鐵電材料普遍存在各種缺陷，缺陷的存在對鐵電材料的性能及應用產生很大的影響。對於摻雜鑭的鈦酸鋇，通常認為導致其導電性的不同是由於缺陷的存在，本研究以第一原理計算來模擬不同實驗條件下，鈦酸鋇及鈦酸鋇摻雜鑭元素後容易產生的缺陷。本研究將含多種不同缺陷的超晶胞假想成孤立缺陷超晶胞的組合，利用第一原理計算具有孤立缺陷的鈦酸鋇和鈦酸鋇摻雜鑭的缺陷生成能。這種孤立缺陷法需要考慮帶電缺陷會產生的電荷補償，所以計算生成能除了需要計算各個超晶胞的總能和其化學勢能以外，還需要修正電子能帶偏移量以及靜電交互作用，最後將多個孤立缺陷超晶胞結合起來，模擬多種不同缺陷的系統，相較於計算一個含複合缺陷的晶胞需要考慮缺陷間有可能的距離組合，這種方法相較來說更省時，只是這種方法忽略了由於缺陷產生的庫倫力。
對於以孤立缺陷法計算的鈦酸鋇摻雜鑭的缺陷生成能，從結果可知，在氧的化學勢能小於-5.0 eV時，2La∙+VO∙∙+4Ti'具有最低生成能，故其為主導補償機制；在氧的化學勢能介於-5.0 eV和-1.4 eV時，2La∙+2Ti'為主導補償機制；而在氧的化學勢能大於-1.4 eV時，2La∙+VBa"為主導補償機制。本研究透過分析孤立缺陷的點電荷，利用其來計算庫倫力，將得到的庫倫力用來修正孤立缺陷超晶胞組合，並與一個含複合缺陷的晶胞之缺陷生成能來相比較。結果證明這種方法沒辦法將組合缺陷的缺陷生成能修正到和複合缺陷的缺陷生成能相同，雖然利用庫侖能找到的晶體總能與文獻找到的最低能量非常接近，但庫侖能與缺陷距離的趨勢和晶體結構的總能量沒有一定的關聯性，因此這種方法不能用來預測缺陷分佈的能量趨勢變化。

Barium titanate is a perovskite ferroelectric material, and it also has high permittivity. Rare-earth doping could be used to modify the performance of barium titanate. For example, if doping concentration of lanthanum is between 0.3 and 0.5 at%, barium titanate will become the semiconductor and has the positive temperature coefficient of resistance (PTCR) effect. When lanthanum doped barium titanate, the charge compensation effects induced by aliovalent doping. This study investigate the defect compensation mechanism of La-doped BaTiO3 by point defect calculations to build the multi-defect supercell. About the result of this study when μ_O is smaller than -5.0 eV, 2La∙+VO∙∙+4Ti' has lowest defect formation energy; when μO is between -5.0 eV and -1.4 eV, 2La∙+2Ti' has lowest defect formation energy; when μO is larger than -1.4 eV, 2La∙+VBa" has lowest defect formation energy. However, the difference between the linear combination of point defects and the multi-defect supercell is that the former doesn’t include Coulomb energies, so we try to calculate Coulomb energy to decide the distribution of complex defect. The trend of Coulomb energy and the distance of defect distribution has no correlation with the total energy of crystal structure. Only considering Coulomb energy interaction is not enough to predict the complex defect distribution, the calculation of Coulomb energy can’ t be used to predict the change of total energy for the trend of defect distribution.

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