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 ${\mathrm{I}}^{-}$ interstitials or lead $\left(2-\right)$ 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 $\left(2-\right)$ 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.

Figure 1

Calculated stability diagrams of (a) ${\mathrm{MAPbI}}_3$, (b) ${\mathrm{MASnI}}_3$, and (c) ${\mathrm{CsPbI}}_3$. The stability diagrams of ${\mathrm{MAPbBr}}_3, {\mathrm{MAPbCl}}_3$, and ${\mathrm{FAPbI}}_3$ are qualitatively similar to (a). ${\mu }_{\mathrm{I}}={\mu }_{{\mathrm{I}}_2,\mathrm{molecule}}/2$ corresponds to $\mathrm{\Delta }{\mu }_{\mathrm{I}}=0$ in the figures, and ${\mu }_{\mathrm{M}}={\mu }_{\mathrm{M},\mathrm{bulk}}$ defines $\mathrm{\Delta }{\mu }_{\mathrm{M}}=0$ for $M=\text{Pb}$, Sn. The points A and B define iodine-rich and iodine-poor conditions, respectively. Iodine-medium conditions (point C) are defined as halfway between points A and B.

Figure 2

(a)–(f) Defect formation energies in six $AM{X}_3$ perovskites calculated at halide-medium conditions, using the $\text{SCAN}+\text{rVV}10$ functional: the vertical dashed lines represent the intrinsic Fermi level with respect to the VBM, the solid lines represent the energetically most favorable defects, and the dashed lines other defects. (g)–(l) Charge state transition levels: the most important ones are indicated by colored lines, representing a change of a single unit $\pm e$ starting from one stable charge state of a defect [50]; the bottom and top gray areas represent the valence and conduction bands (calculated with $\text{SCAN}+\text{rVV}10$ without SOC), aligned at the VBM.

Figure 3

(a) Defect formation energies at intrinsic conditions of ${\mathrm{MAPbI}}_3, {\mathrm{MAPbBr}}_3$, and ${\mathrm{MAPbCl}}_3$; (b) volume per formula unit of the pristine perovskite lattices; and (c) Pb-$X_6$ bond orders, where larger values indicate stronger covalent bonds [57, 58, 59].

Figure 4

Charge state transition levels associated with ${\text{V}}_X \left[\varepsilon \right(+/0\left)\right]$ and ${\mathrm{Pb}}_{\mathrm{i}} \left[\varepsilon \right(2+/+\left)\right]$ defects in $\text{MAPb}{X}_3, X=\text{I}$, Br, Cl. The colored boxes indicate the relative positions of the valence and conduction bands, according to Ref. [60].

Figure 5

(a) Defect formation energies at intrinsic conditions of ${\mathrm{FAPbI}}_3, {\mathrm{MAPbI}}_3$, and ${\mathrm{CsPbI}}_3$, (b) volume per formula unit of the pristine perovskite lattices, and (c) average Pb-I bond length changes of the six I atoms closest to a Pb vacancy.

Figure 6

(a) Defect formation energies (DFEs) of ${\mathrm{MAPbI}}_3$ and ${\mathrm{MASnI}}_3$ under I-medium and I-poor conditions (see Fig. 1) (the DFEs of ${\mathrm{MAPbI}}_3$ are identical under both conditions, whereas those of ${\mathrm{MASnI}}_3$ vary, see main text); (b) bond order of the $M$-I bond and net atomic charge on $M$ in ${\mathrm{MAPbI}}_3$ and ${\mathrm{MASnI}}_3$; and (c) diagram illustrating the charge spillover upon creating a ${\text{V}}_M{}^{2-}$ defect.