Impact of Dark Excitons on the Population and Relaxation Kinetics of Two-Dimensional Biexcitons in [CH₃(CH₂)₃NH₃]₂Pb_1–xMn_xBr₄ (x = 0–0.09)

Two-dimensional (2D) semiconductors have emerged as an excellent platform for studying various excitonic matter under strong quantum and dielectric confinements. However, such effects can be seriously overestimated for Coulomb binding of two excitons to form a biexciton by a naive interpretation of the corresponding photoluminescence (PL) spectrum. By using 2D halide perovskite single crystals of [CH₃(CH₂)₃NH₃]₂Pb_1–xMn_xBr₄ (x = 0–0.09) as a model system, we investigated both population and relaxation kinetics of biexcitons as a function of excitation density, temperature, polarization, and Mn doping. We show that the biexciton is formed by binding of two dark excitons, which are partially bright, but they radiatively recombine to yield a bright exciton in the final state. This renders the spectral distance between the exciton peak and the biexciton peak as very different from the actual biexciton binding energy (ϕ) because of large bright–dark splitting. We show that Mn doping introduces paramagnetism to our 2D system and improves the biexciton stability as evidenced by increase in ϕ from 18.8 ± 0.7 to 20.0 ± 0.7 meV and the increase of the exciton–exciton capture coefficient C from 2.4 × 10^–11 to 4.3 × 10^–11cm²/ns within our doping range. The precisely determined ϕ values are significantly smaller than the previously reported ones, but they are consistent with the instability of the biexciton against thermal dissociation at room temperature. Our results demonstrate that electron–hole exchange interaction must be considered for precisely locating the biexciton level; therefore, the ϕ values should be reassessed for other 2D halide perovskites that even do not exhibit any dark exciton PL.