Fig.1

The illustration of volume dependent biexciton Auger lifetime and nonlocal effects in perovskites. Auger recombination lifetime linearly increases with volume in strong confinement regime (left side), while exponentially increases in weak confinement regime (center) due to nonlocal effects. The exciton wavefunction is spatially confined in small nanocrystals, and turns to oscillation in large nanocrystals. For bulk materials, Auger recombination is mainly related to the carrier density and band structure with a constant coefficient [32]. For example, a bulk crystal with carrier density of 10¹⁸ is predicted to have a biexciton lifetime of ~ 10 ns [43, 44]