First-principles calculations of defects in metal halide perovskites: A performance comparison of density functionals

Metal halide perovskite semiconductors have outstanding optoelectronic properties. Although these perovskites are defect-tolerant electronically, defects hamper their long-term stability and cause degradation. Density functional theory (DFT) calculations are an important tool to unravel the microscopic structures of defects, but results suffer from the different approximations used in the DFT functionals. In the case of metal halide perovskites, qualitatively different results have been reported with different functionals, either predicting vacancy or interstitial point defects to be most dominant. Here, we conduct a comprehensive comparison of a wide range of functionals for calculating the equilibrium defect formation energies and concentrations of point defects in the archetype metal halide perovskite, ${\mathrm{MAPbI}}_3$. We find that it is essential to include long-range van der Waals interactions in the functional, and that it is vital to self-consistently optimize structure and volume of all compounds involved in the defect formation. For calculating equilibrium formation energies of point defects in ${\mathrm{MAPbI}}_3$ and similar metal halide perovskites, we argue that the exact values of the chemical potentials of the species involved, or of the intrinsic Fermi level, are not important. In contrast to the simple Schottky or Frenkel pictures, we find that the dominant defects are MA and I interstitials, and Pb vacancies.

Figure 1

Defect formation energies, Eq. (1), calculated using (a) ${\mu }_{{\mathrm{I}}_2,\mathrm{molecule}}$ in Eq. (3), or (b) ${\mu }_{{\mathrm{I}}_2,\mathrm{bulk}}={\mu }_{{\mathrm{I}}_2,\mathrm{molecule}}+4\delta$, where $\delta =-0.19\mathrm{eV}$. The vertical dotted line indicates the intrinsic Fermi level $E_F^{\left(i\right)}$, calculated from Eq. (5). Note that the difference in $E_F^{\left(i\right)}$ between (a) and (b) is $-\delta$, and the DFEs at $E_F^{\left(i\right)}$ are unchanged. The DFEs are calculated using the $\mathrm{SCAN}+\mathrm{rVV}10$ functional.

Figure 2

Defect formation energies of the two most prominent defects calculated with the PBE functional, as a function of $E_F$. The band edges (VBM and CBM) are indicated by red solid vertical lines. Adding spin-orbit coupling (SOC) decreases the band gap, and shifts the band edges (green dashed-dotted lines), as does replacing the functional by rev-vdW-DF2 (purple-dashed lines). Although the intrinsic Fermi level $E_F^{\left(i\right)}$ relative to the VBM (black-dotted line) is different in all three cases, the (PBE-calculated) DFEs at $E_F^{\left(i\right)}$ remain the same.

Figure 3

(a) Defect formation energies of vacancies and interstitials calculated with PBE; the solid lines give the most stable defects; the dashed lines represent other defects; the dashed-dotted lines represent three charge states of interstitial iodine. (b) Charge state transition levels; the most important ones are indicated by colored lines.

Figure 4

Differences between defect formation energies $\mathrm{\Delta }{H}_f\left[X^{*}\right]$, calculated with different functionals for PBE optimized structures, and $\mathrm{\Delta }{H}_f\left[\mathrm{PBE}\right]$ calculated with PBE.

Figure 5

(a) Differences between defect formation energies $\mathrm{\Delta }{H}_f\left[X\right]$, calculated with different functionals with optimized structures, and $\mathrm{\Delta }{H}_f\left[X^{*}\right]$ with PBE structures. (b) Differences between $\mathrm{\Delta }{H}_f\left[X\right]$ and $\mathrm{\Delta }{H}_f\left[\mathrm{PBE}\right]$ (DFEs calculated with PBE).

Figure 6

Deviations of equilibrium volumes of ${\mathrm{MAPbI}}_3$, Pb metal and ${\mathrm{PbI}}_2$, calculated by different functionals, relative to the experimental volumes [70, 71, 72].

Figure 7

Defect formation energies calculated by different functionals including structure optimization.

Figure 8

Charge state transition levels calculated by different functionals including structure optimization.