From a numerical solution of the master equation for hopping transport in a disordered energy landscape with a Gaussian density of states, we determine the dependence of the charge-carrier mobility on temperature, carrier density, and electric field. Experimental current-voltage characteristics in devices based on semiconducting polymers are excellently reproduced with this unified description of the mobility. At room temperature it is mainly the dependence on carrier density that plays an important role, whereas at low temperatures and high fields the electric field dependence becomes important. Omission in the past of the carrier-density dependence has led to an underestimation of the hopping distance and the width of the density of states in these polymers.

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Recent success in achieving highly stable Rb-containing organolead halide perovskites has indicated the possibility of incorporating small monovalent cations, which cannot fit in the lead-halide cage with an appropriate tolerance factor, into the perovskite lattice while maintaining a pure stable "black" phase. In this study, through a combined experimental and theoretical investigation by density functional theory (DFT) calculations on the incorporation of extrinsic alkali cations (Rb , K , Na , and Li ) in perovskite materials, the size-dependent interstitial occupancy of these cations in the perovskite lattice is unambiguously revealed. Interestingly, DFT calculations predict the increased ion migration barriers in the lattice after the interstitial occupancy. To verify this prediction, ion migration behavior is characterized through hysteresis analysis of solar cells, electrical poling, temperature-dependent conductivity, and time-dependent photoluminescence measurements. The results collectively point to the suppression of ion migration after lattice interstitial occupancy by extrinsic alkali cations. The findings of this study provide new material design principles to manipulate the structural and ionic properties of multication perovskite materials.