Generalized Reciprocity Relations in Solar Cells with Voltage-Dependent Carrier Collection: Application to p-i-n Junction Devices

Two reciprocity theorems are important for fundamental understanding of the solar cell operation and applications to device evaluation: (1) the carrier-transport reciprocity connecting the dark-carrier injection with the short-circuit photocarrier collection and (2) the optoelectronic reciprocity connecting the electroluminescence with the photovoltaic quantum efficiency at short circuit. These theorems, however, fail in devices with thick depletion regions such as p-i-n junction solar cells. By properly linearizing the carrier-transport equation in such devices, we report that the dark-carrier injection is related to the photocarrier collection efficiency at the operating voltage, not at short circuit as suggested in the original theorem. This leads to the general form of the optoelectronic reciprocity relation connecting the electroluminescence with the voltage-dependent quantum efficiency, providing a correct interpretation of the optoelectronic properties of p-i-n junction devices. We also discuss the validity of the well-known relation between the open-circuit voltage and the external luminescence efficiency. The impact of illumination intensity and device parameters on the validity of the reciprocity theorems is quantitatively investigated.