量子井與量子點光學性質之模擬

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姓名

徐培倫(Pei-Lun Hsu) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

量子井與量子點光學性質之模擬
(Optical properties of quantum well and quantum dot)

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摘要(中)

論文摘要
本篇論文主要目的是利用等效質量理論和瑞利里茲變分法來解量子點的能階與波函數，而所得到的結果可以讓我們初步分析量子點元件的特性以及給予實驗上在製作前的參考和特性預測。
首先我們先利用量子井解析解研究量子井的電性與光性，包括在均勻電場下電子的穿隧速率、動態行為分析以及次能帶的吸收光譜探討，藉由這些探討，可以對能階與波函數的物理以及影響它們的因素更加的了解，這將有助於我們對量子點的研究。
等效質量理論在計算上不但簡易迅速，且要加入新的場作用與新的結構也是很容易的。我們先將等效質量理論和瑞利里茲變分法應用在一維量子井中，計算的結果與解析解比較可證明此數值方法的可靠性，之後將其推廣應用到三維的量子點中。
由於量子點的形狀會影響到電子結構，所以我們會探討不同形狀量子點的能階與波函數分佈，並考慮外加電場的影響，接著探討垂直耦合量子點系統，包括其鍵結與反鍵結能階和波函數，以及影響耦合強度的因素。
最後將理論應用在分析量子點雷射上。這邊分為三個部份來探討。第一部份，由於量子點的均勻性對雷射特性有很大的影響，所以我們引入高斯分佈函數來模擬量子點大小的分佈，並利用費米黃金規則來計算量子點雷射的發光光譜與雷射增益。第二部份探討不同形狀的應力緩衝層對於能階的影響。第三部份，由於加入銻元素會縮小應力緩衝層的能隙，當銻成份達到某一比例時會使得砷化鎵與應力緩衝層之間的能帶形成Type II的結構，我們將探討這對量子點雷射發光波
長的影響。

摘要(英)

Abstract
The main goal of this dissertation is to calculate the energy levels and wave functions of quantum dots using the Raleigh-Ritz variation method in the framework of effective mass method. Based on the calculated energy levels and wave functions, the optical and transport properties of devices made from individual QDs can be fully analyzed. To clarify the Raleigh-Ritz variation method, we use a single quantum well system as an example due to one-dimensional Schrödinger equation with an exact solution. The optical and transport properties of quantum wells such as tunneling rate, emission and absorption spectrum and dynamic property are investigated. The results obtained using the Raleigh-Ritz variation method are in a good agreement with those obtained by the exact solution. Subsequently, the Raleigh-Ritz variation method is extended into a quantum dot system. The energy levels and wave functions of pyramidal, conical and disk QDs under a uniform electric field are calculated. In addition, we also calculate the energy levels of double quantum dots. The coupling strength between two quantum dots is readily obtained. In the framework of effective mass method, the energy levels of QDs are mainly attributed to volume effect rather than shape effect. Finally, the optical properties of quantum dot laser are theoretically studied. We have employed the Fermi golden rule to calculate the emission spectrum and modal gain of quantum dot laser in which dot size fluctuations are included using the Gaussian distribution function. We found that effects of the different shape of strain reducing layers significantly influence the emission spectrum. Due to the type-II band alignment between InAs quantum dots and antimony strain reducing layers, how the type-II structure of band alignment influences the emission spectrum of QDs is discussed.

關鍵字(中)

★ 光學性質
★ 量子點
★ 量子能階

關鍵字(英)

★ energy level
★ quantum dot
★ optical properties

論文目次

目錄
論文摘要......................................................................i
Abstract.....................................................................ii
誌謝........................................................................iii
目錄.........................................................................iv
圖目錄.......................................................................ix
表目錄......................................................................xiv
一、導論：....................................................................1
1.1 量子點簡介..............................................................1
1.2文獻回顧整理與發展近況...................................................7
1.3 研究動機與章節概述.....................................................11
二、量子井的動態行為與吸收譜線...............................................13
2.1在均勻電場下量子井系統波函數解析解與穿隧行為............................13
2.1.1 簡介與原理.........................................................13
2.1.2 結果與分析.........................................................15
2.2 在均勻電場下量子井系統的電子動態行為分析...............................20
2.2.1 簡介與原理.........................................................20
2.2.2 結果與分析.........................................................22
2.2.3 結論...............................................................29
2.3 均勻電場下量子井的吸收譜線.............................................30
2.3.1簡介與原理..........................................................30
2.3.2 結果與分析.........................................................31
2.3.3 結論...............................................................34
2.4 利用數值解模擬計算量子井能階與穿隧速率.................................35
2.4.1 簡介與原理.........................................................35
2.4.2 數值解方法解量子井能階與單量子井穿隧行為並與解析解結果比較.........36
2.4.3 結論...............................................................41
三、量子點的特性分析.........................................................43
3.1各種形狀量子點的能階與波函數............................................43
3.1.1圓柱型量子點與圓錐型量子點..........................................43
3.1.2金字塔型量子點與梯狀金字塔型量子點..................................47
3.1.3比較與結論..........................................................50
3.2外加電場的研究..........................................................52
3.3 垂直耦合雙量子點的模擬.................................................56
四、量子點雷射模擬...........................................................61
4.1 量子點均勻性對雷射的影響...............................................61
4.1.1 簡介與動機.........................................................61
4.1.2 量子點均勻性對雷射光譜的影響.......................................62
4.1.3 量子點均勻性對雷射增益的影響.......................................71
4.2 不同形狀的複合式應力緩衝層對量子點能階的影響...........................75
4.2.1 簡介與動機.............................................................75
4.2.2 結果與分析.............................................................75
4.3 加入銻元素的四元材料應力緩衝層對量子點雷射的影響.......................81
4.3.1 InGaAsSb 應力緩衝層................................................81
4.3.2 InAlAsSb 應力緩衝層................................................86
4.3.3 結論與未來工作.....................................................90
五、結論.....................................................................92
參考文獻.....................................................................95
附錄A........................................................................99
附錄B.......................................................................105
附錄C.......................................................................107

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指導教授

綦振瀛、郭明庭
(Jen-Inn Chyi、David M. T. Kuo)

審核日期

2006-7-21

推文