鐵電材料的命名來自於其具有自發極化(spontaneous polarization)的性質，其中鈦酸鉛系列材料是具有很高的自發極化以及壓電響應能力的鐵電體材料，常被應用在隨機記憶體、傳感器以及機電轉換設備。近年來，電子元件的尺寸日益縮小，然而性能的要求卻與日俱增，因此為了使鐵電材料的性質最佳化，開發具有高電容量以及低矯頑電場(coercive field)的材料成為關鍵議題。摻雜各種元素進入鈦酸鉛系列材料是一種常用的方法改變材料的電性，而鑭的摻雜可以很容易的調整鈦酸鉛材料的極化量、介電常數、矯頑電場和電阻率等性質，因此摻雜鑭是目前常見用於改變鈦酸鉛材料電性的方法。人們過去的研究著重於對鐵電材料的電域壁研究，然而鐵電材料在合成時會有許多種缺陷被引入，這些缺陷會影響材料的電性表現，因此這樣的缺陷形成機制是不可忽略的，然而在實驗中要準確量測缺陷的形成是很困難並具有挑戰性的，但我們的結果能以第一原理計算的方式模擬鈦酸鉛材料在摻雜鑭的情況下容易形成的缺陷。

The purpose of this paper is to study the defect formation of lanthanum doped lead titanate by First-principles calculation. Due to the ionic radius, lanthanum ions tend to replace lead ions site. Under the premise of neutral electricity of the system, eight different charge compensation mechanisms are assumed. Based on these assumptions, the model with defects is constructed. The total energy of these model are calculated by VASP and valid chemical potentials that are constrained according to thermodynamic laws are used to calculate the defect formation energy. By comparison of defect formation energy, lead vacancy and titanium vacancy are more likely to form.

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