Understanding halide segregation in metal halide perovskites through defect thermodynamics

Abstract

Halide segregation in metal halide perovskites limits their bandgap tunability and hinders their adoption in tandem solar cells and light emitting diodes. Here, we reveal the thermodynamic driving force behind halide segregation in mixed halide (Br-I) perovskites. By performing first-principles calculations on slab models with varying bromide and iodide distributions, we demonstrate that bromide ions preferentially occupy surface sites over bulk sites. Our simulations show that the segregation tendency is higher in MAPb(Br$_x$I$_{1-x}$)$_3$ (MA=methylammonium) compared to FA$_{0.8}$Cs$_{0.2}$Pb(Br$_x$I$_{1-x}$)$_3$, highlighting the role of the A-site cation. To quantify this effect, we establish a descriptor for halide segregation: the difference in defect formation energies of Br antisite defects between the bulk and the surface, which confirms the role of the A-site cation at equimolar Br-I concentration. Furthermore, we identify the localization of photo-generated holes near iodide ions, which triggers their oxidation and accelerates the formation of iodide vacancies, thereby promoting segregation. Overall, this work establishes defect thermodynamics as a framework for understanding halide segregation and provides a structural basis for designing stable mixed halide perovskites.

Figures (6)

• Figure 1: Energies of (a) MAPb(Br$_{0.5}$I$_{0.5}$)$_3$ and (b) FA$_{0.8}$Cs$_{0.2}$Pb(Br$_{0.42}$I$_{0.58}$)$_3$ slabs in the constrained configuration where middle few layers were kept fixed. In both cases the homogeneous mixture is taken as reference state. The structure with a Br-enriched surface in both the materials (a and b) exhibits the lowest total energy, in contrast, surfaces enriched with I show the highest energies for both materials, indicating a thermodynamic preference for iodine to remain in the bulk rather than segregate to the surface. Homogeneous halide distributions fall in between.
• Figure 2: Depth-dependent properties of the Br antisite defect. For all panels, data are plotted against the layer index (0 = surface). (a-c) Variation in DFE as a function of depth from the surface is presented for (a) 17-layer MAPbI3, (b) 17-layer FAPbI3, and (c) 19-layer FA$_{0.8}$Cs$_{0.2}$PbI$_3$ slabs. In all cases, the DFE is substantially lower near the surface compared to the bulk, indicating a thermodynamic preference for Br to localize at the surface. An exponential increase in DFE with depth is observed. (d-f) Pb–Br bond lengths in the presence of a Br antisite defect for (d) MAPbI3,(e) FAPbI3 and (f) FA$_{0.8}$Cs$_{0.2}$PbI$_3$. The two different bond lengths are shown in the inset of (d). Different Pb–Br-Pb bond angles in the presence of a Br antisite defect for (g) MAPbI3,(h) FAPbI3 and (i) FA$_{0.8}$Cs$_{0.2}$PbI$_3$. The different angles are shown in the inset of (h). The variation in bond lengths across layers reflects how structural relaxation influences the DFE, causing it to converge toward the bulk value.
• Figure 3: Change in DFE from bulk to surface (DFE$_{bulk}$-DFE$_{surface}$) for various perovskite compositions as a function of Br concentration ($x$). The DFE difference depends on the Br/I ratio in each structure. At 0% Br, MAPbI$_3$ shows the highest resistance to surface segregation. However, as Br content increases, FA$_{0.8}$Cs$_{0.2}$Pb(Br$_x$I$_{1-x}$)$_3$ exhibits progressively greater resistance, reaching the highest stability at a 1:1 Br:I ratio.
• Figure 4: Position of VBM in different materials. (a-c) VBM position in different types of slabs of MAPb(Br$_{0.5}$I$_{0.5}$)$_3$. (a)Homogeneous mixture of I and Br. (b)Br atoms are near the surfaces.(c)I atoms are near the surfaces. (d-f)VBM position in different types of slabs of FA$_{0.8}$Cs$_{0.2}$Pb(Br$_{0.42}$I$_{0.58}$)$_3$ . (d) Homogeneous mixture of I and Br. (e) Br atoms are near the surfaces. (f) I atoms are near the surfaces. In all surface-segregated models (b, c, e, f), the middle 5 layers are kept fixed.
• Figure 5: Defect formation energies of I ($V_\mathrm{I}^{\bullet}$) and Br ($V_\mathrm{Br}^{\bullet}$) vacancies at the surface of (a) MAPb(Br$_{0.5}$I$_{0.5}$)$_3$ and (b) FA$_{0.8}$Cs$_{0.2}$Pb(Br$_{0.50}$I$_{0.50}$)$_3$ as a function of Fermi level across the bandgap. The valence band maximum (VBM) and conduction band minimum (CBM) are indicated by dashed lines. In both materials, $V_\mathrm{I}^{\bullet}$ exhibits consistently lower formation energy than $V_\mathrm{Br}^{\bullet}$ over the full Fermi level range, indicating a stronger thermodynamic preference for $V_\mathrm{I}^{\bullet}$ formation at the surface.