光子晶體結構應用於光電元件上之特性研究

Abstract

本篇論文旨在研究光子晶體結構在光電元件上的特性及應用。內容大致分為兩個主題。在第一部分，我們利用二維嚴格耦合波分析(2D-RCWA)和時域有限差分法(2D-FDTD)，成功地建構出具有高折射率差異的氮化鎵次波長光柵，並驗證其高反射率的特性。當設定入射波為460奈米的橫電波(TE wave)時，我們觀察到此結構具有寬頻譜高反射率(反射率大於90%)的現象。此外，我們對關鍵設計參數進行一系列製程容忍度分析，以期能降低實驗誤差對於優化結構的影響。最後，我們成功地製造出具有掏空結構的高反射率光柵結構，並對其相關特性進行探索。量測結果顯示其具有極佳的極化選擇比，且與模擬的資料呈現高度一致性，故適合在光電元件整合中作為反射鏡使用。而在第二部分，我們利用轉移矩陣法(transfer matrix method)及耦合波理論(coupled-wave theory)探討不同磊晶層厚度對於閥值增益變化的對應關係。此部分的研究著重於面射型出光的Γ1能帶。此外，光子晶體結構的填充因子也一併列入研究範圍。經過一系列的優化演進，最終結果顯示，對於砷化鎵光子晶體面射型雷射而言，光子晶體層的垂直光學侷限率可大幅提高至12.6%，且結構的閥值增益驟降至50 cm-1左右。另外，我們也對模態頻譜和結構電性等做詳細地分析比較。

In this thesis, we investigated some applications of photonic crystals in optoelectronic devices. The content is divided into two subjects. In the first part, the high reflectivity GaN-based sub-wavelength high-contrast grating (HCG) had been demonstrated. Based on the 2D rigorous coupled-wave analysis (2D-RCWA) and finite-difference time-domain method (2D-FDTD), we found and confirmed the optimal structure that exhibits high reflectance (R > 0.9) for TE-polarized light over a wide spectral range (ΔλR ≈ 105 nm) centered at λ = 460 nm. Moreover, we decided some critical designs via parameter mapping which could realize the intended results with high fabrication tolerance to reduce the difficulties in the process. Finally, we successfully fabricated the membrane HCG and exploring the associated characteristics. It has excellent polarization selectivity and the measurement results were in good agreement with the simulation data. In the second part, through the transfer matrix method and coupled-wave theory, we studied the influence of various thicknesses on different layers in our structure. We especially focus on the band edge at Γ1 point because of the characteristic of photonic crystal (PC) surface emitting. The relationship between the threshold gain and filling factor had also been considered. In our ultimate results, the best value of vertically optical confinement factor of PC in the optimized GaAs-based PCSELs is calculated to be 12.6% and the threshold gain is reduced to 50 cm-1. In addition, we made some extended investigation about mode spectra identification and electrical property discussion.