臺灣博碩士論文加值系統

本研究利用第一原理計算二氧化鈦摻雜不同元素其電子結構變化、形成能隨濃度變化趨勢等。密度泛函理論(DFT)本身在描述能帶結構對於許多系統是相當成功的，但是對於強關聯已不適用，為了正確的描述局域化的電子軌域，本文採用DFT+U (Hubbard U correction)的方法對模型結構進行運算。由模擬顯示，氮摻雜後主要貢獻於價帶前端，且因為氮2p軌域上存在著電子空缺而形成受體能階。態密度分析方面，在純二氧化鈦中價帶的組成大都由O 2p提供，導帶則由Ti 3d所貢獻。二氧化鈦中如含有氧空缺，則會造成空缺附近鈦原子轉變為正3價，產生的Ti3+位於能隙間與導帶底方，且若含有氮摻雜則會填滿N 2p空軌域，如氮置換含氧空缺，發現氮置換所產生的受體能階因電子填滿而消失，氮插入亦是如此。雙摻雜會因摻雜距離而有不同的電子結構，如最鄰近建結時，氮原子p軌域存在電子空缺且較單一摻雜時多，故在態密度圖可發現，能隙間有兩處分佈因不同量子態。較遠鍵結時，則可看成單一氮與鐵摻雜。

In this study, calculations of titanium dioxide doped with different elements of the electronic structure changes and formation energy with concentration from first principles. Density functional theory (DFT) in describing the band structure is quite successful for many systems, but no longer applicable for strongly correlated, in order to correct the description of localized electron orbitals, we use DFT + U (Hubbard U correction) method for computing the model structure. From the simulation show that N impurities introduce some energy levels above the top of the O 2p valence band.Density of states analysis, the major component of the conduction band of anatase TiO 2 is the Ti 3d states, while that of the valence band is the O 2p states. Such as titanium dioxide in the presence of oxygen vacancies, Titanium atoms near the oxygen vacancies into the trivalent positive, Ti3+ produced in the band gap and bottom of conduction band, And adding nitrogen-doped is filled N 2p orbital, Such as nitrogen substitutet with oxygen vacancies and found that the receptor produced by nitrogen substitute to fill the order by electroni. Double doping due to different doping distance electronic structure, such as the closest bonds, P orbitals of nitrogen atoms and the existence of electronic vacancies more than a single doping, it can be found in the density map, due to band to band, there are two different quantum state distribution. Far bond, the nitrogen and iron can be seen as a single doping.

明志科技大學碩士學位論文指導教授推薦書 i
明志科技大學碩士學位論文口試委員審定書 ii
明志科技大學學位論文授權書 iii
誌謝 iv
中文摘要 v
英文摘要 vi
目錄 vii
表目錄 ix
圖目錄 x
第一章 簡介 1
1.1研究背景 1
1.2不同元素摻雜於二氧化鈦之文獻回顧 4
1.3研究動機與目的 8
第二章 理論基礎 11
2.1薛丁格方程式 11
2.2 Born-Oppenheimer近似 13
2.3 Hartree近似 14
2.4 Hartree-Fock近似 15
2.5密度泛函理論 17
2.6 Hohenberg-Kohn方法 18
2.7局部密度函數近似法 29
2.8自洽方程式 20
2.9贋勢 20
第三章 結果與討論 23
3.1共同部分 23
3.1.1 TiO2與不同元素doped TiO2模型建構 23
3.1.2計算參數之選取 25
3.1.3 Hubbard U值決定 26
3.2 TiO2摻氮之理論計算 28
3.2.1晶體結構 28
3.2.2形成能 28
3.2.3電荷密度 29
3.2.4不同氮濃度摻雜於二氧化鈦之電子結構 30
3.3 TiO2摻鐵之理論計算 33
3.3.1晶體結構 33
3.3.2形成能 33
3.3.3電荷密度 34
3.3.4不同氮濃度摻雜於二氧化鈦之電子結構 34
3.4 TiO2摻鐵之理論計算 36
3.4.1晶體結構 36
3.4.2形成能 37
3.4.3電荷密度 38
3.4.4不同氮摻雜含氧空缺於二氧化鈦之電子結構 39
3.5 TiO2雙摻之理論計算 41
3.4.1晶體結構 41
3.4.2形成能 41
3.4.3電荷密度 42
3.4.4雙摻雜於二氧化鈦之電子結構 43
第四章 結果 72
參考文獻 75

表 目　錄

表1-1 二氧化鈦性質 11
表3-1 軟體輸入晶格常數與實驗值 44
表3-2 不同截斷動能對晶格常數差異 44
表3-3 幾何優化於不同K-point，Cut off energy= 400eV 45
表3-4氮摻雜於二氧化鈦之晶格常數、鍵長、體積及形成能 46
表3-5鐵摻雜於二氧化鈦之晶格常數、鍵長、體積及形成能 46
表3-6不同摻雜形式於二氧化鈦之晶格常數、鍵長、體積及形成能 46
表3-7雙摻雜於二氧化鈦之晶格常數、鍵長、體積及形成能 46

圖 目 錄

圖1-1二氧化鈦不同晶體結構 12
圖1-2光催化反應機制 12
圖2-1自洽場過程 24
圖3-1二氧化鈦不同晶胞大小 47
圖3-2氮摻雜於二氧化鈦 47
圖3-3鐵摻雜於二氧化鈦 48
圖3-4不同摻雜形式於摻雜於二氧化鈦 48
圖3-5雙摻雜不同形式摻雜於二氧化鈦 49
圖3-6不同Cut off energy 對TiO2能隙之關係圖 49
圖3-7不同Cut off energy 對TiO2 Total energy 之關係 50
圖3-8不同Hubbard 所對應能隙值 50
圖3-9不同U值所對應FeO能隙值 51
圖3-10不同U值所對應Fe2O3能隙值 51
圖3-11 Ti-N之鍵結 52
圖3-12不同氮濃度之電荷密度 53
圖3-13 不同氮濃度摻雜於二氧化鈦之能帶結構 54
圖3-14 2at%和4at%氮摻雜之部分態密度分佈 54
圖3-15不同軌域對態密度貢獻 55
圖3-16不同氮濃度其態密度分佈 57
圖3-17 8at%與10at% 鈦與氧原子部份態密度 58
圖3-18鐵摻雜之電荷密度 59
圖3-19鐵掺雜於二氧化鈦之能帶結構 59
圖3-20鐵濃度2at%掺雜於二氧化鈦之態密度與部份態密度 60
圖3-21鐵濃度4at%掺雜於二氧化鈦之態密度與部份態密度 60
圖3-22鐵濃度6at%之鈦密度與部份態密度 61
圖3-23 Ti-O 鍵結(a)與Ti-N鍵結(b) 62
圖3-24 不同摻雜形式之電荷密度 65
圖3-25不同摻雜形式之能帶結構圖 65
圖3-26不同摻雜形式之態密度 68
圖3-27雙摻雜之電荷密度 69
圖3-28雙摻雜之能帶結構圖 69
圖3-29雙摻雜態密度與部份態密度 71

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