• Schiller, Andreas

Abstract

Hybrid organic-inorganic perovskite compounds have established themselves as the most promising one among the emerging photovoltaic technologies, reaching efficiencies of 26.1% for single-junction and 33.9% for perovskite-silicon tandem solar cells. Perovskites are mixed electronic-ionic conductors, leading to characteristic measurement results, like e.g. current-voltage hysteresis or large capacitance at low frequencies, caused by the screening of the electric field by ionic charges accumulated at the interfaces.A well established, commercial drift-diffusion simulation software for thin-film devices is extended to model mixed electronic-ionic transport. Unrealistically high ion accumulation at interfaces is suppressed by a steric potential model. The mobility difference of several orders of magnitude between electronic and ionic transport creates a numerically stiff problem.This problem is solved in steady-state, transient, and frequency-domain. The steady-state solver primarily implements a damped, fully-coupled Newton algorithm, which uses an initial guess computed by a decoupled Gummel algorithm. A semi-analytical solution for the equilibrium ion distribution in steady-state reduces the number of equations to solve. In frequency-domain, a small signal approach is used to compute the linearized solution. A semi-implicit, transient Rosenbrock-Wanner algorithm for solving differential algebraic systems of equations is extended to support non-autonomous problems and discontinuities over time in the boundary conditions. The error estimation is optimized for the specific model and adaptive timesteps are introduced. Negative charge carrier densities are inhibited by a logarithmic variable transformation.As the model is prone to numerical cancellation, precision is crucial for all solvers. Ways to improve the precision of an iterative matrix solver and of function evaluations are discussed and effects of cancellation are rectified.Those various numerical methods are combined to improve the convergence behavior and numerical stability. The simulation software is then applied to a range of semiconductor thin-film devices:An observed color change during turn on of sandwich polymer light-emitting electrochemical cells is traced back to a shift of the emission zone using optical simulations. Using a qualitative drift-diffusion device model, the emission zone shift can be ascribed to an imbalance of anion and cation mobility for both constant-voltage and constant-current operation. It is shown, that the voltage rise respectively current decrease after the point of peak performance is partially intrinsic and cannot be completely ascribed to degradation, as is often found in literature. The steric potential model is employed to avoid an unphysically strong accumulation of ions.Illumination and voltage dependent electrochemical impedance spectroscopy measurement results of a perovskite solar cell are qualitatively reproduced by drift-diffusion simulations of a simplified device structure. Features at low frequencies sometimes ascribed to a photo-effect on ion conductivity can be entirely depicted by mixed electronic-ionic transport, but a photo-effect cannot be ruled out. Using the simulation results, the underlying physical processes causing these effects are unveiled.A novel characterization technique for the detection of a photo-effect on ion conductivity, based an a qualitative analysis of illumination dependent capacitance measurements, is developed and applied to a perovskite solar cell. The measurements confirm the presence of a photo-effect on the ion conductivity. As an outlook, a physically motivated model extension to explain the photo-effect on ion conductivity is sketched.A benchmark comparing simulations in an earlier and the present implementation shows a significant speedup of up to a factor of 400, especially for transient simulations. Automated algorithms greatly reduce the need for numerical adjustments by the user, improving the feasibility of the solvers for being used in automated fitting and optimization algorithms.In the results of many characterization techniques, the parameters ion mobility and concentration are strongly correlated and only their product, the ion conductivity, can be fitted reliably. Using drift-diffusion simulations, several characterization techniques are evaluated for their feasibility to overcome this correlation.

Topics

• perovskite
• impedance spectroscopy
• compound
• polymer
• mobility
• simulation
• semiconductor
• Silicon