鈦酸鋇屬於鈣鈦礦結構的鐵電性材料，在無外加電場的情況下即有自發極化的現象，同時具有優異的介電系數，且在居禮溫度時達到最大值，透過少量鑭元素的添加可以使其在室溫具有更高的介電系數。然而鑭摻雜鈦酸鋇在不同的燒結氣氛 (氧化、還原)及摻雜濃度下，材料之導電性也截然不同 (半導體、絕緣體)。其導電性的變化可以藉由缺陷補償機制來探討，目前最被廣泛討論的機制為四個帶正三價電荷的鑭離子取代四個帶正二價的鋇離子，多出正四價的電荷利用帶負四價的電荷來補償，此機制被認為會使材料成為電的絕緣體，而出現半導體的主因為鑭的摻雜容易誘發氧空缺的生成，為了補償氧空缺帶來的電性不平衡，會生成兩個帶負一價的自由電子保持電性平衡，此機制被認為會使材料成為電的半導體，然而至今仍未有直接的實驗證據顯示其摻雜缺陷生成機制對其電性之影響。
本研究提出八種缺陷補償機制，利用第一原理計算各別對不同缺陷機制的鑭鈦酸鋇作結構優化，並且發現當鑭離子距離陰離子缺陷越近，其能量較穩定，同時確保系統在摻雜之後其力量及能量有達到收斂的要求，在計算缺陷機制之缺陷生成能時考慮化學勢，以熱力學觀點探討在不同的環境 (氧化、還原)下系統是否由不同的缺陷生成機制所主宰。

Barium titanate, BaTiO3, is a perovskite ferroelectric material, known for its high permittivity, making it a desirable material for applications in capacitor. Rare-earth doping has been widely used to modify the dielectric performance of BaTiO3-based ceramics. For example, a resistivity minimum occurs at
La concentrations of around 0.3– 0.5 at.%. The effect is observed in samples
which have been heated in air at high temperatures (1350°C), followed by rapid cooling. In this stage, BaTiO3 also exhibits the positive temperature coefficient of resistance (PTCR) effect. A famous interpretation of this results based on a switch in doping mechanism with increasing doping concentration. Although the improvement in properties is clear, the underlying dominant doping mechanisms for the effects are not well understood. For high level doping electrical insulators, the principal doping mechanism remain controversial whether ionic mechanism is through the creation of barium or titanium vacancies. In this study, first-principles calculation is applied to predict the energetics in different doping mechanism. The purpose is finding the most favor doping mechanism by comparing the substitutional energies and defect formation energies in different forms of defect system. The study improves the understanding about how doping mechanism influence the electrical properties of this material.

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