Radiative recombination of large polarons in halide perovskites

In halide perovskites, electrons (holes) exist as electronic (hole) polarons, excitons, free and trapped electrons (holes). Six kinds of collisions could lead to annihilation of electron and hole, three of them involve polaron(s). In the annihilation channel of each collision process, there is a certain probability to form a dying pair which the average distance between electron and hole is smaller than a critical distance. The annihilation probability per unit time of a collision process is a product of the formation probability of the dying pair in the annihilation channel and the annihilation probability per unit time of dying pair. To annihilate an electronic (hole) polaron, electron (hole) must break away from the distorted environment, which can be achieved either by tunneling or by thermal activation. The observed temperature dependence of monomolecular and bimolecular recombination rates, the peak frequency and line width of photoluminescence spectrum are reproduced.