指導教授：郭錦龍臺灣大學：材料科學與工程學研究所陳韋光Chen, Wei-GuangWei-GuangChen2014-11-262018-06-282014-11-262018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/262079二氧化鈦在光催化反應中所表現的腐蝕抗性、耐久性與良好的氧化還原能力，以及在自然界含量豐富且成本相對低廉等特性，因而被視為最重要的光觸媒材料之一。對於擁有多種晶相的二氧化鈦而言，實際用以進行催化反應與相關研究主要為常溫常壓下較為穩定的金紅石與銳鈦礦晶相；然而，受到於材料能隙與電子電洞再結合率等電子性質的限制，使得金紅石與銳鈦礦的光催化效率有其極限，因此如何改善材料的電子性質以提升二氧化鈦的光催化效率表現一直是重要的研究課題。先前文獻中有報導機械應變的施加以及銳鈦礦與金紅石晶相共存對於二氧化鈦光催化行為能有所提升，然而目前對於此二項變因如何改變二氧化鈦性質表現的細節與相關物理機制仍有許多等待釐清。因此本研究嘗試以第一原理計算針對上述的行為進行探討，而論文撰寫則依分為機械應變與兩晶相共存的機制探討兩部分。 第一部份的研究將焦點專注在電荷分離效率較佳的銳鈦礦在承受平行於(101)、(100)與(001)此三組較為穩定之表面的雙、單軸應變時，其結構的能隙值、載子的等效質量、以及價帶上緣(VBM)與導帶下緣(CBM)的變動趨勢，藉此模擬二氧化鈦薄膜結構於製備過程中因與基材的晶格常數、熱膨脹係數等性質的差異所造成結構內部晶格變形(lattice deformation)而導致之光催化性質的變動趨勢。計算的結果顯示在正負4%之應變施加範圍內，在(101)表面承受[1 ¯01]的單軸壓應變、 (100)表面承受[001]單軸壓應變，以及(001)表面同時承受[100]與[010]的雙軸張應變等狀態下皆可以使結構能隙值呈現下降的行為；然而在考量到導帶下緣(CBM)位置相對於氫的還原電位之變化，僅有(001)表面在承受雙軸張應變狀態下能夠使能隙值變小，並保有導帶下緣相對於氫還原電位的相對能量以維持光催化分解水反應之活性。在所有達到能隙值下降的應變結構，等效質量的變動方向大致有利於光催化反應的進行。而根據我們的計算結果與分析，總體而言，(001)之承受張應變的結構之光催化效率的提升值得期待。 論文研究的第二部分則是針對在實驗上觀察到由二氧化鈦金紅石與銳鈦礦兩相共存結構在光催化反應所呈現出之共伴(synergistic)效應的行為與機制進行探討。此現象一般被認為是和銳鈦礦與金紅石晶相於介面結構所表現的價帶上緣(VBM)、導帶下緣(CBM)能量差異而提升光致電子電洞的分離效率有關，然而實驗上對於此電荷分離的流向仍舊存有爭議而等待釐清。對此，我們嘗試建立銳鈦礦(112)-金紅石(100)與銳鈦礦(110)-金紅石(011)兩組不同表面接合的介面結構模型，並藉此分析金紅石與銳鈦礦在結構接合之後所表現能帶並列行為，以判斷光致電子、電洞於介面結構間的遷移方向。我們計算的結果顯示兩組介面結構所呈現的能帶並列行為，皆推論出金紅石的價帶與導帶在能量上分別高於銳鈦礦的現象。在價帶上緣與導帶下緣的能量差值上，以銳鈦礦(112)-金紅石(100)介面結構中能量表現最為穩定的三組結構所得到的平均數值分別為0.468±0.12 eV，0.268±0.12 eV；而對於銳鈦礦(110)-金紅石(011)而言則為0.467±0.07 eV，0.267±0.07 eV。從此訊息可以推論出二氧化鈦兩相共存結構之中的電子將會從金紅石往銳鈦礦遷移，而電洞則聚集於金紅石晶相之中，達到光致電荷分離效率的提升以解釋兩相共存結構在光催化反應中所呈現的共伴效應。此外，我們亦嘗試各自對銳鈦礦以及金紅石的表面結構進行電子位能與真空能階的分析，並藉由真空能階並列的方式以近似能帶並列的行為。與實際建立介面結構而得到的結果相互比較下，兩種方法得到之結果相當接近。對此，我們認為省略建立實際介面結構的真空能階並列方法亦能夠適度地對能帶並列結果提供簡單的預測。TiO2 is considered as one of the most important photocatalysts to date primarily due to many of its superior physical and chemical properties. Among its various polymorphs, rutile and anatase TiO2 are the two most important phases and have been widely used in many practical applications. However, due to its relatively large band gap, only a small portion of the solar spectrum in the ultraviolet light region can be absorbed to excite electrons to generate photocurrents for use in photocatalytic reactions. To further improve its performance, many research efforts have been made to increase its photocatalytic efficiency under sunlight, including chemical doping, mechanical strain and formation of heterojunction structures. Nevertheless, the progress of current research in photocatalysis for water splitting reaction is still very slow, and many fundamental details and underlying mechanisms remain unraveled. In this study, we employed first-principles density functional theory calculations to investigate the electronic property changes of the strained anatase TiO2 as well as the band lineup at the rutile-anatase interface. There are two main focuses in this thesis: In the first part of the thesis, we investigated the effect of mechanical strains on the electronic property changes of anatase TiO2, which include the variations of electronic bang gaps, energy levels of VBM and CBM, and the effective masses of charge carriers. In our strained models, biaxial and uniaxial strains were imposed along the directions parallel to the (101), (100), and (001) surfaces, respectively, to mimic the lattice deformations arising from the lattice mismatch with the underlying substrates. Our calculated results show that the band gap of anatase TiO2 can be effectively reduced when [1 ¯01] uniaxial compressive strain is in the (101) surface, [001] uniaxial compressive strain is in the (100) surface, and [100]&[010] biaxial tensile strains is in the (001) surface, respectively. Our calculations also show that it is possible to make the energy level of CBM go upward while the band gap is reduced in the meanwhile when the (001) surface is under biaxial tensile stress. Furthermore, for all the strained structures that can cause band gap reduction, the variations of the effective masses for electrons and holes do not show negative impact on charge carrier separation. These results indicate that the photocatalytic activity of anatase TiO2 can be fine-tuned by applying mechanical strain along certain direction on this material system. In the second part of the thesis, we studied the intrinsic band alignment at the rutile-anatase interface to understand the origins of the synergistic effect observed in the mixed phase TiO2 system. This synergic effect to enhance the separation of photo-excited charge carrier is generally believed to be attributed to a staggered band offset between the two phases. Nevertheless, the explicit direction of charge flow remains controversial and is still under intensive debate. To clarify this controversy, we have constructed two interface models, anatase(112)/rutile(100) and anatase(110)/rutile(011), respectively, to calculate their band alignments using first-principles density functional theory calculations. Our calculated results show that there is indeed a staggered band lineup at the rutile/anatase interface and both VBM and CBM of rutile lie higher in energy than those of anatase phase. The offset values of VBM/CBM were found to be 0.468 ±0.12eV/0.268 ±0.12eV for rutile(100)/anatase(112) interface, and 0.467±0.07eV/0.267±0.07eV for rutile(011)/ anatase(110) interface, respectively. Based on this result, the photo-excited electrons would majorly transport from rutile to anatase while the hole would favor in the opposite direction, which can help enhance the charge carrier separation resulting in better photocatalytic activity of the mixed phase TiO2. On the other hand, we also employed the vacuum level alignment method to study the band lineup at the rutile/anatase interface without acquiring detailed knowledge of the interface structures. Basically, the band alignments obtained using this method are consistent with those predicted based on the realistic interface structure models, providing a convenient way to acquire the preliminary guess for the band lineup of the heterojunction material systems.口試委員審定書 ii 誌謝 iv 摘要 vi Abstract viii 目錄 xii 第一章 緒論 1 1.1研究背景 1 1.2二氧化鈦之基本性質 5 1.3針對二氧化鈦之研究動機與目的 8 第二章 研究方法與理論基礎 9 2.1波恩-歐本海默近似法(Born-Oppenheimer approximation) 10 2.2密度泛函理論 (Density Functional Theory, DFT) 10 2.2.1 Thomas-Fermi Model 10 2.2.2 Hohenberg-Kohn方程式 11 3.2.3 Kohn-Sham 方程式 11 3.2.4交換相干泛函(exchange-correlation functional) 14 3.2.5虛位勢法 (pseudopotential method) 16 3.2.6分子動態模擬 (Molecular Dynamics Simulations) 17 第三章 承受應變之二氧化鈦銳鈦礦的電子性質變化 19 3.1文獻回顧與研究動機 19 3.2研究方法 21 3.2.1 計算方法與條件 21 3.2.2 結構模型建立 21 3.2.3 數據分析與方法 24 3.3計算結果與討論 27 3.3.1 應力釋放之結構性質分析 27 3.3.2 承受應變之結構與能量分析 30 3.3.3 結構承受機械應變之電子性質分析 35 3.3.4 數據統整與討論 55 第四章 二氧化鈦銳鈦礦與金紅石介面結構的能帶並列 63 4.1文獻回顧與研究動機 63 4.2研究方法 65 4.2.1初始結構模型的建立 65 4.2.2結構最適化計算條件與流程 76 4.2.3結構分析與能帶並列的計算方法 79 4.3結果與討論 84 4.3.1結構分析 84 4.3.2價帶上緣(VBM)與導帶下緣(CBM)能量並列 94 4.3.3 真空能階並列 100 第五章 結論 103 參考文獻 1057029088 bytesapplication/pdf論文公開時間：2019/08/22論文使用權限：同意有償授權(權利金給回饋學校)二氧化鈦機械應變等效質量異質介面能帶並列[SDGs]SDG7thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/262079/1/ntu-103-R01527013-1.pdf