Abstract
The hybrid organic-inorganic lead halide perovskite materials have emerged as remarkable materials for photovoltaic applications. Their strengths include good electric transport properties in spite of the disorder inherent in them. Motivated by this observation, we analyze the effects of disorder on the energy eigenstates of a tight-binding model of these materials. In particular, we analyze the spatial extension of the energy eigenstates, which is quantified by the inverse participation ratio. This parameter exhibits a tendency, and possibly a phase transition, to localization as the on-site energy disorder strength is increased. However, we argue that the disorder in the lead halide perovskites corresponds to a point in the regime of highly delocalized states. Our results also suggest that the electronic states of mixed-halide materials tend to be more localized than those of pure materials, which suggests a weaker tendency to form extended bonding states in the mixed-halide materials and is therefore not favourable for halide mixing.
Highlights
Hybrid organic-inorganic lead halide perovskites, with the representative material methylammonium lead iodide (CH3NH3PbI3), have recently emerged as promising materials for optoelectronic applications, such as being the light-absorbing material in a solar cell[1,2,3]
We do not include any orbitals associated with the MA molecules, because these orbitals are far away from the valence band maximum (VBM) and conduction band minimum (CBM)
We find that the inverse participation ratio (IPR) for states near the VBM increases by about 10% in 50-50 mixed-halide materials as compared to pure I or pure Br materials, which suggests that the hole mobility will be almost unaffected by halide mixing
Summary
In the model where the hopping strengths change when substituting Br for I, all three bands exhibit some increase in the IPR for mixed-halide materials with the most pronounced increases occurring at x = 0.8 These results suggest that halide mixing with relatively small Br concentrations is easier than mixing with small I concentrations. The IPR for states near the CBM is essentially independent of halide concentrations, suggesting that the disorder resulting from halide mixing has a lower effect on the electron mobility than it does on the hole mobility. This result makes sense, because the states near the CBM are composed mainly of Pb orbitals. Such defects are not included in our model, and we would not expect to capture these effects in our calculations
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