Rise and Decay of the Photovoltage
Distinguishing between recombination and charge extraction is a challenge for solar cell characterization. Using the rise and decay of the transient photovoltage after a laser pulse can be a solution for the problem.
The processes of photogenerated charge-carrier extraction and photovoltage generation are fundamental to any solar cell. However, these processes do not occur instantaneously, but rather have finite time constants, such as the time constant related to the rise of the open circuit voltage following a short light pulse. Previous approaches to analyze small-signal transient photovoltage data have generally focused on obtaining only the decay time constant. While it was possible to determine rise times, there was no model to relate rise times to device functionality. Here, we introduce a model for charge recombination and extraction that can be solved analytically. The solutions for the rise and decay time of the transient photovoltage follow from the inverse eigenvalues of a matrix and can be related to physical mechanisms such as extraction, recombination, and capacitive charging and discharging of the electrodes. We apply the model to experimental data and identify the physical mechanisms that determine the rise and decay times at different bias conditions. From the absolute value, their bias dependence, and the ratio of the rise and decay times, we can clearly distinguish the time constants of recombination and extraction from time constants related to capacitive effects that are irrelevant for steady-state device performance. By adjusting the rise and decay times for the impact of the electrode capacitance, we obtain figures of merit for charge extraction that connect the data obtained from the transient with the current-voltage curves and, thus, the performance of the device. Our observations reveal that the adjusted rise and decay times result in estimated losses of approximately 10% in short-circuit current as well as minor losses in the fill factor. The matrix model concept is applicable to a range of small-signal transient and frequency-domain methods that are frequently used to analyze the electronic properties of halide perovskite solar cells.
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