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two-band k•p方法，來研究纖維鋅礦結構內之電子自旋分裂。為了解釋實驗中在纖維鋅礦氮化鎵二維電子氣中所發現的零磁場大自旋分裂，我們提出了一個新的機制(ΔC1–ΔC3 耦合)，此機制是由內禀的纖維鋅礦效應(band folding效應以及纖維鋅礦塊材反轉不對稱)所產生。其中，band folding效應使的導帶電子在接近由兩個最低能量之導帶(ΔC1和ΔC3)所形成的反交錯(anticrossing)區時，p軌道的成份產生很大的變化。我們的計算結果顯示，由band folding效應以及纖維鋅礦結構反轉不對稱所產生的自旋分裂能量，遠大於Kane model所計算出的自旋分裂能量。我們嘗試以氮化鎵/氮化鋁之超晶格來模擬量子井，並發現此量子井中電子的自旋分裂對電場非常敏感。
另一方面，在計算纖維鋅礦塊材的導帶電子自旋分裂能量時，我們發現纖維鋅礦不只有自旋分裂簡併線(沿kz軸)，我們也同時發現了纖維鋅礦塊材存在最小自旋分裂面，這個最小自旋分裂面在靠近Γ點附近時，相當於自旋分裂簡併面，並可由 (b≈4)來描述。我們稱此現象為纖維鋅礦材料塊材中的Dresselhaus效應(由k的三次方項構成)，因為此效應在two-band k•p漢彌爾頓中產生了 γwz(bkz2- k//2)(σxky-σykx)=0項。我們也證明了在k•p範疇中，自旋分裂可收斂至k的三次方項。所以，在D’yakonov-Perel’ (DP)自旋遲緩的機制之下，我們預期[001]方向成長的纖維鋅礦量子井中的電子自旋生命期，可藉由適當的形變、外加電壓或照光等的元件設計來做調控。
總結： (1)纖維鋅礦中的塊材反轉不對稱會增強自旋分裂的能量；(2) 電子在纖維鋅礦結構量子井中的自旋分裂能量，對電場非常的敏感； (3) 纖維鋅礦材料中，不只有time reversal的簡併線，在k•p scheme下還存在自旋分裂的簡併面。因此，我們認為纖維鋅礦材料(如InGaN/AlGaN或InN/AlInN)是一個非常具有潛力的自旋電子元件材料，例如可用來作為自旋生命期共振態電晶體的基礎材料。

The spin-splitting energy in wurtzite structure semiconductors had been investigated by linear combination of atomic orbital method (LCAO), atomic bond orbital method and two-band k•p method. In order to explain the large zero field spin splitting in wurtzite GaN, a different mechanism (ΔC1–ΔC3 coupling) was proposed, which originated from the intrinsic wurtzite effects (band folding and wurtzite bulk inversion asymmetry). The band-folding effect generates two conduction bands (ΔC1 and ΔC3), in which p-wave probability has tremendous change when kz approaches the anticrossing zone. The spin-splitting energy induced by theΔC1–ΔC3 coupling and wurtzite bulk inversion asymmetry is much larger than theory calculation of Kane model. When we apply the coupling to GaN/AlN quantum wells, we find that the spin-splitting energy is sensitively controllable by an electric field.
It is also found that ideal wurtzite bulk inversion asymmetry yields not only a spin-degenerate line (along the kz axis; time reversal axis) but also a minimum-spin-splitting surface, which can be regarded as a spin-degenerate surface in the form of bkz2- k//2=0 (b≈4) near the Γ point. This phenomenon is referred to as the Dresselhaus effect (defined as the cubic-in-k term) in bulk wurtzite materials because it generates a term γwz(bkz2- k//2)(σxky-σykx)=0 in the two-band k•p Hamiltonian. And it is also demonstrated that in the k.p scheme, the spin splitting vanishes to cubic order in k. Consequently, the D’yakonov-Perel’ (DP) spin relaxation mechanism can be effectively suppressed for all spin components in [001] wurtzite quantum wells (QWs) at a resonance condition through device design with appropriate strain, gate voltage or optical illumination.
In conclusion: (1) the spin-splitting energy is enhance by wurtzite bulk inversion asymmetry; (2) the spin-splitting energy in wurtzite quantum well is sensitively controllable by electric field; (3) there exist a spin degenerate surface for wurtzite materials in k•p scheme. Therefore, wurtzite QWs (e.g., InGaN/AlGaN and InN/AlInN) are potential candidates for spintronic devices such as the resonant spin lifetime transistor.

Acknowledgement 3
Abstract 8
Publication List 11
Acronyms, Notations and Symbols 14
Spin splitting of zinc-blende structure 15
1.1 Kane model 15
1.2 Rashba and Dresselhaus effect derived from Kane model 16
Spin splitting of wurtzite structure 20
2.1 Motivation 20
2.2 Spin splitting in wurtzite materials 20
2.3 Calculation results 23
Minimum spin-splitting surface & two-band k•p Hamiltonian 29
3.1 Minimum spin-splitting surface in wurtzite structure 29
3.2 Degenerate surface in k•p scheme 32
3.3 Resonant spin-lifetime transistor 35
Summaries, conclusion and future work 44
Appendix I. 8-band Taylor Expansion of Atomic Bond-Orbital Model for Wurtzite Structure 46
Part a. Find 8 symmetry bond-orbital states at Γ-point 46
Part b. Perform Taylor series expansion on ABOM Hamiltonian to quadratic-order in k 54
Part c. Obtain the general form of TABOM Hamiltonian 84
Part d. The the spin-orbit term for TABOM Hamiltonian 94
Appendix II. WBIA terms derived from second-order perturbation 96

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