圖形化藍寶石基板氮化鎵發光二極體之光萃取效率分析

Abstract

本論文中，我們使用波動軟體-有限差分時域(FDTD)模擬軟體-和幾何光學軟體-LTs模擬軟體-來模擬奈米級圖形化藍寶石基板發光二極體。首先，為了縮減模擬時間和記憶體容量,我們使用二維的有限差分時域模擬軟體並且找出光萃取效率提升的趨勢和一組最佳解，我們利用嚴格耦合波分析(RCWA)來推算這個設計找到的趨勢。接著，將從最佳解帶入三維有限差分時域模擬軟體和LTs模擬軟體中。由於兩種軟體在小的模擬範圍下有相似的結果而且其出光萃取效率相差小於8.5%，所以我們使用LTs模擬軟體來模擬實際大小的奈米級圖形化藍寶石基板發光二極體。相較於使用三維有限差分時域模擬軟體，使用LTs模擬軟體能縮減至少104倍的記憶體容量。此外，使用LTs模擬軟體還能觀察到側邊的光萃取效率提升。由於以上的理由，我們使用LTs模擬軟體來模擬真實大小的奈米級圖形化藍寶石基板發光二極體。最後藉由LTs模擬軟體模擬奈米級圖形化藍寶石基板發光二極體並且搭配最佳解做為微結構，相較於傳統發光二極體,其光萃取效率提升307%。

In this paper we discuss the simulation of a nano-patterned sapphire substrates (NPSS) light emitting diode (LED) with two kind of optics software: wave optics software, Finite-Difference Time-Domain (FDTD) simulations, and the ray optics software, Light Tools (LTs) simulation. First, we find the trends and an optimal solution for the Light Extraction Efficiency (LEE) enhancement when the 2D-FDTD simulations are used to save on simulation time and computational memory. The rigorous coupled wave analysis (RCWA) method is utilized to evaluate the designs. The optimal solution is then applied in 3D-FDTD and LTs simulations. The results are similar and the difference in the LEE enhancement between the two simulations does not exceed 8.5% in the small LED chip area. More than 104 times computational memory is saved during the LTs simulation in comparison to the 3D-FDTD simulation. Moreover, the LEE enhancement from the side of the LED can be obtained in the LTs simulation. An actual size NPSS LED is simulated using the LTs. The results show a more than 307% improvement in the total LEE enhancement of the NPSS LED with the optimal solution compared to the conventional LED.