Intrinsic defects in primary halide perovskites: A first-principles study of the thermodynamic trends

Defects in halide perovskites play an essential role in determining the efficiency and stability of the optoelectronic devices based on these materials. We present a systematic study of intrinsic point defects in six primary metal halide perovskites, ${\mathrm{MAPbI}}_{3}, {\mathrm{MAPbBr}}_{3}, {\mathrm{MAPbCl}}_{3}, {\mathrm{FAPbI}}_{3}, {\mathrm{CsPbI}}_{3}$, and ${\mathrm{MASnI}}_{3}$ (where MA denotes methylammonium and FA denotes formamidinium), based upon density functional theory calculations. Within a single computational scheme, using the $\text{SCAN}+\text{rVV10}$ functional, we compare the impact of changing anions and cations on the defect formation energies and the charge state transition levels in the six compounds, and identify the physical origins underlying the observed trends. Dominant defects in the lead iodide compounds are the ${A}^{+}$ cation interstitials ($A=\text{Cs}$, MA, FA), charge-compensated by ${\mathrm{I}}^{\ensuremath{-}}$ interstitials or lead $(2\ensuremath{-})$ vacancies. In the lead bromide and lead chloride compounds, halide interstitials are most prominent, and for ${\mathrm{MAPbCl}}_{3}$, the chlorine vacancy also becomes important. These trends can be explained in terms of the changes in electrostatic interactions and chemical bonding upon replacing cations and anions. Defect physics in ${\mathrm{MASnI}}_{3}$ is strongly dominated by tin $(2\ensuremath{-})$ vacancies, promoted by the easy oxidation of the tin. Intrinsically, all compounds are mildly $p$ doped, except for ${\mathrm{MASnI}}_{3}$, which is strongly $p$ doped. All acceptor levels created by defects in the six perovskites are shallow. Some defects, halide vacancies and Pb or Sn interstitials in particular, can create deep donor traps. Although such traps might hamper the electronic behavior of ${\mathrm{MAPbCl}}_{3}$, in bromine- and iodine-based perovskites their equilibrium concentrations are too small to affect the materials' properties.