調變a面氮化鎵銦/氮化鎵光子晶體極化特性以增強自發性輻射

Abstract

本論文主要是在探討，利用光子晶體微共振腔的特性提高非極性氮化銦鎵/氮化鎵量子井的自發輻射。在一般的假設下，自發性輻射速率的提高可以使用Purcell factor來定義，而Purcell factor在定義上只與共振腔共振模態的品質因子(Quality factor)與等效模態體積(effective modal volume)有關，本研究從費米黃金定律(Fermi golden rule)出發推導Purcell factor，推導的過程中發現，自發輻射速率的增強除了與品質因子(Q-factor) 以及等效膜態體積(effective modal volume) (Vm)有關外，還與光源的自發輻射以及共振模態的極化特性有關。 本文分兩大部分討論，第一部份討光子晶體共振腔的設計，我們討論光子晶體共振腔的空氣柱的調變對品質因子(Q-factor)、共振模態的等效膜態體積(Vm) 以及共振模態的極化特性的影響，並藉由空氣柱的調變將光子晶體共振腔做最佳化設計；第二部分討論a-plane氮化銦鎵/氮化鎵單一量子井，隨著調整不同的銦含量與量子井的厚度，其自發輻射的電場極化特性將會有所改變，我們考慮自發輻射與共振模態的極化特性計算得到自發輻射增強因子(Spontaneous emission enhancement factor, SpE factor)，與Purcell factor 做比較，最後我們發現到在當自發輻射在低極化率下必須將Purcell factor 因子做修正，而在高極化率的情況下SpE-factor 會與Purcell factor非常地接近。

In this article, we discussed the utilization of photonic crystal microcavity for the enhancement of spontaneous emission rate of the a-plane InGaN/GaN single quantum well by reducing threshold power of laser. In general assumption, spontaneous emission rate enhancement factor can be defined by Purcell factor, and Purcell factor is proportional to the quality factor of photonic crystal microcavity and inversely-proportional to effective modal volume of cavity mode. We derived the Purcell factor from Fermi golden rule. During the deriving process, we found the spontaneous emission rate enhancement factor is not only related to the quality factor and effective modal volume of cavity mode but also polarization characteristic of spontaneous emission rate and cavity mode. In the first of the thesis, we discussed the influence of the quality factor, effective modal volume and polarization characteristic of cavity mode by tuning air holes of photonic crystal microcavity. And we optimize the photonic crystal microcavity by tuning air hole. In the second part, we discuss the variation of polarization characteristic of spontaneous emission rate of a-plane InGaN/GaN single quantum well by different indium composition and quantum well width. Finally, the calculated spontaneous emission enhancement factor considering polarization characteristic of spontaneous emission rate and cavity mode was compared with Purcell factor. We found the value of spontaneous emission enhancement factor in high polarization was closed to Purcell factor but the Purcell factor in low polarization ratio needed to be revised.