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研究生:蔡家瑋
研究生(外文):Chia-Wei Tsai
論文名稱:三個量子點串接耦合而成的分子之熱電特性分析:平均場論與多體理論之比較
論文名稱(外文):Thermoelectric properties of a serially coupled triple quantum dot molecule:comparison between the mean-field theory and the many-body theory
指導教授:郭明庭
指導教授(外文):Ming-Ting Kuo
學位類別:碩士
校院名稱:國立中央大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:中文
論文頁數:94
中文關鍵詞:熱電量子點多體理論平均場論塞貝克效應奈米
外文關鍵詞:thermoelectricquantum dotmany-bodymean-fieldSeebeck effectnano
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本論文中利用Hubbard模型與Anderson模型來研究三個量子點串接耦合而成的分子與金屬電極連接形成的接面系統之熱電特性。利用格林函數,我們可以得到量子點系統中的電子狀態密度。在格林函數的建立上,我們考慮了平均場論和多體理論兩種推導方法。我們藉由凱帝旭格林函數的技巧可以計算出系統中的電流及熱流,探討在線性響應區下的電導、塞貝克(Seebeck)係數、電子熱導以及熱電優值(ZT)。我們發現使用平均場論時所得到的熱電優值是高估於多體理論的。在低溫區,塞貝克係數會在Hubbard能隙中出現異常的提升。在高溫區,電導會高估。此外,我們利用多體理論的方法來分析及討論量子點大小不一致、量子點間電子跳躍強度和庫倫交互作用改變時對於熱電優值的影響。
The thermoelectric properties of a serially coupled triple quantum dot molecule connected to the metallic electrodes are theoretically studied by using the Hubbard model and Anderson model. The charge and heat currents are calculated in the framework of Keldysh Green’s function technique. The electrical conductance, Seebeck coefficient, electron thermal conductance and figure of merit(ZT) are calculated in the linear response regime. We consider two procedures to evaluate Green’s functions : mean-field theory and many-body theory. We find that the ZT calculated by the mean-field theory is overestimated, in the comparison between two theories. In the low temperature regime, Seebeck coefficient appears an abnormal enhancement in the Hubbard gap. In the high temperature regime, the electrical conductance is overestimated. Based on the many-body theory, the effects of quantum dot size fluctuation, interdot hopping strength variation and interdot Coulomb interaction change on the figure of merit are analyzed and discussed.
摘 要 i
ABSTRACT ii
致謝 iii
目錄 iv
圖目錄 vii
表目錄 xi
第 1 章 、導論 1
1-1 前言 1
1-2 熱電元件的背景 1
1-3 文獻回顧 3
1-4 研究動機 6
第 2 章 、串接耦合量子點系統模型與電子傳輸特性 8
2-1 前言 8
2-2 理論模型 9
2-2.1 系統模型建構 10
2-2.2 穿隧電流及熱流 11
2-3 格林函數與電子傳輸係數 12
2-3.1 Hartree-Fock近似法 13
2-3.2 Many-body理論 14
2-4 電子佔據率對電子傳輸係數的影響 21
2-5 熱電響應函數及熱電參數的定義 26
第 3 章 、三個串接耦合量子點之熱電特性的平均場論近似與非平均場論近似之比較 30
3-1 前言 30
3-2 量子點能階位置的影響 31
3-2.1 平衡溫度在低溫區( T ≤ Γ0 ) 32
3-2.2 平衡溫度在中間溫區 38
3-2.3 平衡溫度在高溫區 41
3-3 量子點內庫倫交互作用的影響 45
3-4 電子跳躍強度改變下的影響 47
3-5 量子點能階不一致 51
3-6 小結 54
第 4 章 、考慮量子點間庫倫交互作用情況下的熱電特性 55
4-1 前言 55
4-2 共振通道耦合強度 55
4-3 系統量子點密度 57
4-3.1 量子點間庫倫交互作用 57
4-3.2 量子點間電子跳躍強度 60
4-4 量子點與電極的耦合強度 64
4-5 量子點能階與EF相對位置的影響 67
4-5.1 量子點能階在EF以上 67
4-5.2 量子點能階在EF以下 69
4-6 量子點大小不一致的影響 70
第 5 章 、結論 73
參考文獻 75

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