Simulation of Optical Properties ofGaN/AlN Quantum Dots
Date Issued
2005
Date
2005
Author(s)
Chen, Chih-Yao
DOI
en-US
Abstract
由於氮化鎵量子點具有介穩態(Metastable-state) 的閃鋅結構
(Zinc-Blende Structure)和穩態的烏采結構(Wurtzite Structure)再加上其
本身就擁有的壓電性質(Piezoelectric Effect)，以往『不』考慮壓電效
應下閃鋅結構的砷化銦鎵量子點(InGaAs Quantum dots)的計算已經無
法再適用。因此參考安得列夫(A. D. Andreev)和奧瑞立(E. P. O’Reilly)
於公元兩千年提出的理論。我們進行了氮化鎵量子點光學性質的理論
計算，關於計算的方法和要點簡述如下
首先由傅氏轉換求得單一量子點幾何形狀的特徵函數(Geometric
Characteristic Function)，再根據傳統的彈性力學中的格林函數(Green’s
Function)和特徵函數的關係經過一連串推導得到形變量和特徵函數
對於波數向量的關係。接著由求得的形變量可以推得因形變引起的壓
電位能，再將得到的壓電位勢(Piezoelectric Potential)，與形變量分別
帶入八能帶k．P 模型(Eight-Band k．P strain-dependent Hamiltonian )
中的應變和動量交互作用矩陣與動量相關矩陣，並對兩個矩陣相加所
得到全部的漢米爾頓矩陣求其特徵值和特徵向量，將可以得到該量子
點的能階分佈，波函數和可能的光學躍遷態。而這些參數的計算對於
將來設計氮化鎵量子點的半導體元件，如量子點雷射和量子點記憶
體，甚至量子計算是非常重要的。
最後我們將由計算所得到的能態與之前的研究團隊計算或實驗
所得到的結果做詳盡的比較，除此也將討論壓電場的存在對於量子點
內量子侷限史塔克效應的影響。
Due to the intrinsic built-in piezoelectric effect, the conventional calculation of
InAs quantum dot without considering the piezoelectricity is not suitable. Referring
to the study proposed by A. D. Andreev et al. in 2000, we perform the optical
property calculation about the GaN quantum dots.
First, we obtain the characteristic function of the QD shape, then applied it to
obtain the strain distribution according to the classical elasticity. Second from
obtained strain tensors, we can derived the piezoelectric potential and substitute it
into strain-moment interaction element in the k·p matrix. Then solve the
eigen-value problem to obtain the eigen energy and eigen vector which will be
utilized in the calculation of the optical transition. The parameters such as
eigen-energy and electron wave function are very important in the design of the
GaN quantum dot device especially in the quantum dot laser, quantum memory and
quantum computation.
Finally we will compare the calculated eigen-energy, wave-function, and the
optical properties with theoretical calculation or the experiment data from other
researchers. Moreover, we will discuss how dose the existence of the piezoelectric
field affect the quantum confined stark effect of the zinc-blende and wurtzite
quantum dot.
Subjects
氮化鎵
量子點
應變
Quantum dot
GaN
Strain
Type
thesis
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