Exchange current density model for the contact-determined current-voltage behavior of solar cells

An analytic expression for the current-voltage [J(V)] behavior of a solar cell as limited by equilibrium exchange current densities of both carriers at both contacts is derived. The partial currents at both contacts to a generic semiconductor absorber are assumed to be linearly proportional to the excess carrier concentration at the interface with the contacts (e.g., as with Schottky-like contacts). The assumption that the quasi-Fermi levels in the absorber are approximately flat leads to an algebraic solution for the applied voltage as a function of current, which is inverted to obtain the analytic J(V) curve. The J(V) curve reveals distinct behavior associated with electrons and holes, separately, and allows for the determination of all critical performance parameters. In particular, it demonstrates how the characteristic features of the J(V) curve depend on the relative rate at which a particular carrier (electron or hole) is collected at one contact vs the other, rather than the relative rate of electron vs hole collection at a single contact. Furthermore, the model provides a unified explanation of how majority carrier extraction limitations cause nonideal J(V) behaviors such as S-shaped curves and dark/light crossover (i.e., failure of superposition). The efficacy and limitations of the model when applied to Schottky-type and doped semiconductor contacts are discussed. The work serves as a theoretical guide to scientists studying solar cells that are thought to be primarily limited by their contacts.