上海理工大学学报  2020, Vol. 42 Issue (2): 115-121 PDF

Analysis thermodynamic properties of intrinsic point defects in Y2O3 crystal based on the First-Principle
WANG Bingjia, LIU Tingyu, YAO Juntao
Colloge of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: The lattice constant, vibration entropy, thermodynamic transition energy level and intrinsic point defect formation energy in Y2O3 crystal were studied by computer simulations with VASP and GULP softwares. Considering the contribution of lattice vibration entropy, the formation energy of defects in the form of vacancies, interstitial and antisite with the changes in temperature and oxygen partial pressure was investigated. The results show that with the increase of temperature and oxygen partial pressure, the most stable defects near the top of the valence band is ${\rm{Y}}_{\rm{i}}^{ \rm{\text{···}}}$ , and the most stable defect near the bottom of the conduction band changes from ${\rm{V}}_{\rm{Y}}^{'''}$ to ${\rm{O}}_{\rm{i}}^{''}$ . The calculations also prove that the type and concentration of oxygen vacancies can be adjusted by varying the temperature and controlling the oxygen partial pressure. In addition, the point defects distribution varying with environmental conditions was clearly presented by using two and three dimensional diagrams, which provides the theoretical basis for crystal growth and annealing environment selection.
Key words: Y2O3     density functional theory     point defects     thermodynamics

1 研究方法 1.1 电子结构计算

 图 1 氧化钇晶体结构（灰色原子代表24d和8b位置上的钇原子，红色原子代表48e位置上的氧原子） Fig. 1 Crystal structure of Y2O3 (Gray atoms represent yttrium atoms at 24d and 8b, and red atoms represent oxygen atoms at 48e)
1.2 势参数选取及振动熵计算

 $U_{ij}^{}({r_{ij}}) = \frac{{{{\rm{Z}}_i}{Z_j}{{{e}}^{\rm{2}}}}}{{{r_{ij}}}}$ (1)

 $U_{ij}^{}({r_{ij}})_{\rm B} = {b_{ij}}\exp \left( { - \frac{{{r_{ij}}}}{\rho }} \right) - \frac{C}{{r_{_{ij}}^6}}$ (2)

 $A = U - TS_{\rm{vib}}$ (3)

 $\left\{\begin{split}&{Z_{{\rm{vib}}}}{\rm{ = }}{\sum\limits_{{K}} {{\omega _k}\sum\limits_{} {\left( {1 - \exp \left( { - \frac{{h\upsilon }}{{kT}}} \right)} \right)} } ^{ - 1}}\\&{S_{{\rm{vib}}}}\left( T \right) = Nk\ln\; {Z_{{\rm{vib}}}} + NkT\left( {\frac{{\partial \ln\; {Z_{{\rm{vib}}}}}}{{\partial T}}} \right)\end{split}\right.$ (4)

1.3 缺陷形成能的计算

 $\begin{split} &\Delta {G_{\rm f}}(\alpha ,q,T,P) \cong {E_{\rm{tot}}}(\alpha ,q) - {E_{\rm{tot,p}}} + \sum\limits_i {{n_\alpha }{\mu _\alpha }(T,P)} +\\&\quad q{\varepsilon _{\rm f}} - T \Delta S_{\rm{vib}}^{}(T),\quad{\varepsilon _{\rm f}} = {E_{\rm{VBM}}} + {E_{\rm f}} + \Delta V\\[-12pt] \end{split}$ (5)

 $\begin{split}{\mu _{\rm O}}(T,P) =& \frac{1}{3}\big[{\mu _{{{\rm{Y}}_2}{{\rm{O}}_3}}} - 2{\mu _{\rm{Y}}}(T,P) - \Delta {G_{f,{{\rm{Y}}_{\rm{2}}}{{\rm{O}}_{\rm{3}}}}}\big] +\\& \Delta {\mu _{\rm{O}}}(T) + \frac{1}{2}{k_{\rm{B}}}T\left( {\frac{P}{{{P^0}}}} \right)\end{split}$ (6)

2 结果和讨论 2.1 晶格结构参数

2.2 振动熵计算结果

 图 2 不同缺陷的振动熵（TΔSvib）随温度的变化 Fig. 2 Vibration entropy （TΔSvib） of different defects with the change of temperature
2.3 热力学跃迁能级

 ${\varepsilon _{{\rm{(}}{q_1}/{q_2})}} = \frac{{\Delta G(\alpha ,{q_1},{\varepsilon_{\rm{f}}}{\rm{ = }}0) - \Delta G(\alpha ,{q_2},{\varepsilon_{\rm{f}}}{\rm{ = }}0)}}{{{q_2} - {q_1}}}$ (7)

 图 3 氧化钇本征点缺陷的热力学跃迁能级示意图 Fig. 3 Schmatic diagram of the thermodynamics defect transition levels of Y2O3 crystal
2.4 缺陷形成能

 图 4 在考虑振动熵影响后氧化钇的点缺陷形成能变化示意图 Fig. 4 Schematic diagram of the point defect formation energy of Y2O3 considering the influence of vibration entropy

 图 5 不同费米能级下最稳定的本征缺陷与温度和氧偏压之间的二维关联图 Fig. 5 Two-dimensional diagram of the most stable intrinsic defect under varying temperature and oxygen partial pressure at different Fermi levels

 图 6 本征点缺陷形成能随氧偏压、温度、费米能级变化的三维分布图（空间被划分成4个区域） Fig. 6 Three-dimensional diagram of intrinsic point defect formation according to the oxygen partial pressure, temperature, and Fermi level (The space is divided into four regions)
3 结　论

a. 在费米能级很大的变化范围内， ${{\rm{O}}_{\rm{i}}}$ ${\rm{V}}_{\rm{Y}}^{'''}$ 为氧化钇的主要本征点缺陷。

b. 随着温度和氧偏压的升高，费米能级处于价带附近时，主要缺陷依次为 ${\rm{O}}_{\rm{i}}^ \times$ - ${\rm{V}}_{\rm{O}}^{ {\text{···}} }$ - ${\rm{Y}}_{\rm{i}}^{ {\text{···}} }$ ，而 ${\rm{V}}_{\rm{Y}}^{'''}$ 易存在于费米能级靠近导带底的位置， ${\rm{V}}_{\rm{O}}^{ {\text{···}} }$ 的存在则与温度关系密切。

c. 制备氧化钇时，若要排除氧空位缺陷对晶体本身的影响，应采用高温或低氧偏压的环境，以适合晶体的生长。

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