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博碩士論文 etd-0721105-234910 詳細資訊
Title page for etd-0721105-234910
論文名稱
Title
二維電子系統中低磁場下的藍道量子化效應之研究
Studies on the effects of low-field Landau quantization in a two-dimensional electron system
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
115
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2005-06-16
繳交日期
Date of Submission
2005-07-21
關鍵字
Keywords
藍道量子化、Shubnikov-de Hass效應、異質結構半導體、平台間相變化、整數霍爾效應、二維電子系統
quantum Hall effect, Landau quantization, two-dimensional system, plateau-plateau phase transition, Shubnikov-de Hass effect, heterostructure semiconductor
統計
Statistics
本論文已被瀏覽 5660 次,被下載 13
The thesis/dissertation has been browsed 5660 times, has been downloaded 13 times.
中文摘要
在本論文中主要是探討在高遷移率之砷化鎵/砷化鋁鎵異質結構半導體中二維電子氣體在低溫高磁場下的傳輸特性。我們分析了五組不同溫度下所量測到的縱向電阻與霍爾電阻。我們觀察到在小於0.25 Tesla的磁場範圍時古典霍爾效應是成立的;而在大於1.6 Tesla時則明顯地出現了量子霍爾平台。我們是對介於0.477到1.483 Tesla之間的磁場所產生的縱向電阻振盪進行分析。根據Lifshitz-Kosevich (LK) formula,我們可以由量子磁阻振盪的量測求出二維電子密度、電子有效質量、量子散射時間。我們的結果指出LK formula成立的範圍會比一般所預設的來的大。而在高磁場下的量子霍爾效應機制中,我們可以由實驗的量子霍爾平台值去推算物理量h/e2之值。
在古典霍爾效應的機制下,可以求出電子的三
Abstract
In this paper, we mainly discuss the transport properties of the two-dimensional gas of a high-mobility GaAs/AlGaAs semiconductor heterostructure in high magnetic fields and low temperatures. We analyzed the measured longitudinal resistivity and Hall resistivity at the five different temperatures. We observed that the classical Hall effect is valid when the magnetic field is less than 0.25 Tesla; and the quantum Hall plateaux appeared obviously when the magnetic field is larger than 1.6 Tesla. We proceeded to analyze the longitudinal resistivity oscillation occurred in the magnetic fields between 0.477 Tesla and 1.483 Tesla. According to the Lifshitz-Kosevich (LK) formula, we can get the two-dimensional electron concentration, effective mass, and quantum scattering time from the quantum magnetoresistivity oscillation measurement. Our results suggested that the applicable range of the LK formula could be broader than the generally-assumed one. In quantum Hall effect regime at high magnetic field, we can calculate the h/e2 value from the quantum Hall plateaux value.
In classical Hall effect regime, the three-dimensional electron concentration and classical mobility (classical scattering time) can be obtained. However, we find out that the zero-field Hall resistivity experimental value is not equal to zero, and this is not conformed to the standard theory. We tried to use the magnetic field shift and Hall resistivity shift to solve the problem, and compared both advantages of them.

Finally, we observed the plateau-plateau phase transitions of the two-dimensional electron system
目次 Table of Contents
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 5
1-2-1 自由電子的特性 5
1-2-2 位能井中二維電子的特性 6
1-2-3 異質結構半導體中二維電子的特性 8
1-3 二維電子氣系統的應用 10

第二章 實驗背景 12
2-1 在半導體異質介面中的二維電子氣 12
2-2 二維電子系統在磁場中的物理現象 14
2-2-1 古典霍爾效應 14
2-2-2 量子霍爾效應 19
2-2-3 Shubnikov-de Hass效應 31
2-2-4 散射機制 34

第三章 實驗系統 39
3-1 實驗樣品 39
3-1-1 樣品性質 39
3-1-2 樣品處理 41
3-2 實驗儀器 42
3-2-1 杜瓦瓶 43
3-2-2 Insert 46
3-2-3 超導磁鐵 50
3-3 實驗步驟 51
3-3-1 置放樣品於insert上 51
3-3-2 抽真空 53
3-3-3 預冷 54
3-3-4 吹出液態氦、檢查毛細管與針狀閥、傳輸液態氦 56
3-3-5 降低樣品層溫度 57
3-3-6 補充液氦層液氦 59

第四章 實驗結果 60
4-1 實驗條件 60
4-2 整數量子霍爾效應結果 62
4-3 SdH振盪數據分析結果 65
4-3-1 有效質量 66
4-3-2 量子散射時間 68
4-3-3 二維電子密度 71
4-3-4 Lifshitz-Kosevich formula 之驗證 74
4-4 由量子霍爾平台實驗值求h/e2值 76
4-4-1 填充因子 76
4-4-2 h/e2實驗值 79
4-5 古典霍爾效應結果 80
4-6 考慮系統誤差後對原始數據的修正 83
4-6-1 磁場平移-13 mT 84
4-6-2 霍爾電阻平移+26
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