準週期量子井之光致發光與超輻射

Photoluminescence and Superradiance in Quasiperiodic Quantum Wells

張家豪(Chia-Hao Chang)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/博士(2015年)

https://doi.org/10.6342/NTU.2015.11236

摘要

本論文研究多重量子井結構中光致發光以及超輻射之特性。本論文討論了傳統週期結構與三種代表性的準週期結構：Fibonacci、Thue-Morse以及double-period序列。對於光致發光特性，研究結果顯示了Fibonacci量子井中最大的光致發光強度顯著地強於滿足Bragg或anti-Bragg條件之週期量子井的強度，此歸因於其中電場分佈的峰值位置非常接近於量子井的位置。對於Fibonacci量子井，其最佳的光致發光頻譜為非對稱的形式，而非如週期量子井中對稱的形式，且最大的光致發光強度與相對應的厚度比例，即結構的A層厚度與A層和B層厚度總和之比值，會隨著結構階數增加而增加。此外，也顯示了Thue-Morse量子井的光致發光特性不同於Fibonacci量子井的特性。對於Thue-Morse量子井，其最大與最小的光致發光強度分別發生於anti-Bragg與Bragg條件，而當厚度比例從0.25增加到0.5時，光致發光強度之最大值會逐漸地衰減，此歸因於此結構中量子井位置處的場值會隨著其偏離anti-Bragg條件而減小。研究結果也展現了double-period量子井中雙特高的光致發光。對於double-period量子井，其具有兩個光致發光強度的最大值，此現象不同於Fibonacci量子井、Thue-Morse量子井和傳統的週期量子井。其最大的光致發光強度則強於滿足anti-Bragg條件之週期量子井以及Fibonacci量子井的強度。雖然對應於此雙特高光致發光的電場之峰值位置皆很接近量子井的位置，但是電場分佈卻相異於彼此。
對於超輻射現象，本論文提出了在Fibonacci量子井中發生超輻射模態之精確範圍，此範圍是以帶隙圖而非以傳統的共振Bragg條件得到。研究結果顯示藉由帶隙圖可得到三個受限的範圍，其各別對應不同的帶隙寬度，而未能發生超輻射模態之範圍也被清楚定義。在double-period量子井中超輻射模態之存在也被提出，而該現象在先前的研究中未能被觀察到。對於滿足使用帶隙圖方法所得到的條件之反射頻譜，顯示了在頻譜中間會產生凹陷，且頻譜的線寬會呈線性成長，此即為超輻射現象的直接展現。此外，也發現經由帶隙圖所得到的條件被分成三個範圍，其各別具有不同的帶隙寬度。

關鍵字

量子井 ； 激子 ； 電磁極化子 ； 準週期 ； 超輻射模態 ； 光致發光

並列摘要

Photoluminescence (PL) and superradiance in multiple quantum wells (QWs) with traditional periodic and various quasiperiodic arrangements, including Fibonacci, Thue-Morse and double-period sequences, which are representative one-dimensional quasicrystals, are studied in this dissertation. For PL characteristics, strong PL emission from a Fibonacci QW is shown. The maximum PL intensity in the Fibonacci QW is significantly stronger than that in a periodic QW under the Bragg or anti-Bragg conditions. The peaks of the squared electric field in the Fibonacci QW are located very near the QWs. The optimal PL spectrum in the Fibonacci QW has an asymmetrical form rather than the symmetrical one in the periodic case. The maximum PL intensity and the corresponding thickness filling factor in the FQW become greater with increasing generation order. The results also show that the PL properties of a Thue-Morse QW are quite different from those of a Fibonacci QW. The maximum and minimum PL intensities respectively occur under the anti-Bragg and Bragg conditions. The maxima of the PL intensity gradually decline when the filling factor increases from 0.25 to 0.5. Accordingly, the squared electric field at the QWs decreases as the Thue-Morse QW deviates from the anti-Bragg condition.
Moreover, twin extra high PL in double-period QWs for higher generation orders is demonstrated. In the double-period QW, the number of maxima in the maximum values of the PL intensity is two, which is different from Fibonacci QWs, Thue-Morse QWs and traditional periodic QWs. The maximum PL intensity in a double-period QW is stronger than that in a periodic QW under the anti-Bragg condition and that in a Fibonacci QW. Although the peaks of the squared electric field for the twin PL are both located near the QWs, their field profiles are very different.
For superradiance phenomena, it is firstly proposed that superradiant modes occur in Fibonacci QWs within the exact regions that are obtained using the gap map diagram, rather than the traditional resonant Bragg condition. The results show that three limited regions are derived from the diagram, which correspond to bandgaps with widths that differ from each other. The regions in which the superradiant modes do not occur are also defined clearly. The existence of superradiant modes in double-period QWs, which has not been observed using the previous method of analyzing the structure factor, is also presented. Using the gap map method, the reflection spectra under the relevant conditions show that there are dips in the middle and the linewidth grows linearly, despite the dips, as the number of QWs increases, which is a direct demonstration of superradiance. It is also found that the relevant conditions are divided into three regions, each of which has a different width of bandgaps.

並列關鍵字

quantum well ； exciton ； polariton ； quasiperiodic ； photoluminescence ； superradiant mode

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