Extended Data Fig. 5: Correlation between degradation of V_OC and decrease in electroluminescence intensity.

To quantify the effect of recombination on the performance of the device, we express the change in V_OC as: \(\Delta {V}_{{\rm{OC}}}={V}_{{\rm{OC}}}\left(0\right)-{V}_{{\rm{OC}}}\left(t\right)=\frac{{k}_{{\rm{B}}}T}{q}{\rm{ln}}\left(\frac{{J}_{{\rm{SC}}}\left(0\right)}{{J}_{{\rm{SC}}}\left(t\right)}\frac{{{\rm{EQE}}}_{{\rm{EL}}}\left(t\right)}{{{\rm{EQE}}}_{{\rm{EL}}}\left(0\right)}\frac{\int {{\rm{EQE}}}_{{\rm{PV}}}\left(t\right){\Phi }_{{\rm{BB}}}{\rm{d}}E}{\int {{\rm{EQE}}}_{{\rm{PV}}}\left(0\right){\Phi }_{{\rm{BB}}}{\rm{d}}E}\right)\) where k_B is Boltzmann’s constant, T is the cell temperature, q is the charge of an electron, EQE_EL is the electroluminescence quantum efficiency of the charge-transfer states, EQE_PV is the photovoltaic quantum efficiency, Φ_BB is the black-body flux incident on the device, and E is the photon energy²². Predicted values of ΔV_OC calculated using the above equation are plotted as a function of time along with the measured change in V_OC. For the above equation to accurately predict the change in V_OC, each of the parameters should be measured under an illumination intensity of 1 Sun. Because EQE_EL was measured in the dark at a constant current density of 4 mA cm⁻² rather than at J_SC (that is, under 1-Sun illumination), the absolute value of the prediction from the above equation differs from the measured ΔV_OC by approximately a factor of 2. Nevertheless, there is a qualitative match between the degradation time constants of the predicted and measured ΔV_OC, which suggests that EQE_EL measurements are a useful test of recombination and voltage loss in photovoltaic-degradation studies.