用單和八能帶模型模擬三五族半導體量子點和分子的等效g因子

Abstract

在本文中，我們使用三種高效率的三維模擬，去計算在複雜幾何形狀和不同材料含量的 半導體奈米物體中的等效g 因子張量。 第一，我們比較了 Rashba 自旋軌道交互作用的兩種不同模型(全三維和“絕熱”二維)， 以及提出映射方法來探討自旋軌道交互作用對於g 因子異向性的影響。這份研究適合用於釐 清一個重要問題，就是哪一種近似方法可以解釋和重現半導體量子點中的內建三維電子g 因 子異向性。我們從理論上證明在g 因子模擬中，全三維的描述是必要的。電子g 因子和因子 異向性的模擬數值與實驗觀測吻合。 第二，考慮自旋軌道交互作用、晶格應變和外部電場，我們使用單能帶模型來探討，砷 化銦/砷化鎵的非對稱透鏡形量子點的橫向排列分子中的電子等效g 因子張量。我們的計算方 法讓我們非常經濟高效地模擬，在廣泛變化系統參數下，考慮Rashba 和Dresselhaus 自旋軌 道耦合之於等效g 因子的特性。我們論證等效g 因子張量的各個分量和三維異向性可以靜態 控制(改變量子分子之原位配置的幾何參數和材料含量)以及動態控制(施加外部電場)。我們取 得的電子g 因子張量的各個分量和異向性與實驗觀測吻合。我們的計算方法可以應用於，選 擇操控在複雜幾何形狀和不同材料含量的半導體奈米物體中的孤立和纏結自旋的實際建模。 第三，我們使用八能帶模型來探討砷化鎵圓柱形量子點中的電子等效g 因子，當周圍材 料砷化鋁x 鎵1-x (0.15 < x < 0.30)的含量改變時。我們使用的g 因子公式，包括遠程能帶的 修正項以及正確的電子波函數歸一化常數。此外，我們引進一個縮放參數來符合日本團隊的 實驗數據。該系統中電子g 因子的模擬數值在砷化鎵/砷化鋁0.15 鎵0.85 比在砷化鎵/砷化鋁 0.30 鎵0.70 較小，亦由實驗測量證實。最後，我們模擬在六個不同周圍材料的原位配置中電 子g 因子數值，並且論證他們是與電子波函數的原位配置有相關的。

In this thesis, we use three efficient full three-dimensional simulation to calculate the effective g-factor tensor in semiconductor nano-objects of complex geometry and material content. First, we compared two different models for the Rashba spin-orbit interaction (full three dimensional and "adiabatic" two dimensional) and proposed mapping method to investigate the impact of the spin-orbit interaction on the g-factor anisotropy. The study is suited to clarify the important question of which approximation can explain and reproduce the build-in three dimensional anisotropy of the electron g-factor in semiconductor quantum dots. We theoretically show that the full three dimensional description is essential in g-factor simulations. The simulated magnitude of the electron g-factor and the factor anisotropy ratio are in a good agreement with the experimental observations. Second, taking the spin-orbit interaction, lattice strain, and external electric field into account, we use one band model to study the effective electron g-factor tensor for InAs/GaAs lateral asymmetrical lens-shaped quantum dot molecules. Our calculation method allows us very cost-effectively to simulate the effective g-factor properties within a wide range of the system parameters change when the Rashba and Dresselhaus spin-orbit couplings are considered. We demonstrate that the components, and three-dimensional anisotropy of the effective g-factor tensor can be controlled statically (in-situ configuration of the quantum molecule geometrical parameters and ii material content) and dynamically (by application of the external electric field). We have obtained the components of the electron g-factor tensor and the anisotropy ratio in good agreement with the experimental observations. Our computational approach can be applied for the realistic modeling of selective manipulations of isolated and entangled spins in semiconductor nano-objects of complex geometry and material content. Third, we use eight band model to study the effective electron g-factor of GaAs cylindrical quantum dot varying the content of the surrounding material AlxGa1-xAs (0.15<x<0.30). We use the g-factor formula including the corrections from the remote band and with the proper normalization constant for the electron wavefunction. Furthermore, we introduce one scaling parameter to fit the experimental data from the Japanese team. The simulated value of the electron g-factor in GaAs/Al0.15Ga0.85As is smaller than in GaAs/Al0.30Ga0.70As which is confirmed by the measurement. Finally, we simulate the value of the electron g-factor in six different in-situ configurations of the surrounding material and demonstrate that they are correlated to the in-situ configuration of the electron wave function.