Figure 5: Physical picture of exciton localization.

(a) The density of the extended and localized states, and emission in perovskites (schematic). The density of the localized states is approximated by an exponential tail with the form of ∼exp(−E/E₀). The localized and extended states are divided by the mobility edge. Under low excitation, the excitons mainly occupy the localized states. Under high excitation, the localized states can be filled and the photocarriers also occupy the extended states, leading to emissions of free carriers. (b) Schematic drawing of exciton localization in space coordinates. With the presence of structural disorder, the tails of the localized states form local potential fluctuation in the energy bands. These potential minima can localize electrons and holes to form localized excitons. The carriers can transfer between the local potential minima, leading to long PL lifetime.