臺灣博碩士論文加值系統

我們計算具有拉什巴自旋軌道交互作用(Rashba spin-orbit interaction, R-SOI) 之準一維電洞系統的能帶結構和電導，並且考慮施加一個磁場所感應之賽曼(Zeeman)效應。最後再分析施加不同方向的單軸應變對能帶結構的影響。Zeeman效應會使能帶上下分裂，而R-SOI會導致電洞能譜左右分裂。我們研究具有賽曼以及R-SOI的P型量子通道，在Zeeman和R-SOI不為零時，量子化電導將會出現一異常的峰值，然而，只有輕電洞會出現電導異常峰而不是重電洞。此電導的不規則特徵之穩定性可以通過操縱Zeeman、Rashba參數和電洞奈米通道寬度來進行調整。當R-SOI為強耦合，並且在一固定磁場時，SO能隙不會隨著Rashba參數的大小而有所變化。考慮P型量子通道施加應變自旋軌道作用且在傳輸方向施加單軸拉伸應變時，其輕重電洞能隙(lh-hh gap)會增加，若是將單軸拉伸應變施加在通道方向，其輕重電洞能隙會下降，且會出現能帶反交叉(anti-crossing)現象。我們分析出P型量子通道受應變效應而使輕重電洞能隙下降的極值為應變正負2%。

We calculate the band structure and conductance of a p-type quasi-one- dimensional system with a Rashba spin-orbit interaction (R-SOI) and a magnetic field induced Zeeman effect. The Zeeman effect causes energy band splitting longitudinally, and the R-SOI leads to a lateral hole spectroscopy division. In the presence of Rashba-Zeeman effect of the p-type quantum channel, the quantization conductance will be an anomalous peaks. However, only light hole occur anomalous peaks for the ballistic conductance rather than heavy holes. The robustness of the anomalous features in the ballistic conductance can be tuned by manipulating the effective Rashba and Zeeman parameters as well as the hole-nanowire width. When R-SOI is in the strong coupling regime for a given magnetic field, it is found that the SO gap size is not changed by the Rashba parameter. We consider that the p-type quantum channel can increase the light hole-heavy hole gap (lh-hh gap) when applying a strain spin-orbit with uniaxial tensile strain in the transport direction. If the uniaxial tensile strain is applied in the direction of the channel, the gap between light hole and heavy hole will decrease. We have analyzed the p-type quantum channel by the strain spin-orbit and the energy gap is not the extent of the endless, the extreme value of +-2%

摘要 III
Abstract IV
致謝 V
目錄 VI
圖目錄 VIII
第一章 緒論 1
1.1 前言 1
1.2 一維量子理論 3
1.2.1 自由粒子的波動力學 3
1.2.2 位勢台階 6
第二章 能帶基礎理論 9
2.1 量子元件傳輸簡介 9
2.2 自旋軌道耦合交互作用 13
2.2.1 Rashba效應 15
2.2.2 Zeeman效應 17
2.3 量子通道元件簡介 19
2.3.1 N型量子通道能帶理論 21
2.3.2 一維輕電洞能帶理論 24
2.3.3 準一維輕電洞能帶理論 28
2.4 輕電洞自旋能帶理論 33
2.4.1 Rashba效應對輕電洞能帶結構的影響 34
2.4.2 Zeeman效應對輕電洞能帶的影響 40
2.4.3 Rashba-Zeeman效應對輕電洞能帶結構的影響 45
2.5 P型輕電洞閘控元件 52
2.5.1 P型輕電洞閘控元件的Rashba效應 54
2.5.2 P型輕電洞閘控元件的Zeeman效應 58
第三章 P型輕重電洞自旋元件 62
3.1 P型量子通道輕重電洞能帶理論 64
3.1.1 準一維通道中的電洞基本能帶 65
3.2 數值結果與分析 71
3.2.1 Zeeman效應對輕重電洞能帶結構的影響 71
3.2.2 Rashba效應對輕重電洞能帶結構的影響 75
3.2.3 Rashba-Zeeman效應對輕重電洞能帶結構的影響 77
第四章 P型輕重電洞耦合元件受應變之影響 84
4.1 [001]準一維量子通道的Hamiltonian 84
4.1.1 能量算符與其基底分析 84
4.1.2 [001]方向準一維電洞系統座標轉換 88
4.2 通道方向在[001]中所受應變影響的能帶結構 90
4.2.1 受應變影響的Hamiltonian 91
4.2.2 應力與應變關係式 93
4.2.3 [001]準一維輕重電洞受應變影響的能帶結構與分析 96
第五章 結論 112
參考文獻 114
附錄 117
附錄 A 電洞能量算符之合併計算過程 117
附錄 B 材料參數表 [14]： 120

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