  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.
