External stokes shift of perovskite nanocrystals enlarged by photon recycling

Lead halide perovskite nanocrystals (NCs) have rapidly emerged as promising materials for low-cost and high-efficiency photovoltaic, optoelectronic, and photonic devices. The Stokes shift is a crucial parameter affecting their performance. In this work, we find that the external Stokes shift is strongly dependent on photon recycling. Due to the nonlinear nature of the quantum confinement effect (QCE), the bandgap distribution becomes extremely broad when the sizes are ultra-small, resulting in many repetitions of photon recycling and substantial emission redshift. Thereby, the smaller NCs exhibit larger external Stokes shifts. In detail, for the small NCs with the most probable size of 6.4 nm, the intrinsic Stokes shift is about 71 meV, but the observed external Stokes shift becomes 143.4 meV in the concentrated solution, whereas the intrinsic and apparent Stokes shifts are 69 and 97.6 meV for large NCs of 9.7 nm. Therefore, photon recycling significantly contributes to the external Stokes shift of perovs...