在本論文中主要是探討砷化鎵/砷化鋁鎵異質結構半導體中二維電子系統在外加垂直磁場下的半古典與量子傳輸特性。我們研究了樣品A以及樣品B在不同實驗架構下的行為。在樣品A中，我們著重於探討當熱耗（thermal damping）效應被抑制時，Shubnikov-de Haas（SdH）理論的適用性。我們發現SdH理論之有效區可以被延伸，其中正磁阻效應與無序性引致耗散（disorder-induced damping）具有重要的影響。
在樣品B的實驗中，我們以正與負電流的精密量測來去除熱電阻之影響。我們發現SdH理論中半古典的Lifshitz-Kosevich公式在描述磁阻震盪時具有較強的適用性。同時我們還觀察到移動率間隙（mobility gap）之存在，而這顯示了整數量子霍爾效應之特性。我們推論半古典行為是由於藍道能帶尾端之電子所貢獻，並且我們可以考慮量子擴散模型來修正Dingle項。

We study the semiclassical and quantum transport properties of the two-dimensional electron system in GaAs/AlGaAs semiconductor heterostructures under a perpendicular magnetic field. We studied two different samples, A and B under different experimental frameworks. For sample A, we mainly probe the applicable range of the Shubnikov-de Haas (SdH) theory when the thermal damping is reduced with decreasing temperature. We found the applicable range of the SdH theory can be extended, and the positive magneto-resistance and the disorder-induced damping play important roles.
In the experiment of sample B, we removed the influence of thermal resistance by measuring forward and backward currents. We found the semiclassical Lifshitz-Kosevich formula in the SdH theory is more robust in describing the magneto-oscillations. Surprisingly, we found the existence of the mobility gap, which indicates the quantum Hall effect. The semiclassical behavior is attributed to the electrons away from the tails of Landau bands. Our study hints that we shall consider the quantum diffusion model to modify the Dingle term.

第一章 序論 1
1-1 半導體簡介 1
1-2 二維電子氣系統的特性 7
1-2-1 自由電子的特性 8
1-2-2 位能井中二維電子的特性 9
1-2-3 異質結構半導體中二維電子的特性 11
1-3 二維電子氣系統的應用 14

第二章 實驗背景 16
2-1 在半導體異質介面中的二維電子氣 16
2-2 二維電子系統在磁場中的物理現象 18
2-2-1 古典霍爾效應 18
2-2-2 量子霍爾效應 23
2-2-3 Shubnikov-de Hass震盪 35
2-2-4 散射機制 38
2-2-5 激發導電性（Activated conductivity） 43
第三章 實驗系統 45
3-1 實驗樣品 45
3-1-1 樣品性質 45
3-1-2 樣品處理 47
3-2 實驗儀器 48
3-2-1 杜瓦瓶 49
3-2-2 Insert 52
3-2-3 超導磁鐵 56
3-3 實驗步驟 57
3-3-1 置放樣品於insert上 57
3-3-2 抽真空 59
3-3-3 預冷 60
3-3-4 吹出液態氦、檢查毛細管與針狀閥、傳輸液態氦 62
3-3-5 降低樣品層溫度 63
3-3-6 補充液氦層液氦 65

第四章 實驗結果 66
4-1 實驗條件 66
4-2 整數量子霍爾效應結果 69
4-3 SdH振盪數據分析結果 70
4-3-1 有效質量m* 71
4-3-2 量子散射時間

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