在這本論文中，我們分析在二維系統中，bulk inversion asymmetry (BIA)和structure inversion asymmetry (SIA)對自旋與軌道交互作用(spin-orbit interaction)的貢獻。因此，我們先分析材料系統中的Dresselhaus parameterγ 和Rashba parameterα，再分別地利用理論方式計算出 bulk inversion asymmetry (BIA)和 structure inversion asymmetry (SIA)造成的自旋分裂能量(Δso ，spin splitting energy)。其中Dresselhaus parameter決定於材料成長的同時，而Rashba parameter會隨著能帶結構改變，因此Rashba parameter理論上分成field和boundary兩部份貢獻加以討論。
在第一個材料系統中，分別有四個試片，其中wafer1和wafer 3 參雜層在二維量子井之上，wafer 2和wafer 4 參雜層在二維量子井之下，並且在wafer1 和wafer2中，加入25 奈米厚的InP 在量子井成長方向的上方，然後分析這樣的材料系統。經過理論計算之後，發現參雜層的位置決定了 αfield 的符號，並且InP的加入會造成αboundary 貢獻增加而對總的Rashba parameter造成影響，這樣的影響反應在自旋能量的分裂上，可以看出wafer 1和wafer 3 ，SIA 的自旋分裂能量比BIA 的自旋分裂能量來的大；wafer 2因為InP對總的Rashba parameter 有很大的減低作用，所以在sin(2φ)= 0的方向上，SIA 的自旋分裂能量比BIA 的自旋分裂能量來的大，在sin(2φ)= 1的方向上，SIA 的自旋分裂能量比BIA 的自旋分裂能量來的小；而； wafer 4，除了SIA 的自旋分裂能量隨載子密度升高而降低外，BIA的自旋分裂能量貢獻在載子密度大於9.3×1011cm-2超越SIA 的自旋分裂能量。
在第二個材料系統中，我們選擇晶格常數與基板不匹配的材料In0.2Ga0.8As作為二維的通道，參雜層皆在通道上方，並嵌入GaAs取代InP，這樣的用意是使價電帶產生階梯狀的結構，和嵌入InP形成的山谷型結構作區隔，也因為我們使用晶格常數不匹配的材料，因此應力所造成的自旋能量分裂也被考慮進去，結果即使嵌入GaAs，發現SIA 的自旋分裂能量貢獻比BIA 的自旋分裂能量來的小，而應力造成的自旋分裂能量也佔很小的比例。

In this thesis, the contributions of bulk and structure inversion asymmetry
to spin-orbit interaction in two-dimensional system were studied. In the be-
ginning, we calculated Dresselhaus parameter ° and Rashba parameter ®
of material systems, then theoretically estimated the spin splitting energy
¢0 resulting from bulk inversion asymmetry (BIA) and structure inversion
asymmetry (SIA). For Dresselhaus parameter once the structure was grown,
it was decided its value. However Rashba parameter changes with the di®er-
ence of band structure and carrier density, it can be separated into ‾eld and
boundary parts to calculate.
In material system 1, wafer 1 and wafer 3 has a doping layer above the 2D
channel, but wafer 2 and wafer 4 do below the channel. The 25 nm inserted
InP layer inset above the channel for wafer 1 and wafer 2. After calculating,
the doping layer position decided the sign of the ‾eld contribution and the
inserted InP layer enhanced or reduced the total Rashba parameter depend-
ing the doping layer position. It can be observed that for wafer 1 and wafer
3 the contribution to spin splitting energy of SIA is larger than BIA, for
wafer 2 due to InP layer the reduction to total Rashba parameter resulted
in the SIA spin splitting energy is among two of BIA spin splitting energy
of di®erent direction, for wafer4 the SIA splitting energy decreased with a
increasing carrier density, especially over ns = 9:3 £ 1011cm¡2, BIA contri-
bution is larger than SIA.
In material system 2, the lattice mismatch with GaAs material In0:2Ga0:8As
was used for 2D quantum well. The front doping and inserted GaAs was pre-
sented in order to product a step-like valence band ¡8. The strain e®ect was
also considered. The results of our analysis was that the SIA contribution is
smaller than BIA even though GaAs inset into the 2D quantum well.

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