Using density functional theory, we determined that $2\times 2$ and $\left(\sqrt{3}\times \sqrt{3}\right)\mathrm{R}{30}^{\circ }$ surface reconstructions of bulk-terminated GaN (0001) are degenerate in energy but differ in their electronic structure. Consistent with previous reports, our study of the adsorption energy of Ga adatoms shows that a laterally contracted Ga bilayer is the most energetically favorable surface arrangement under Ga-rich conditions, albeit with a different atomic arrangement of the Ga bilayer than previously reported. We also determined the potential energy surfaces for La and Ga adatoms on bulk-terminated GaN (0001) surface and for a La adatom on a bulk-terminated GaN (0001) covered by a contracted Ga bilayer and discuss possible adatom surface migration paths. An exchange reaction of a La adatom with surface Ga was found to be energetically favorable for both the bulk-terminated and the Ga bilayer-covered surfaces, indicating formation of LaN. A careful study of the diffusion of a La adatom through the Ga bilayer toward the bulk-terminated GaN surface suggests that a lower energy arrangement is achieved when the La adatom exchanges positions with a surface Ga atom. This indicates that ${\mathrm{LaGa}}_2$ and LaN are potential materials to form a transition layer to facilitate epitaxial integration of oxides on GaN.

中文翻译：

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富含N和Ga的条件下GaN（0001）表面重建以及La和Ga原子的理论研究

利用密度泛函理论，我们确定 $\mathrm{2个}\times \mathrm{2个}$ 和 $（\sqrt{3}\times \sqrt{3}）\mathrm{[R}{30}^{\circ }$本体终止的GaN（0001）的表面重构在能量上退化，但是其电子结构不同。与以前的报告一致，我们对Ga吸附原子的吸附能的研究表明，在富含Ga的条件下，横向收缩的Ga双层是最有利于能量的表面排列，尽管与以前报道的Ga双层的原子排列不同。我们还确定了在主体端接的GaN（0001）表面上的La和Ga原子以及在主体端接的GaN（0001）覆盖的主体端接的GaN（0001）上的La原子的势能表面，并讨论了可能的原子面迁移路径。发现La原子与表面Ga的交换反应在能量上有利于整体封端和Ga双层覆盖的表面，表明形成了LaN。仔细研究La原子通过Ga双层向本体末端GaN表面扩散的过程表明，当La原子与表面Ga原子交换位置时，​​可以实现较低的能量排列。这表明${\mathrm{拉加}}_{\mathrm{2个}}$ LaN和LaN是形成过渡层以促进氧化物在GaN上外延整合的潜在材料。