此篇論文以原子軌域線性組合法(linear combination of atomic orbital method)，原子鍵結軌域法(atomic bond orbital method)以及雙能帶k•p (two-band k•p)之能帶計算方法來研究III-V半導體之閃鋅礦結構及纖維鋅礦結構塊材之最低導帶電子自旋分裂能量的理論計算。

閃鋅礦結構的自旋分裂理論計算方面：我們發展了16能帶之原子鍵結軌域模型(16-band atomic bond-orbital model,16-band ABOM)，來計算閃鋅礦結構中塊材不對稱性所引起的自旋分裂能量。此模型推導自Td 點群之原子軌域模型理論方法，因此保有閃鋅礦結構之塊材不對稱性，故可計算閃鋅礦結構的自旋分裂。我們藉由對最近鄰LCAO Hamiltonian作矩陣相似轉換成16-band full-zone ABOM (16FZABOM)的Hamiltonian，進而在每一矩陣元對k於Γ 點附近做兩次方泰勒展開，最後導出簡化後的16-band center-zone ABOM (16CZABOM)的Hamiltonian。我們使用16能帶之原子鍵結軌域模型(16-band ABOM)來計算III-V半導體之InSb及GaAs閃鋅礦結構塊材的自旋分裂，我們發現16FZABOM的計算結果與LCAO計算結果完全一致並與第一原理計算結果近似；16CZABOM的計算結果與LCAO計算結果極近似，並與第一原理計算結果相近。此外，我們發現16能帶之原子鍵結軌域模型的Hamiltonian可直接算出p鍵結軌域與p反鍵結軌域之自旋軌道交互作用對最低導帶自旋分裂能量的貢獻為最大，其主導了最低導帶電子自旋分裂能量的大小。

纖維鋅礦結構的自旋分裂理論計算方面：我們使用原子軌域模型理論計算纖鋅礦結構氮化鋁材料之自旋分裂能量的大小，進而使用具解析解形式之雙能帶k．p理論計算擬合分析其最小自旋分裂能量簡併面及其附近之自旋分裂等能量面（ESS）的分佈情形。我們發現在k值較小( Γ 點附近)處，雙能帶k．p理論計算結果與原子軌道模型理論計算結果吻合。我們亦發現雙能帶k．p理論計算結果在雙軸壓縮應變(exx= -3%)的情況下，其結果會出現橢圓球形狀之最小自旋分裂簡併面及其附近亦會出現橢圓球形狀之自旋分裂等能量面；然而，此結果與原子軌道模型理論計算結果並不吻合。最後我們證實了在原子軌道模型理論計算中，不同的雙軸應變情況下，從雙軸壓縮應變(exx= -3%)至雙軸擴張應變(exx= +3%)，纖維鋅礦結構的AlN晶體之最小自旋分裂簡併面的形狀僅有三種基本形狀，其順序分別是雙葉雙曲面、圓錐面，及單葉雙曲面。同時，我們也證實了其最小自旋分裂簡併面附近之自旋分裂等能量面分佈的形狀也有三種基本形狀，分別為近似不對稱雙葉雙曲面、單葉雙曲面，及反向單葉雙曲面。

In this study, the spin-splitting energy of the lowest conduction bands in bulk zincblende and wurtzite structures of III-V semiconductors had been investigated by the linear combination of atomic orbital (LCAO) method, the atomic bond-orbital model (ABOM), and the two-band k．p (2KP) model.

Spin-splitting calculation for zincblende structures:
We develop a 16-band atomic bond-orbital model (ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16-band center-zone ABOM (CZABOM) is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion over k at the Γ point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin-orbit coupling between bonding and antibonding p-like states, evaluated by the 16CZABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials.

Spin-splitting calculation for wurtzite structures:
The spin-splitting energies in biaxially strained bulk wurtzite material AlN are calculated using the linear combination of atomic orbital (LCAO) method, and the equi-spin-splitting distributions in k-space near the minimum-spin-splitting (MSS) surfaces are illustrated. These data are compared with those derived analytically by two-band k．p (2KP) model. It is found that the results from these two methods are in good agreement for small k. However, the ellipsoidal MSS surface under biaxial compressive strain does not exist in the 2KP model, because the data points are far from the Γ point. Instead, three basic shapes of the MSS surface occur in the wurtzite Brillouin zone: a hyperboloid of two sheets, a hexagonal cone, and a hyperboloid of one sheet, evaluated from the LCAO method across the range of biaxial strains from compressive to tensile. The shapes of the equi-spin-splitting (ESS) surfaces near these MSS surfaces have also three types: a hyperboloid of one sheet, an approximate, asymmetric hyperboloid surface, and an opposing hyperboloid of one sheet.

Contents

Abstract ii
List of Tables vi
List of Figures vii

Chapter 1 Introduction 1

Chapter 2 Calculation Methods 10
2.1 Linear Combination of Atomic Orbitals (LCAO) Method for Zinc-blende and Wurtzite Structures 10
2.2 16-band Atomic Bond-Orbital Model (ABOM) for Zinc-blende Structure 25
2.3 2-band k•p (2KP) Model for Wurtzite Structure 30

Chapter 3 Spin-Splitting Calculation for Bulk Zinc-blende InSb and GaAs 32
3.1 Calculation Details for Bulk Zinc-blende InSb and GaAs 32
3.2 Spin Splitting Calculated by the 16-band ABOM for Bulk Zinc-blende InSb and GaAs 36
3.3 Spin Splitting Contributed by Three Different Couplings between Three Different States Calculated by the 16-band ABOM for Bulk Zinc-blende InSb and GaAs 40

Chapter 4 Spin-Splitting Calculation for Strained Bulk Wurtzite AlN 47
4.1 Calculation Details for Strained Bulk Wurtzite AlN 47
4.2 Spin Splitting Induced by the Type I and Type II Wurtzite Bulk Inversion Asymmetry (WBIA) Effects Calculated by the 2KP Model for Strained Bulk Wurtzite AlN 53
4.3 Equi-Spin-Splitting (ESS) distribution near Minimum Spin-Splitting (MSS) Surface Calculated by the LCAO Method for Strained Bulk Wurtzite AlN 58
4.4 A Comparison of the ESS and MSS Surfaces Calculated by both the 2KP and the LCAO Methods for Strained Bulk Wurtzite AlN 62

Chapter 5 Conclusion 68

Reference 71

Publication List 74

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