臺灣博碩士論文加值系統

在這論文中，我們在實驗方面研究了電導量子化的現象，並且得到我們樣品之二維電子氣的基本特性。最後，在窄通道(NC)中加有限範圍的時空週期性位能，其特性將在理論方面被研究。
在實驗方面，我們量測了Hall bar的磁電阻Rxx與霍爾電阻RH，並且用以決定二維電子氣的電子密度ns與μe遷移率。我們也量測窄通道的電阻，並藉由量測到的電阻得到量子化的電導。窄通道是藉由在GaAs/AlxGa1-xAs異質結構的表面上製造分離閘極(split gate)並加負偏壓來得到。
在理論方面，我們外加一時間與空間均為週期性改變的位能於窄通道上，並研究其特性。我們的結果顯示出，隨著化學位能(μ)的增加，通過窄通道的電導G將出現兩溪谷結構(valley structure)，這是由於電子與光子間的耦合(electron-photon coupling)所引起。除了溪谷結構(valley structure)外，我們另外發現dip結構，此dip結構與準束縛態(quasi-bound-states)的形成有密切的關係，是電子進行同調非彈性散射，躍遷到子能帶的底限能所產生的結果。

In this dissertation, we study the quantized conductance phenomena on the experimental side and obtain the physical parameters of the 2DEG in our samples. Finally, quantum transport in a narrow constriction (NC), and in the presence of a finite-range spatiotemporal periodic potential, is studied on the theoretical side.
On the experimental side, the magnetoresistance Rxx and Hall resistance RH on the Hall bar are measured to determine the electron density ns and mobility μe of the 2DEG. We also measure the resistance in the narrow channel. The quantized conductance is obtained from the measured resistance. The narrow channels are defined electrostatically by means of a split gate on top of the GaAs/AlxGa1-xAs heterostructures.
On the theoretical side, this work investigates the quantum transport in a narrow constriction acted upon by an external driving potential that has both spatial and temporal periodicity：by K and Ω. Our results show that, as the chemical potential μ increases, the conductance G through the narrow constriction exhibits two valley structures due to the electron-photon coupling. Besides the valley structures, we also find dip structures. These dips are associated with the formation of quasi-bound-states by making coherent inelastic scattering to the subband threshold.

目 錄
中文摘要……………………………………………………………………………. i
英文摘要…………………………………………………………………………… ii
誌謝………………………………………………………………………………… iii
目錄………………………………………………………………………………. iv
圖目錄………………………………………………………………………………. vi
第一章 緒論……………………………………………………………………… 1
1.1 動機………………………………………………………………………. 1
1.2 量子傳輸之歷史背景……………………………………………………. 1
1.3 介觀系統…………………………………………………………………. 4
1.4 電導量子化………………………………………………………………. 5
一、實驗方面…………………………………………………………… 5
二、理論方面…………………………………………………………… 5
1.5 論文架構…………………………………………………………………. 6
第二章 GaAs/AlGaAs二維電子系統……………………………………………. 7
2.1 GaAs/AlGaAs之特性…………………………………………………….. 7
2.2 磁電阻與霍爾電阻的量測………………………………………………. 8
2.3 量測結果…………………………………………………………………. 12
第三章 元件之製造……………………………………………………………… 19
3.1 元件製造流程…………………………………………………………… 19
第一部份：平台(mesa)結構的製作……………………………………. 20
第二部份：歐姆接觸(ohmic contact)的製作………………………… 22
第三部份：金屬閘極(metal gate)的製作………………………………. 24
光微影(photolithography)部份………………………………… 24
電子束微影部份(e-beam lithography)………………………… 27
第四部份：接線(wire bonding)………………………………………… 30
3.2 光罩(photomask)的設計…………………………………………………. 32
3.3 微影技術(lithography)……………………………………………………. 33
(1)光微影技術(photolithography)……………………………………… 33
反轉光微影技術(reversal photolithography)………………………… 36
(2)電子束微影技術(e-beam lithography)……………………………… 38
3.4 溼式蝕刻(wet etching)………………………………………………… 40
3.5 熱蒸鍍(thermo-evaporation)…………………………………………….. 40
3.6 歐姆接觸(ohmic contact)……………………………………………… 43
3.7 接線(wire bonding)……………………………………………………… 45
第四章 窄通道(NC)之電導的量測……………………………………………… 46
4.1低溫系統(cryostats system).…………………………………………… 46
一、4He低溫系統…………………………………………………… 46
二、3He低溫系統……………………………………………………… 47
4.2電導量測…………………………………………………………………. 50
一、四點量測法………………………………………………………… 50
二、量測過程…………………………………………………………… 50
4.3量測結果與討論…………………………………………………………. 53
第五章 窄通道中電導的時變效應……………………………………………… 59
5.1 準束縛態的概念(Quasi-bound-states)…………………………………… 59
5.2 理論……………………………………………………………………… 60
5.3 數值分析結果與討論……………………………………………………. 67
5.4 結論……………………………………………………………………… 75
第六章 未來工作………………………………………………………….……… 76
參考文獻……………………………………………………………………………. 77

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