的電場值。由這些電場的解析解，可以得到層狀發光元件在加入光柵後的發光效率以及遠場的場形；我們發現在加入光柵後，元件整體的發光效率不一定會是提升的，發光效率與遠場的場形跟加入光柵的週期有著密切的關係。從這些分析中我們可以看出，在層狀發光元件中，加入適當設計的光柵，可以大幅的增加發光效率，或者優化遠場的場形。
關鍵字：傳遞矩陣法、嚴格耦合波分析、有機發光半導體、光柵、萃取發光效率、遠場場形

關鍵字

傳遞矩陣法 ； 嚴格耦合波分析 ； 有機發光半導體 ； 光柵 ； 萃取發光效率 ； 遠場場形

並列摘要

In recent years, light emitting device (LED) and organic light emitting device (OLED) are widely studied. Due to the convenience in fabrication, these device are usually made as layered structure, which represents that the lateral size is much larger than the thickness in the emission layer. Generally, there are two kinds of analytical method most popularly used in the simulation of light propagation in these devices. The first one is the finite-difference time-domain method, which allows more flexibility for the simulation structure. However, it consumes vast CPU resource and executing time, and usually be used in the cases when the simulation structure has complicate substructures, i.e. like grating. The second one is the transfer matrix method. In contrast, transfer matrix method requires lesser computation. However, traditional transfer matrix method can only be used in the simulation of layered structure, and suffers difficulty for special simulation structures.

In this thesis, we use the classical electromagnetic theory to analyze and model the optical properties of layered structure. In general, the source of layered structure can be expressed as a periodic resonating dipole source, which can be expanded as plane wave radiating to all directions. Using the transfer matrix method matching the boundary conditions at each junction, the analytical solutions of the electric fields in each layer can be obtained. In addition, we will combine the rigorous couple-wave analysis and traditional transfer matrix method to model the structures with grating. In other word, traditional transfer matrix method only uses the Fresnel's equations to match the boundary condition of zero order mode. Using rigorous couple-wave analysis or other grating modeling methods, we can furthermore match the boundary conditions of higher modes. As a result, transfer matrix method can calculate the electric field of the high order modes. Furthermore, we can use the obtained electric fields to calculate the extraction efficiency and the far-field pattern of the device. From the simulation results, we found that the extraction efficiency will not always increase when the grating is including in the structure, and the grating period will strongly effect the extraction efficiency and the far-field pattern. A well designed grating can enhance the extraction efficiency and optimize the far-field pattern.

並列關鍵字

Transfer matrix method ； Rigorous couple-wave analysis ； organic light emitting device ； grating ； extraction efficiency ； far-field pattern

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