以蒙地卡羅射線追跡法模擬垂直型氮化鎵發光二極體之光萃取效率

Abstract

本論文中，吾人發展一套蒙地卡羅射線追跡法，並針對具表面圖樣化之垂直型氮化鎵發光二極體進行光萃取效率模擬。吾人選擇三種圖樣化表面，分別是一維弦波光柵、二維微透鏡陣列與粗糙表面，並分析圖樣化上表面與圖樣化底部反射鏡對光萃取效率與遠場分佈的影響。藉由改變週期性結構的高度與週期，或改變粗糙表面的均方根高度與相關長度，觀察光萃取效率之變化趨勢，且探討封裝造成的影響。此外，吾人亦使用蒙地卡羅射線追跡法對單一表面進行模擬，得到光射線於介面之穿透機率分佈、反射角機率分佈與多重反射穿透次數等資訊，並分析光射線於單一介面上的散射行為，以了解具表面圖樣化之垂直型發光二極體的光萃取機制。

In the thesis, a Monte Carlo ray tracing method is developed to simulate the light extraction efficiency of a vertical GaN LED with textured surface. We select three kinds of textured surfaces, including one-dimensional sinusoidal gratings, two-dimensional micro-lens arrays and rough surfaces, and analyze the effects of textured upper surface and bottom mirror on the light extraction efficiency and the far-field pattern. By changing the height and the period of a periodic surface structure or by changing the RMS height and the correlation length of a rough surface, the variation of light extraction efficiency is examined. Also investigated is the effect of encapsulation. In addition, we use the Monte Carlo ray tracing method to simulate the scenario of a single surface. The transmission probability distribution, the reflection angle probability distribution and the number of multiple reflection or transmission are calculated to analyze the scattering of light at an interface, leading to understanding the light extraction mechanisms of vertical LEDs with textured surfaces.