Quantifying polaronic effects on the scattering and mobility of charge carriers in lead halide perovskites

The formation of polarons due to the interaction between charge carriers and lattice ions has been proposed to have wide-ranging effects on charge carrier dynamics in lead halide perovskites. The hypothesis underlying many of those proposals is that charge carriers are `protected' from scattering by their incorporation into large polarons. Following the approach of Kadanoff for scattering due to polar optical phonons, we derive expressions for the rates of scattering of polarons by acoustic phonons and ionized impurities, and compute the energy and angular dependent rates for electrons and holes in $\mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{I}}₃, \mathrm{M}\mathrm{A}\mathrm{Pb}{\mathrm{Br}}₃$, and $\mathrm{Cs}\mathrm{Pb}{\mathrm{I}}₃$. We then use the ensemble Monte Carlo method to compute polaron distribution functions which satisfy a Boltzmann transport equation incorporating the same three scattering mechanisms, from which we extract mobilities for temperatures in the range 50--500 K. A comparison of the results with those of analogous calculations for bare band carriers indicates that polaronic effects on the scattering and mobilities of charge carriers in lead halide perovskites are more limited than has been suggested in some parts of the recent literature.