The PPI method is based on a detailed balance approach, considering that in steady state, the current density measured at the outer solar cell contacts, J(V), can be expressed by the current density of the photo-generated charge carriers, Jgen, and the (internal) recombination in the perovskite layer and at respective interfaces, Jrec(V),
![](data:image/png;base64,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)
Here, we assume that in the considered operation range (0 V ≤ V≤ Voc), the internal generation current Jgen is not affected by the applied bias. Moreover, without loss of generality, we assume that the photon flux to illuminate the sample is constant over time and spatially homogeneous.
The internal recombination processes comprise non-radiative and radiative components, Jn.r. and Jrad, respectively: Jrec = Jn.r. + Jrad. They can be related to each other by
![](data:image/png;base64,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)
Equation (2) is generally valid if k is a function of the applied bias, k = k(V). Here, we show that, if the probed sample has a diode ideality factor close to one and displays negligible resistive losses (high shunt resistance, low series resistance), then it is justified to assume a linear relationship between Jn.r.(V) and Jrad(V) and hence k = const., which we will assume in the following. Empirical indications for this circumstance in perovskite solar cells have already been presented by Stolterfoht and coworkers.23 A detailed theoretical discussion of this assumption as well as a general expression are presented in the Supporting Information (SI section B).
Now, Equation (1) can be expressed as
![](data:image/png;base64,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)
J rad(V) can be related to the signal of a photodetector SPL(V) by
![](data:image/png;base64,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)
where c describes the probability that photons created by radiative recombination enter the detector area and are translated into a detector signal.
Using Equation (3), and (4), we can now relate the electrical photocurrent to the difference between the voltage-dependent PL intensity PL(V) and the PL at open circuit. By normalizing the term, the expression becomes independent of setup-specific factors which makes the technique independent from elaborate calibration measures. We find that
![](data:image/png;base64,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)
This relation shows that photoluminescence microscopy can be used to derive spatially as well as time-resolved images of the local J(V) performance of a photovoltaic device. Two applications are especially interesting: First, by recording only two PL images, one at open circuit and one at short circuit, the image of the local short-circuit photocurrent density Jsc can be derived. Secondly, by recording PL images at various voltages, the local J(V) of specific spots on the cell can be investigated. These approaches are investigated in the following. Thereby, the J(V)/Jgen results determined by PL microscopy will be denoted as J(V)/Jgen |PL.