利用二維數值模擬軟體分析UVB邊射型雷射之閾值電流與發光頻譜

Abstract

邊射型雷射為發展最早且廣泛應用的雷射之一，其優點在於可以透過增長共振腔長度以及結構設計以提升光場及電流侷限性來達到低閾值增益，並進而達到低閾值電流。其中以氮化鋁鎵為基底的邊射型雷射的中波紫外光波段在生物醫療上有重要的應用，然而目前實驗上仍有閾值電流偏高的現象，約為 25kA/cm2。但一維模擬因為缺少了水平方向資訊所以無法正確評估發生的原因，為此，在這篇文章中建立了一個二維光電數值模擬軟體，是以有限元素分析求解二維光學模態結合二維泊松擴散飄移電流與 localization landscape 理論並耦合一維薛丁格組成的模型，用以分析邊射型雷射出射面的穩態光學模態以及量子井中因為電流匯聚造成本質增益的分布，並透過疊合來得到邊射型雷射的模態增益、閾值增益、閾值電流及輸出功率-電流-電壓曲線。利用這個模型我們發現了實驗用的氮化鋁鎵為基底的邊射型雷射會因為設計問題導致光場與增益區不對齊，以及強電流聚集效應導致的負增益區被放大而產生高閾值電流，因此，我們試著藉由對齊基態光場與增益區域來降低閾值電流，而本文中所提出的設計最低能將閾值電流減至僅1.33 kA/cm2。另外，此二維模型也結合了含時雷射速率方程式模型以獲得光致發光頻譜以及利用惠更斯-菲涅爾原理以得到遠場圖形。

Edge emitting laser diodes are one of the most original and widely used forms of semiconductor lasers. The advantage of edge emitting lasers is that they can achieve the low threshold gain by increasing the cavity length and through the structure design to enhance the optical and current confinement, further reaching the low threshold current. However, with this design, the aluminium gallium nitride (AlGaN)-based ultraviolet-B (UV-B) band edge emitting laser diodes, which are widely used in biotechnology and medicine, still suffers from the high threshold current issue, about 25 kA/cm2, in the reported experimental results. However, it cannot be evaluated properly by using one-dimension (1-D) model due to the leakage of lateral information. Therefore, in this thesis, a two-dimensional (2-D) electro-optical numerical model was built to simulate the edge emitting laser properties and try to find the critical issues limiting threshold current density. This model used a finite-element method cavity mode solver coupled with 2-D Poisson, drift-diffusion, localization landscape solver, and coupled with one-dimensional Schrödinger solver. Hence, it can analyze the steady optical mode along the light emitted face and the intrinsic gain distribution in the quantum well due to the current crowding. By overlapping the optical and electrical information, we can obtain the modal gain, threshold gain, threshold current, and L-J-V curve for the modeling edge emitting laser diode. With this model, the reason for the high threshold current density in the reported experimental results is blamed on the design-induced misalignment between the optical cavity mode and gain region and the enhancement of the negative gain region due to the high current crowding effect. Therefore, we try to align the fundamental optical mode and the gain region to decrease the threshold current. In this thesis, we can finally reduce the threshold current density to only 1.33 kA/cm2. Also, our 2-D model coupled with a time-dependent laser rate equation solver to obtain the electroluminescence (EL) spectrum and could get the far-field pattern by using Huygens–Fresnel principle.