Tolerance Factor and Cooperative Tilting Effects in Vacancy-Ordered Double Perovskite Halides

Abstract

Lattice dynamics and structural instabilities are strongly implicated in dictating the electronic properties of perovskite halide semiconductors. We present a study of the vacancy-ordered double perovskite Rb<sub>2</sub>SnI<sub>6</sub> and correlate dynamic and cooperative octahedral tilting with changes in electronic behavior compared to those of Cs<sub>2</sub>SnI<sub>6</sub>. Though both compounds exhibit native n-type semiconductivity, Rb<sub>2</sub>SnI<sub>6</sub> exhibits carrier mobilities that are reduced by a factor of ~50 relative to Cs<sub>2</sub>SnI<sub>6</sub>. From synchrotron powder X-ray diffraction, we find that Rb<sub>2</sub>SnI<sub>6</sub> adopts the tetragonal vacancy-ordered double perovskite structure at room temperature and undergoes a phase transition to a lower-symmetry monoclinic structure upon cooling, characterized by cooperative octahedral tilting of the [SnI6] octahedra. X-ray and neutron pair distribution function analyses reveal that the local coordination environment of Rb<sub>2</sub>SnI<sub>6</sub> is consistent with the monoclinic structure at all temperatures; we attribute this observation to dynamic octahedral rotations that become frozen in to yield the low-temperature monoclinic structure. In contrast, Cs<sub>2</sub>SnI<sub>6</sub> adopts the cubic vacancy-ordered double perovskite structure at all temperatures. Density functional calculations show that static octahedral tilting in Rb<sub>2</sub>SnI<sub>6</sub> results in marginally increased carrier effective masses, which alone are insufficient to account for the experimental electronic behavior. Rather, the larger number of low-frequency phonons introduced by the lower symmetry of the Rb<sub>2</sub>SnI<sub>6</sub> structure yield stronger electron–phonon coupling interactions that produce larger electron effective masses and reduced carrier mobilities relative to Cs<sub>2</sub>SnI<sub>6</sub>. Further, we discuss the results for Rb<sub>2</sub>SnI<sub>6</sub> in the context of other vacancy-ordered double perovskite semiconductors, in order to demonstrate that the electron–phonon coupling characteristics can be predicted using the geometric perovskite tolerance factor. This study represents an important step in designing perovskite halide semiconductors with desired charge transport properties for optoelectronic applications.