Polaron Plasma in Equilibrium with Bright Excitons in 2D and 3D Hybrid Perovskites

Abstract

spectrum featuring a marked excitonic resonance, the majority optical excitation in prototypical HP materials for photovoltaics are not bound excitons, but unbound charge carriers. Therefore, electrons and holes excited by solar light can be directed to the electrodes at a negligible energy cost, without the need to split tightly bound excitons as in organics. Taking advantage of the flexibility of the materials class, layered 2D HPs are obtained by inserting bulky organic cations into the formulation, leading to materials inherently more stable than their 3D counterparts against degradation. [8][9][10] However, in 2D HPs the exciton binding energy can be as large as 400 meV, [8] so that it is commonly assumed that their excited states are mostly excitons.A second peculiar characteristic of the excited states in perovskites is the formation of large polarons, that is, charge carriers coupled to lattice deformations and delocalized over many crystal lattice sites. [11][12][13][14][15][16][17][18][19][20] Unlike small polarons in organics, localized in a single molecule, large polarons are compatible with band transport, but are also able to screen the excited states from scattering with defects and reduce non-radiative recombination through trap states, resulting in large mobilities and long lifetimes. Large polarons are also believed to reduce scattering with phonons and have been proposed as an explanation for hot carriers persisting for several nanoseconds at temperatures significantly higher than the lattice one. [12,16,17,[21][22][23][24][25][26] Large polarons may therefore be the enabling microscopic mechanism for efficient solar cells, including innovative architectures that exploit photoconversion with hot carriers. [27,28] Theoretical estimations forecast that the energy associated with polaron formation is comparable with the binding energy gained by forming an exciton, maybe even larger in some materials. [12,14,24,[29][30][31][32] When do polarons form and whether excitons or polarons are the lowest-energy optical excitations is still an open question. The issue is particularly relevant for layered 2D HPs, where polaronic effects have been demonstrated, although it is not clear if small or large polarons are formed. [33][34][35][36][37] In spite of the large exciton binding energy, unbound charge carriers have been reported, so that it is not clear yet how much energy needs to be spent in solar cells to split bound excitons.

Direct measurement of radiative decay rates in metal halide perovskites

“…21 Yet, as discussed in ref. 13, the quadratic dependence of the PL intensity can be naturally explained by assuming that charged carriers represent the majority population, while excitons are minority bright species, formed following bimolecular pairing of charges with opposite sign (see Fig. 4a in ref.…”

“…In Fig. 2(a-c) Markov plots are shown, 13 obtained by shifting each PL transient along the time axis until it overlaps with the decay curve corresponding to the next higher fluence. In each of the investigated films of MAPI, mixed perovskite and MAPB, the resulting PL transients merge with each other, identifying a single decay curve extending over more than six orders of magnitude in the PL instantaneous intensity.…”

“…Energy & Environmental Science neutral bright excitons, the former constituting the majority population and the latter the minority one. 13 Since all decay rate constants are known to depend on temperature, our analysis was extended from 300 K down to 130 K (see Fig. S4 and S5, ESI †).…”

“…[8][9][10][11] Such time-domain determination of radiative recombination rates is however based on the unproven assumption that, since radiative recombination is a bimolecular recombination process between two free carriers, then all bimolecular recombination in perovskites is radiative, even though some studies have suggested otherwise. [12][13][14][15][16] Restricting the field to methylammonium lead halide CH 3 NH 3 PbI 3 (MAPI), the prototype of perovskites successfully employed in solar cells, analyses based on rate equations produced a wide variety of results for the bimolecular radiative recombination rate coefficients, within the range 2 Â 10 À11 C 2 Â 10 À8 cm 3 s À1 . [17][18][19][20][21][22][23][24][25] Such a wide spread cannot be attributed to variations in the oscillator strength of optical transitions, given that measurements for the absorption coefficient at the exciton peak, which results from the inverse process of optical emission, 26,27 are for MAPI consistently reported within a much narrower interval, around 3 Â 10 4 cm À1 .…”

“…21,[27][28][29][30][31][32] This inconsistency has been tentatively attributed to either extrinsic effects, like spatial diffusion and vertical inhomogeneity of charge carriers, 19,20,33,34 or to intrinsic effects that breach the symmetry between absorption and emission, like Rashba effect or the formation of large polarons. 13,[35][36][37][38][39][40][41] It appears therefore of paramount importance to establish a reliable value for the radiative recombination rate.…”