Quantifying Charge Extraction and Recombination Using the Rise and Decay of the Transient Photovoltage of Perovskite Solar Cells

The extraction of photogenerated charge carriers and the generation of a photovoltage belong to the fundamental functionalities of any solar cell. These processes happen not instantaneously but rather come with finite time constants, e.g., a time constant related to the rise of the externally measured open circuit voltage following a short light pulse. The present paper provides a new method to analyze transient photovoltage measurements at different bias light intensities combining rise and decay times of the photovoltage. The approach uses a linearized version of a system of two coupled differential equations that is solved analytically be determining the eigenvalues of a 2 x 2 matrix. By comparison between the eigenvalues and the measured rise and decay times during a transient photovoltage measurement, we determine the rates of carrier recombination and extraction as a function of bias voltage and establish a simple link between their ratio and the efficiency losses in the perovskite solar cell.