利用二維嚴謹耦合波分析發光二極體之光萃取效率

Abstract

在本篇論文中，我們利用嚴格電磁數值分析法來模擬並分析含有週期結構發光二極體的發光特性，目前被視為能夠有效改善光萃取效率(light extraction efficiency, LEE)的方法，是在氮化鎵發光二極體(GaN-based LED)表面製作一層週期性結構，利用週期性結構具有繞射的特性來提升光萃取效率。我們所使用的模擬方法是利用電偶極作為光源，並將電偶極在層狀結構中所產生的電磁場以平面波的方式表示，而經由週期性結構所產生的繞射波，可藉由嚴格耦合波分析法計算獲得，此分析法主要是利用平面波展開法的方式，解得各個滿足馬克斯威爾方程式的繞射波之解析解。我們的研究工作主要是模擬並分析薄膜垂直型發光二極體，在不同的結構參數下對光萃取效率所造成的影響，並試著提出一系列的設計準則在這一堆的結構參數中找出最佳化的數值，以達到最大光萃取效率改善的目的。我們所提出的設計準則，不但是藉由理論分析的方式找出各個結構參數與光萃取效率之間的關係，並且利用數值模擬的方法來驗證，以獲得最佳化的結構參數。最後我們證明薄膜垂直型氮化鎵發光二極體結合週期性結構，在適當的設計結構參數下，可得到超高光萃取效率~90%。

In this thesis, we model and analyze the emitting properties of the LED combined with periodic structure by using the rigorous electromagnetic analysis. Taking advantageous of the diffractive property of periodic structure is viewed as the promising method to improve the poor light extraction efficiency (LEE) of the gallium nitride based light-emitting diode (GaN-based LED). A key of our simulation method is the decomposition of the electric dipole embedded in the layered structure into plane waves, and the effect of the periodically patterned layer on the reflected and transmitted diffraction waves can be calculated by the rigorous coupled-wave analysis (RCWA) which is based on the plane wave expansion and is an exact solution of Maxwell’s equations. In our work, we investigate the various structural effects on the LEE in the thin film vertical LED, and then we try to guide some design trends to optimize the structural parameters for high LEE. The manner of design is not only theoretically analyzed but quantitatively demonstrated by the numerical simulation. Finally, we show that the ultra-high LEE~90% can be realized by the properly designed parameters of structure.