We characterized the formation of vacancies at a surface slab model and contrasted the results with the bulk of lead-halide perovskites by using cubic and tetragonal CsPbI₃ as representative structures. The defect-free CsI-terminated (100) surface does not trap charge carriers. In the presence of defects (vacancies), the surface is expected to exhibit a p-type behavior. The formation energy of cesium vacancies V_Cs^– is lower at the surface than in the bulk, while iodine vacancies V_I⁺ have a similar energy (around 0.25–0.4 eV) within the range of chemical potentials compatible with solution processing synthesis conditions. Lead–iodine divacancies (V_PbI^–) are expected to dominate lead-only vacancies at the surfaces. Major surface vacancies create shallow host-like energy states with a small Franck–Condon shift, making them electronically harmless (same as in bulk). The spin–orbit coupling contributes to the defect tolerance of lead-halide perovskite surfaces by causing delocalization of electronic states associated with n-type defects and retraction of the lowest unoccupied states from the surface due to a mixing of Pb-p_x,y,z orbitals. These results explain a high optoelectronic performance of two-dimensional structures, nanoparticles, and polycrystalline thin films of lead-halide perovskites despite the abundance of interfaces in these materials.

中文翻译：

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卤化铅钙钛矿 (100) 表面相对于块体的缺陷容限：能带弯曲、表面状态和空位特征

_{我们表征了表面板模型中空位的形成，并使用立方和四方 CsPbI 3}作为代表性结构，将结果与大部分卤化铅钙钛矿进行了对比。无缺陷的 CsI 端接 (100) 表面不会捕获载流子。在存在缺陷（空位）的情况下，表面预计会表现出p型行为。铯空位V _Cs ^–表面的形成能低于本体，而碘空位V _I ⁺在与溶液加工合成条件兼容的化学势范围内具有相似的能量（约 0.25–0.4 eV）。铅-碘双空位 ( V _PbI ^– ) 预计将主导表面的纯铅空位。主要的表面空位会产生浅层的类似宿主的能量态，并具有小的弗兰克-康登位移，使它们在电子上无害（与散装相同）。自旋轨道耦合通过导致与n型缺陷相关的电子态离域以及由于 Pb-p _x、y、z轨道。这些结果解释了卤化铅钙钛矿的二维结构、纳米粒子和多晶薄膜的高光电性能，尽管这些材料中存在丰富的界面。