Reduced Dimensionality in Drift-Diffusion Models of Back-Contact Solar Cells and Scanning Photocurrent Microscopy

Abstract

Solar cells are three-dimensional objects frequently modeled as being one-dimensional for convenience. However, for more complex designs of solar cell or if the cell is only illuminated at one point, one-dimensional modeling is insufficient. Here, some conditions for reducing the complexity of multidimensional drift-diffusion simulations are investigated in realistic situations for a back-contact perovskite solar cell. The analysis investigates under what situations we may neglect vertical carrier density variation and approximate extraction currents to be linearly dependent on the vertically averaged carrier concentration. Analytic expressions for the linear relationship in both the low and high extraction velocity regimes are demonstrated, and the conditions where these approximations break down are investigated. It is shown that recombination is usually accurately modeled using only vertically averaged carrier concentrations when the distance between electrodes is many times the height and when less than half the charges that are generated recombine, although edge effects around the onset of electrodes are noted. These findings are then applied to a problem that often emerges in scanning photocurrent microscopy, a point-excited film with a laterally offset electrode. It is demonstrated that we expect the current recorded in this case to decay exponentially with the distance between excitation and electrode, with a decay constant that can be related to device parameters. The characteristic equilibration time for the system to reach this current, which can be extracted from the phase delay in a lock-in amplifier measurement, is demonstrated to increase linearly with distance. It is shown that information about the diffusion and recombination rates can be extracted from a wide variety of planar systems.