量子點光源中精細結構匹裂與光學特性之研究

本論文主要以理論方法討論尺寸效應下量子點的精細匹裂(fine structure splitting)與光學異相性(optical anisotropic)。文中討論兩種具代表性的量子點光源: InAs/GaAs 自組式(self-assembled)量子點，以及hierchical GaAs/AlGaAs 量子點。文中使用單能帶以及四能帶k．p 模型並搭配三維簡協振子(3-D parabolic model)模型分別計算激子(exciton)系統的電子與電動結構。光學偏振部分以費米黃金定律(Fermi’s Golden Rule)計算各方向之發光強度及異相性。文中討論的兩種量子點中，InAs/GaAs 自組式量子點因兩種材料晶格不匹配於量子點內部存在的應變效應可由解析方式得到量子點中心點的應變量；此應變解析值亦可與套裝軟體Comsol multiphysicsⓇ比較。除四能帶模型的數值模擬以外，文中亦以微擾方式簡化系統並得易分析的解析解。由解析解中可得量子點中的精細匹裂的消長乃由於長程作用力(long-range interaction)及短程作用力(short-range interaction)兩者的相互競爭引起。除最基本的尺寸效應探討以外，量子點的精細匹裂與光學異相性亦可由外加應力調控。文中於GaAs塊材外加單軸應力(uni-axial stress)，並探討塊材在應力下的能帶、光學偏振以及微觀尺度的Bloch function變化。對塊材在應力之下的變化有基本認知後，我們未來工作更可將應力作用延伸至量子點。

關鍵字

量子點；精細匹裂；光學異相性；尺寸效應；應力

並列摘要

This thesis theoretically studies the size effects of quantum dots (QDs) on the fine structure properties as well the optical polarization. Known as representative excellent quantum light sources, two semiconductor QDs, InAs/GaAs self-assembled QDs and hierarchical GaAs/AlGaAs QDs are considered. Excitonic structures of the QDs are computed numerically by combining the four-band Luttinger-Kohn kp’s model for valence hole and single-band model for conduction electron within the 3D-parabolic potential model of QD. Optical polarizations of the single excitons in the dots are calculated by using Fermi’s Golden rule. Initial strain in InAs/GaAs self-assembled QDs induced by lattice mismatch is formulated as a function of size analytically and numerically calculated using finite-element software package, Comsol multiphysicsR. Analytical results indicate that the energetic competition of the size-dependent short- and long-ranged e-h exchange interactions diminish the fine structure splitting of an elongated QD. Moreover, the electronic structures and optical polarization properties of GaAs bulk under stress control were studied theoretically, in which the corresponding microscopic Bloch wave functions were visualized under applied stress by using the Slater Orbital model.

並列關鍵字

Quantum dot ； Fine structure splitting ； optic anisotropy ； size effect ； stress

參考文獻

1. M. Grundmann, O.Stier, and D. Bimberg, ” InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonons, and electronic structure”, Phys. Rev. B 52, 11969–11981 (1995).

2. S. Kumar, R. Trotta, E. Zallo, J. D. Plumhof, and P. Atkinson, “Strain-induced tuning of the emission wavelength of high quality GaAs/AlGaAs quantum dots in the spectral range of the 87Rb D2 lines”, Appl. Phys. Lett. 99, 161118 (2011).

3. R. Singh and G. Bester, ”Lower Bound for the Excitonic Fine Structure Splitting in Self-Assembled Quantum Dots”, Phys. Rev. Lett 104, 196803 (2010).

4. S. L. Chuang, “Physics of Photonic Devices”, Second Edition, Wiley (2008).

5. M. Gong, W. Zhang, G. C. Guo and L. He, “Exciton Polarization, Fine-Structure Splitting, and the Asymmetry of Quantum Dots under Uniaxial Stress”, Phys. Rev. Lett 106, 227401 (2011).

國際替代計量

量子點光源中精細結構匹裂與光學特性之研究

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