Challenges in predicting positron annihilation lifetimes in lead halide perovskites: correlation functionals and polymorphism

TL;DR

This study addresses the challenge of predicting positron annihilation lifetimes in lead halide perovskites, focusing on how the electron–positron correlation functional (EPCF) and polymorphism affect results. Using a two‑component density functional theory framework, it compares several EPCFs, including a non‑local weighted density approximation (WDA), across MAPbI$_3$ and inorganic analogues CsPbI$_3$ and CsPbBr$_3$ in multiple phases, and extends to vacancies and vacancy complexes. The findings reveal large, functional‑dependent variations in lifetimes—especially for methylammonium vacancies—and show that lifetimes correlate with Voronoi volumes, with polymorphous cubic phases introducing defect‑state distributions. Overall, the work emphasizes caution when interpreting experimental lifetimes, demonstrates the need for robust EPCF benchmarking, and suggests Voronoi‑volume metrics as practical predictors for lifetimes in polymorphous perovskites.

Abstract

Halide perovskites have emerged in the last decade as a new important class of semiconductors for a variety of optoelectronic applications. A lot of previous studies were thus devoted to the characterisation of their point defects. Positron annihilation spectroscopy is a well recognized tool for probing vacancies in materials. Recent applications of this technique to APbX$_3$ halide perovskites are sparse, and the rare theoretical predictions of positron lifetimes in these materials, published in association with experiments, do not fully agree with each other. These works suggest that vacancies on the A site are not detected. In our theoretical study we focus on the role of the electron-positron correlation functional. We thoroughly revisit and compare several approximations when applied to methylammonium lead iodide (MAPbI$_3$) with or without vacancies, as well as inorganic perovskites CsPbI$_3$ and CsPbBr$_3$, in various phases. We show also the relationship between the size of the voids, through Voronoi volumes, and the calculated lifetimes. For the cubic phases we investigate in detail the role of polymorphism, including the distribution of vacancy formation energies and positron annihilation lifetimes. In our lifetimes calculations, apart from older and more recent semi-local approximations for the electron-positron correlation potential, we also consider the weighted density approximation (WDA), which is truly non-local and should better describe positron annihilation in regions with strong electronic density variations. We show that for this class of materials, and especially for cations vacancies, the influence of the chosen approximation is crucial, much stronger than in metals, alloys and conventional semiconductors. This influence may induce to reconsider the interpretation of experimentally determined lifetimes.

Figures (5)

• Figure 1: Calculated positron lifetimes for the pristine phases of MAPbI$_3$, CsPbBr$_3$ and CsPbI$_3$$vs$ the volume per formula unit (a) or the largest Voronoi volume in the cell (b). Lines are linear regressions to the data. For each structure we show both positron lifetimes calculated with DFT electronic charge densities and with a superposition of atomic densities (AtSup).
• Figure 2: Comparison of lifetimes in tetragonal MAPbI$_3$ with and without vacancies for various enhancement factors. The charge states are -2 for the lead vacancy, -1 for the methylammonium one, and neutral for the MAI divacancy. Defects calculations were in 16 fu supercells. (a) Lifetimes are presented as a function of the volume of the void in which the vacancy is trapped (i.e., the largest Voronoi volume of the cell) for various approximations. The right panel (b), shows the comparison of three approximations (with the longest lifetimes) with ortho-positronium lifetime according to the Tao-EldrupTaoEldrup_1972 model and the corrected version by ZgardzinskaZgardzinska_2015, for the same void volumes.
• Figure 3: Comparison of electron (red) and positron (blue) charge density isosurfaces for the pristine tetragonal phase (a, b, c), a lead vacancy (d, e, f) and a methylammonium vacancy (g, h, i) for three different choices of the electron-positron correlation functional: GGA-B15Barbiellini_2015 (a, d, g), GGA-B95Barbiellini_1995 (b, e, h), and WDACallewaert_2017 with Q=1.25 (c, f, i). Isovalues for the densities are all at 0.16 electrons/bohr$^3$, but positron densities have been scaled to be comparable to electron densities (scaling factors of 50, 10, and 4 for pristine phases, methylammonium vacancies, and lead vacancies, respectively).
• Figure 4: Influence of the chosen value of the WDA screening charge Q on the calculated positron lifetimes (panel a) and binding energies (panel b). Vacancies are all in the tetragonal phase. The corresponding values obtained with the B15-GGA enhancement factor are shown with dashed/dotted lines. In panel a) results were obtained with 8fu supercells.
• Figure 5: Positron lifetime in lead and methylammonium vacancies, with the B15-GGA approximation, as a function of the binding energy of the positron to the vacancy, in polymorphous cubic and tetragonal MAPbI$_3$. The lines are linear fits to the vacancies in the polymorphous cubic only. The two panels on the right are zooms on the relevant regions of the left panel.