Two-Dimensional Modelling of Novel Back-Contact Solar cells

This dissertation computationally and analytically investigates ways to model solar cells when the lateral motion of charge carriers and light are relevant. We focus on back-contact perovskite solar cells as an example system, and assess the experimental technique of scanning photocurrent microscopy as a means to investigate them. Solar cells are three-dimensional objects frequently modelled as being one-dimensional. However, for laterally variable designs of solar cell or if the cell is only illuminated at one point, one-dimensional modelling is insufficient. In the first study, some conditions for reducing the complexity of multi-dimensional drift-diffusion simulations are investigated for a back-contact perovskite solar cell. This frequently occurs if the system length is many times the height and when less than half the charges that are generated recombine, although there is deviation from these rules near the edges of electrodes. Analytic expressions for the relationship in both the low extraction velocity and high extraction velocity regimes are demonstrated, and the conditions where these approximations break down are investigated. These findings are then applied a point-excited film with an extended electrode, a problem encountered during scanning photocurrent microscopy. It is demonstrated that we expect the current recorded in this case to decay exponentially with the distance between the excitation point and the electrode, with a decay constant that can be related to device parameters. The characteristic equilibration time for the system to reach this current, which we show can be extracted from the phase delay in a lock-in amplifier measurement, is demonstrated to increase linearly with distance. Between this gradient and the exponent, information about the diffusion and recombination mechanics can be extracted from a wide variety of systems. Photon recycling is the process in solar cells whereby photogenerated carriers recombine to generate light that is absorbed again within the solar cell. In the second section, we apply the findings of the first section to show that experimental results published elsewhere are best explained by photon recycling in methylammonium lead iodide perovskite backcontact solar cells. However we do not have an established theoretical model for long-ranged lateral optical transport in these solar cells. Three models are developed: a bimolecular model for unscattered, coherent transport; a photon diffusion model for frequently scattered, noncoherent light; and a monomolecular, assisted-diffusion model. The modal nature of coherent optical transport is considered and modifications to previous one-dimensional theories are made. The nature of the photon diffusion model is discussed, as are theoretical shortcomings of this and the assisted-diffusion model. All three models are then solved numerically and compared to experimental results. The low-scattering photon diffusion models correspond well to the experiment. The third investigation involves the performance of different architectures of back-contact perovskite solar cells. These cells potentially offer increased current due to less shadowing by front electrodes. We compare them to each other and to traditional vertical structures. It is found that, in terms of internal transport, the back-contact solar cells give less efficient performance than the vertical design. The best of the back-contact cells investigated is a flat interdigitated design. The increase in efficiency from optical factors would have to exceed 10% for the overall efficiency of back-contact cells to be higher than vertical devices. We develop a model of photon recycling appropriate for short-ranged, bulk 2D transport and demonstrate that in our perovskite systems under uniform illumination, it produces little change in predicted power conversion efficiency (although a small change in short-circuit voltage) when compared with the standard drift-diffusion equations with the second-order recombination constant adjusted.