氮化鎵二維面射型光子晶體雷射閾值增益之研究

Abstract

本篇論文旨在利用多重散射法模擬不同結構設計下造成二維面射型光子晶體雷射之閾值增益變化。根據光子晶體的布拉格理論，光子晶體必須滿足特定的布拉格繞射條件才能產生雷射。我們研究部份，則著重於在面射型出光的Γ2能帶。我們將分為三個部分討論在不同結構變化下對於面射型光子晶體雷射的影響。第一部分討論當光子晶體層數改變時對閾值增益及正規劃頻率的變化。我們發現當層數超過20層時，光子晶體的影響將會趨緩且正規化頻率會趨近能帶邊緣。第二部分，藉由改變空氣填充因數來研究不同的模態，面射型光子晶體雷射的雷射閾值增益。第三部分，我們設計了不同PCSELs邊界條件。發現圓形邊界比一般六角邊界有著更低的閾值增益。最後，根據模擬結果，我們在GaN材料發光二極體上設計了，在Γ2點附近，晶格常數約190nm的面射型光子晶體雷射。

In this thesis, we investigated the different lasing behaviors of threshold gain in GaN-based 2D photonic crystal surface emitting lasers (PCSELs) according to Multiple Scattering Method (MSM). Based on the Bragg diffraction theory for PCs period structure, the lasing behavior could only be happened when the Bragg condition is satisfied. Our studies are especially focused on the band edge at Γ2 point because of the characteristic of photonic crystal surface emitting. In our study, we divide research into three parts to study the different effect of structure on PCSELs. At first, we change the number of shell for PCSELs that would affect the threshold gain and normalized frequency. When the number of shell is over 20, the influence of photonic crystal will decrease. Secondly, we modify the filling factor of photonic crystal to optimize the threshold gain parameter for PCSELs. The four Γ2 point band-edge of PCSELs have different lasing threshold gain distribution. Finally, we consider the boundary condition for our PCSELs. The circle boundary has the lower threshold gain than the usual hexagonal boundary. As a result, we designed the PCs lattice constant about 190nm for Γ2 point lasing, and successfully fabricated the PCs structure on our novel GaN-based resonance cavity light emitting diode.