臺灣博碩士論文加值系統

本篇論文主要是利用多能帶k∙p法配合波包近似法來討論垂直耦合自組式雙量子點系統的電子結構。對於電子的電子結構部份我們主要是用單能帶模型；而對於電洞的電子結構我們則是採用四能帶模型，在本論文中所用到的數值方法有平面波展開法和有限差分法。
垂直偶合雙量子點系統和單量子點系統來比較，前者提供了額外可調變的參數，例如，利用改變雙量子點系統間的距離、偏壓等，可以大幅改變系統的電子結構。而且在基礎研究方面，雙量子點系統可以類比於人造分子，電子的行為會和分子類似基態通常都是對稱的bonding states ，而第一激發態為反對稱的anti-bonding states。然而，最新的研究卻發現因為重電洞態和輕電洞態的混成大部分的情況下雙量子點中電洞的基態竟是反對稱的anti-bonding states [7]。
這篇論文中，我們利用自行發展的數值程式先驗證了文獻[7]的理論與分析，然後進一步考慮實際量子點的形狀、應變和擴散的效應。我們確認對截角金字塔的雙量子點而言，隨著量子點間距離增加電洞基態轉變為anti-bonding states的臨界距離僅約1 (nm)，而且應變效應有助於anti-bonding states電洞基態的形成。

In this thesis, a theoretical study of the electronic structure of vertically coupled InAs/GsAs self-assembled double quantum dots is presented. The single-band (four-band) k∙p model was used to calculate the electron structure of a single electron (a valence hole) confined in the double dot system. The numerical calculations were implemented using both of the plane wave expansion and finite difference methods.
As compared with single dot systems, coupled double quantum dots with extra tuning parameters for the inter-dot coupling, such as inter-dot distance or applied bias field, allow for more controllability of the electronic structure. With the engineered atomic-like electronic structure, a coupled double dot is often referred to as an artificial molecule and provides an interesting playground for fundamental research. In atomic physics, the ground states of a real molecule are known to be the bounding states and the first excited states to be anti-bounding states. In solid-state artificial molecules, an electron does have bounding-like ground states but a valence hole shows more complex features. Remarkably, recent studies showed that the ground states of a valence hole in a coupled quantum dot show an anti-bounding-like character.[7] The reversal of the type of the hole ground states was attributed to the significant heavy-hole-light-hole intermixing in the spatial region between dots.
In this work, I carried out the numerical k∙p calculations for vertically coupled InAs/InGsAs self-assembled double quantum dots and confirmed the reversal of the type of the valence hole ground states, as previously revealed in literature.[7] Furthermore, I studied the effect of strain on the electronic structure of the double quantum dots. The calculation shows that the critical inter-dot distance is about 1nm, above which the hole ground states of double are anti-bounding-like. The strain in a dot molecule makes the anti-bonding-like ground states even more stable and decreases the critical inter-dot distance.

中文摘要………………………………………………………… i

英文摘要………………………………………………………… ii

致謝……………………………………………………………… iii

目錄……………………………………………………………… iv

表目錄…………………………………………………………… v

圖目錄…………………………………………………………… vi

第一章、導論…………………………………………………… 1
1.1量子點簡介 ……………………………………………… 1
1.2理論文獻 ………………………………………………… 3
1.3研究動機 ………………………………………………… 3
1.4章節概要 ………………………………………………… 4
第二章、K．P法和應變………………………………………… 5
2.1 K•P法……………………………………………………… 6
2.2 Multi-band method………………………………………… 8
2.3 Envelope Function Approximation(EFA) ………………… 10
2.4特徵函數 ………………………………………………… 12
2.5應變的模擬並且文獻的比較……………………………… 14
第三章、數值方法 ……………………………………………… 31
3.1平面波展開法 …………………………………………… 32
3.2有限差分法………………………………………………… 36
3.3四能帶模型收斂性與驗證討論…………………………… 37
第四章、單量子點系統和雙量子點系統 ……………………… 43
4.1單量子點 ………………………………………………… 43
4.2雙量子點 ………………………………………………… 48
第五章、結論 …………………………………………………… 59
參考文獻 ………………………………………………………… 61
附錄A、材料參數 ……………………………………………… 62
附錄B、擴散現象 ……………………………………………… 64

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