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

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.