臺灣博碩士論文加值系統

利用第一原理總能密度泛函計算Ge1-xSnx紅外線化合物半導體之能隙結構，並使用sX-LDA(Screened exchange local density approximation)近似法及HSE06(Heyd scuseria ernzerhof hybrid functional)混合泛函探討Ge1-xSnx合金之能隙結構，sX-LDA近似法配合Ge與Sn之norm-conserving贗勢，藉此計算準確之晶格常數、能隙及電子結構，此兩種計算結果均顯示當錫含量增加至0.125時，由間接能隙半導體轉變為直接能隙半導體。另研究利用鍵結、電子和結構特性分析能隙變化，發現原子鍵結方式為能隙轉變之重要關鍵。

We conduct first-principles total-energy density functional calculations to study the band structures in Ge1-xSnx infrared semiconductor alloys. The sX-LDA(Screened exchange local density approximation) and HSE06(Heyd scuseria ernzerhof hybrid functional) calculations to study the band structure in Ge1-xSnx semiconductor alloys. The norm-conserving optimized pseudopotentials of Ge and Sn have been constructed for lattice constant, band-gap, electronic structure calculations. Our findings show band gap that are predicted to undergo an indirect-to-direct transition for x close to 0.125. The composition-bandgap relationships in Ge1-xSnx lattice are evaluated by a detailed comparison of bonding, electronic, structural properties. The atomic structures play a key role in the indirect-gap to direct-gap transition.

摘要 I
ABSTRACT II
目錄 III
表目錄 V
圖目錄 VI
第一章 序論 1
1-1 前言 1
1-2 研究動機 1
1-3 論文架構 2
第二章文獻回顧 3
2-1 前言 3
2-2 鍺錫化合物半導體的特性與優點 3
2-3 鍺錫化合物半導體的應用與發展 3
第三章 理論計算與方法 5
3-1 前言 5
3-2 絕熱近似 5
3-3 密度泛函理論 5
3-3-1 Hohenberg-Kohn Theorem 6
3-3-2 Kohn-Sham equation 7
3-3-3 局部密度近似法 8
3-4 贗勢 9
第四章 NORM-CONSERVING贗勢修正研究 12
4-1 前言 12
4-2 能隙結構 12
4-3 贗勢修正與測試 13
4-4 贗勢應用與分析 14
第五章 SX-LDA近似應用於鍺錫化合物半導體之能隙研究 25
5-1 前言 25
5-2 晶格常數 25
5-3 能隙結構 26
5-4 原子排列方式對能隙之影響 27
5-5 電子態密度 29
5-6 最高佔據態與最低未佔據態 30
第六章 HSE06混合泛函應用於鍺錫化合物半導體能隙研究 43
6-1 前言 43
6-2 晶格常數 43
6-3 能隙結構 44
第七章 結論 52
參考文獻 54
附錄(A): OPIUM參數設定(一) 59
附錄(B): OPIUM參數設定(二) 61
附錄(C): OPIUM參數設定(三) 62
附錄(D): OPIUM參數設定(四) 63

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