发表机构
Institut für Physik and CSMB, Humboldt-Universität zu Berlin; Fritz-Haber-Institut der Max-Planck-Gesellschaft（柏林洪堡大学物理研究所和CSMB; 马克斯·普朗克学会弗里茨·哈伯研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过第一性原理计算分析β-Ga₂O₃低指数表面的结构与热力学稳定性，明确了不同取向表面的能量排序及化学计量比终止面的主导范围，预测了强还原条件下的富Ga稳定终止面。
AI 中文摘要
我们对β-Ga₂O₃所有对称不等价的低指数表面开展了全面的第一性原理研究，考察了其在实验相关生长条件下的结构性质与热力学稳定性。采用包含半局域（PBEsol）和杂化（PBE0）泛函的密度泛函理论，我们计算了(010)、(100)、(001)、($\bar{2}01$)、(110)、(111)和($11\bar{1}$)取向的表面自由能，包含简谐振动贡献及氧化学势变化的影响。研究表明，不同计算方法得到的能量排序保持一致，且温度达1000 K时振动贡献仍低于0.2 J/m²。基于配位关系的模型将表面稳定性与低配位原子密度关联，发现低配位氧原子和四面体Ga位点会显著降低表面稳定性，而暴露的低配位八面体Ga原子可作为表面稳定性的指标。热力学分析显示，在β-Ga₂O₃稳定性相关的几乎全部化学势范围内，化学计量比终止面占主导，仅在极端还原或氧化条件下才会出现非化学计量比终止面；特别地，我们预测在强还原条件下，(100)和($\bar{2}01$)表面会形成类似Ga吸附层的富Ga稳定终止面。
英文摘要
We present a comprehensive first-principles investigation of all symmetrically inequivalent low-index surfaces of $β$-Ga$_2$O$_3$, examining their structural properties and thermodynamic stability across experimentally relevant growth conditions. Using density-functional theory with both the semi-local functional PBEsol and a modified PBE0 hybrid functional with 26% exact exchange, denoted PBE0(0.26), we calculate surface free energies for the (010), (100), (001), ($\bar{2}01$), (110), (111), and ($11\bar{1}$) orientations, including the effects of harmonic vibrational contributions and varying oxygen chemical potentials. We demonstrate that the energetic ordering remains consistent across computational approaches and that the vibrational contributions remain below 0.2 J/m$^2$ up to temperatures of 1000 K. A coordination-based model that correlates surface stability with the density of under-coordinated atoms reveals that under-coordinated oxygen atoms and tetrahedral Ga sites substantially destabilize surfaces, while exposed under-coordinated octahedral Ga atoms serve as indicators of surface stability. Our thermodynamic analysis shows that stoichiometric terminations dominate over nearly the entire range of chemical potentials relevant for $β$-Ga$_2$O$_3$ stability, while non-stoichiometric terminations emerge only under extreme reducing or oxidizing conditions. Notably, we predict the formation of stable Ga-rich terminations resembling Ga adlayers for the (100) and ($\bar{2}01$) surfaces under highly reducing conditions.
