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We characterized the formation of vacancies at a surface slab model andcontrasted the results with the bulk of lead-halide perovskites using cubic andtetragonal CsPbI$_3$ as representative structures. The defect-freeCsI-terminated (100) surface does not trap charge carriers. In the presence ofdefects (vacancies), the surface is expected to exhibit $p$-type behavior. Theformation energy of cesium vacancies $V_\text{Cs}^{-}$ is lower at the surfacethan in the bulk, while iodine vacancies $V_\text{I}^{+}$ have a similar energy(around 0.25$-$0.4 eV) within the range of chemical potentials compatible withsolution processing synthesis conditions. Lead-iodine divacancies($V_\text{PbI}^{-}$) are expected to dominate over lead-only vacancies at thesurfaces. Major surface vacancies create shallow host-like energy states with asmall Franck-Condon shift, making them electronically harmless (same as inbulk). The spin-orbit coupling contributes to the defect tolerance oflead-halide perovskite surfaces by causing delocalization of electronic statesassociated with $n$-type defects and retraction of lowest unoccupied statesfrom the surface due to a mixing of Pb-$p_{x,y,z}$ orbitals. These resultsexplain a high optoelectronic performance of two-dimensional structures,nanoparticles, and polycrystalline thin films of lead-halide perovskitesdespite the abundance of interfaces in these materials.

Defect tolerance of lead-halide perovskite (100) surface relative to bulk: band bending, surface states, and characteristics of vacancies