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研究生:李俊成
研究生(外文):LEE, CHUN-CHENG
論文名稱:外加磁場下砷化鎵二維電子系統電子傳輸特性之研究
論文名稱(外文):Magneto transport in a two-dimensional GaAs electron gas
指導教授:梁啟德
指導教授(外文):C.-T. Liang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理學研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:75
中文關鍵詞:磁阻砷化鎵
外文關鍵詞:magnetoresistivitytwo-dimensionalmagnetotransporttransport
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本篇論文主要探討砷化鎵二維電子系統在低溫下的電性量測.論文內容分為兩大部分:
1. 在外加磁場下與電子自旋有關的傳輸現象:
我們所使用的樣品是表面有鍍一層金屬的二維電子系統,可以透過對金屬層加不同的電壓來改變二維系統的載子濃度.當對二維電子系統外加一個平行磁場,我們觀察到磁電阻會隨著平行磁場的增加而增加.當外加一個足夠大的平行磁場,我們觀察到磁電阻會有飽和的現象.運用一個簡單的模型,我們可以計算出在這個稀薄的二維電子系統中,它的藍道係數g約等於3.32. 我們計算出的藍道係數(3.32)要比塊材砷化鎵藍道係數(0.44)大上許多,我們相信這是由於在低載子濃度下電子與電子間交互作用的影響.
2. 在傾斜磁場下與電子自旋有關的傳輸現象
我們量測在外加一個傾斜磁場,砷化鎵二維電子系統的電性現象.我們觀察到磁電阻率會隨著平行磁場分量增加而減少;以及在填充係數1.5時,磁電阻率在高磁場下會有飽和的現象.我們也做了一些在垂直磁場下,改變樣品溫度的量側.我們觀察到磁電阻率會隨著樣品溫度增加而增加,這現象可以用半圓理論(semi-circle relation)來加以解釋.最後我們對一個電子自旋分裂的電子系統做了垂直磁場的量測,我們觀察到自旋向上以及自旋向下的峰值會有不等量的減少.但對這現象的成因我們還沒有完整的理論可以來解釋或許將來能有符合的理論.

This dissertation describes the measurements in a two-dimensional GaAs electron gas on low temperature. It consists of the following two parts:
1. Spin-dependent transport in a parallel magnetic field:
Our sample is a high-quality gated two-dimensional electron system. We can change the electron density of the two-dimensional electron system by varying the gate voltage. We apply an in-plane parallel magnetic field to our two-dimensional system and observe an enhancement of magnetoresistivity with increasing the parallel magnetic field. When the parallel magnetic field is big enough, the magnetoresistivity shows saturation. Using a simple model, we estimate the landé g-factor in this dilute two-dimensional electron system to be about 3.32. This enhanced Landé g-factor compared with that of a bulk GaAs two-dimensional electron system (0.44) is ascribed to electron-electron interaction effects at ultra-low electron densities.
2. Spin-dependent Transport in a Tilted Magnetic Field:
We present measurements on a GaAs electron system in a tilted magnetic field. We observe that magnetoconductivity decreases with increasing the parallel magnetic field. I observe saturation of magnetoconductivity at filling factor v=1.5 in a high in-plane magnetic field, corresponding to the case when the spins are aligned in the 2DEG plane. We also perform measurements in a perpendicular magnetic field at various temperatures. In contrast, magnetoconductivity increases with increasing temperature T. This effect can be well described by the semi-circle relation. Finally we perform titled-field measurements for a spin-split electron gas. There is a crossover in which the spin-up peak is bigger than the spin-down one. The physical origins of our new results remain unclear and await further investigations.

Chapter 1. Introduction 1
1.1 Ⅲ/Ⅴ Semiconductors………………………………………………….1
1.2 Properties of GaAs Devices………………………………………2
1.3 Motivation……………………………………………………………………3
Chapter 2. Theoretical Background 6
2.1 Heterostructure…………………………………………………………….6
2.1.1 The Metal-Oxide-Semiconductor Junction (MOS)………………6
2.1.2 The GaAs/AlxGa1-xAs Heterostructure……………………………9
2.2 The Two-Dimensional Electron System……………………………11
2.3 Density of States……………………………………………………12
2.3.1 Density of States in Three-Dimensions……………………12
2.4 Classical Hall Effect………………………………………………17
2.5 Landau Levels…………………………………………………………20
2.5.1 Nonrelativistic Electron System……………………………20
2.5.2 System in a Cube………………………………………………22
2.6 Quantum Hall Effect…………………………………………………25
Chapter 3. Sample Fabrication and Measurements Setup 30
3.1 Sample Fabrication……………………………………………………30
3.1.1 Sample Structure…………………………………………………30
3.1.2 Optical Lithography………………………………………………31
3.2 Cryogenic System: Sorption Pumping 3He Cryostat……………34
3.2.1 Superconducting Magnet…………………………………………34
3.2.2 Condensation of 3He and Controlling the Temperature…34
3.3 Four-terminal Resistance Measurements…………………………36
3.3.1 Measurements Setup………………………………………………36
3.3.2 Data Acquisition and Analysis…………………………………38
Chapter 4. Spin-dependent Transport in a Two-dimensional GaAs/AlGaAS Electron Gas in a Parallel Magnetic Field 40
4.1 Introduction……………………………………………………………40
4.2 Spin Polarization……………………………………………………40
4.3 The Ratio of Coulomb Energy to Kinetic Energy rs…………44
4.4 Density of State Changes by Applying a Parallel Magnetic Field........................................................45
4.5 Varying the Carrier Densities…………………………………49
4.6 Results and Discussion………………………………………………51
4.6.1 Measurements of the Diagonal Resistivity in a Parallel Magnetic Field……...........................................51
4.6.2 Estimating the g-factor in a parallel Magnetic Field Model………………............................................57
4.7 Summary…………………………………………………………………60
Chapter 5. Spin-dependent Transport in a Tilted Magnetic Field .....................................................62
5.1 Introduction to Tilted-field Measurements………………….62
5.2 Tilted-field Measurements………………………………………..64
5.3 Observation of the Magnetoresistance under Varying the Parallel Magnetic Field and the Sample Temperature…………...70
............................................................5.4 Summary………………………………………………………………………73
Chapter 6. Conclusions 75

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