The voltage difference E g / q – V oc as a function of decay time of perovskite films. The lines indicate the relationship between carrier lifetime and energy loss 13 , 14 , which is calculated based on a step function absorptance by taking p 0 = 0, p a = 0, p e = 0.05, G ext = 5.3 x 10 21 cm −3 s −1 and {V}{oc}{SQ} = 1.297 {V} (corresponding to a bandgap of 1.57 eV), where p 0 is the equilibrium carrier concentration, p a is parasitic absorption probability, p e is emission probability, G ext is the generation rate of electron-hole pairs due to external illumination and {V}{oc}{SQ} is the open-circuit voltage in the Shockley-Queisser (SQ) model. Additionally, k rad is the radiative recombination coefficient.
