Current losses caused by MOBILE IONS IN PEROVSKITE SOLAR CELLS
Introduction
At the moment of writing, the highest reported power conversion efficiency (PCE) for a perovskite solar cell is 25.7%. This is impressively high efficiency for a thin-film solar cell, but still far from the theoretical efficiency limit. All PV parameters (Jsc, Voc, FF) have room for improvement with respect to the theoretical efficiency limit. However, while Voc and FF are mainly caused by high recombination rates at the perovskite interfaces, which can be solved with device engineering, the Jsc loss is caused by the presence of mobile ions, which is an intrinsic feature of the perovskite material.
In our previous blog, we demonstrated how ions affect the characteristics of a perovskite solar cell (e.g. hysteresis). It was also pointed out that a large diffusion length and low surface recombination correlate with reduced hysteresis and high efficiency. However, this condition is not sufficient to compensate for the influence of mobile ions on the device's performance.
As we will see here, the presence of ions limits the charge extraction, causing current losses. We used drift-diffusion simulation to validate this hypothesis and propose solutions to limit their influence – hence optimizing the power conversion efficiency.
The content presented below is based on the paper “Universal Current Losses in Perovskite Solar Cells Due to Mobile Ions” written by Thiesbrummel et al. [Thi21] According to the paper, the conclusions of the study are valid for tin and lead-based perovskite solar cells (PSCs).
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Mobile ions in perovskite
Figure 1: device stack (left) and corresponding band diagram (right)
Figure 1 shows the device structure used for the simulations of the study. The perovskite layer presents anions with a concentration of 3.6E16 cm-3 and mobility of 5.0E-9 cm2/Vs and static cations for charge neutrality. Additionally, the simulated device stack includes 1 nm thick perovskite at the interface with the transporting layers (C60 and PTAA) to simulate the interface effect.
The anion’s mobility is up to a billion times smaller than electrons and holes mobility, which causes the presence of a visible hysteresis effect when a voltage scan is performed at slow scan rates (e.g.: 0.1V/s). The ions screen the internal electric field causing the hysteresis effect.
However, in real-case scenarios, the solar cell operates in quasi-steady-state conditions under continuous illumination. To isolate and study the impact of mobile ions on the current in such conditions, the sample is kept under continuous illumination and the bias goes from Voc (no current flowing) to 0V (Jsc conditions). The short-circuit current drops over time until it stabilizes after about 5 seconds (Figure 2 right). In other words, a barrier to charge collection forms within the first two seconds of the simulation, and the current is reduced by more than 1mA/cm2.
Figure 2: Setfos settings to simulate current decay under continous illumination (left). Simulated current decay (right).
By comparison, the same device without ions would experience no current decay. The reason for such disparity can be understood by analyzing the charge density transient, which is associated with the evolution of the band diagram and potential drop across the device. In Table 1 the charge density, band diagram, and potential transients of perovskite devices with and without ions are compared.
At t=25 µs (beginning of the decay), the hole density of the device with ions (light green line) has a smaller gradient throughout the perovskite thickness compared to the device without the ions (blue line). This is reflected in both the band diagram and the built-in potential which present a weaker gradient in the bulk, i.e. a partial screening of the built-in electric field.
A t=760 µs (not shown here) the device without ions is already stabilized with minimal variation compared to the initial instants.
At t=2.5E6 µs the device with ions is now stabilized with anions accumulating at the perovskite/ETL interface. This causes a further reduction in the hole density gradient within the perovskite thickness. The energy bands and the built-in potential are now almost flat, limiting the charge transport.
Table 1: charge density, band diagram and poential drop in the perovskite device at 2.5μs and 2.5E6μs of the simulated current decay.
How to limit (or avoid) the impact of ions on the current?
Mobile ions are an intrinsic characteristic of perovskite materials, one may reduce their density, but one cannot completely get rid of them. So to reduce their impact on performance it is necessary to develop strategies that counteract or compensate for the screening of the built-in potential. Here we analyze two possible strategies: (1) donor doping density of 1E18 cm-3 for the electron transporting layer (C60) to screen the accumulation of anions at the perovskite/ETL interface and (2) increase the electrons mobility of the perovskite layer from 1 to 10 cm2/Vs. According to the current formula shown below, strategy (1) increases the built-in potential, leading to a stronger drift current, while strategy (2) increases both the drift and the diffusion current.
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As it can be observed in Figure 3 the simulated perovskite device with higher mobility (violet line) and donor doping of the C60 (brown line) have a comparable current to the perovskite without ions (green line). Hence, both are good strategies to improve the efficiency close to an ion-free device. But let us also analyze the origin of the improved extraction when the device is stabilized at the instant t=2.5E6 μs.
Figure 3: comparison of current decays for a PSC with ions (red line), without ions (green line), with ions and C60 with donor density of 1E18cm-3 (brown line), and with ions and electron mobility of 10cm2/Vs in the perovskite layer (violet line).
The doping of the C60 pushes back the anions from the interface (Figure 4) allowing a stronger gradient of the hole density (gold line) throughout the perovskite thickness compared to the undoped perovskite (blue line).
Figure 4: comparison of the charge density profile of a PSC with ions with a PSC perovskite with ions and doped C60 at the instant t=2.5E6 μs of the current decay.
On the other hand, the increase of the electron mobility in the perovskite layer leads to a reduction in trapped electron density (yellow vs brown curves) and SRH recombination, while hole and anion densities are unaffected. This is sufficient to compensate for the screening effect of the mobile anions and avoid the loss in short-circuit current. (Figure 5)
Figure 5: comparison of the charge density profile of a PSC with ions with a PSC perovskite with ions and high electron mobility at the instant t=2.5E6 μs of the current decay.
Other strategies include increasing the selectivity of the contacts (stronger band difference) and increasing the work function difference between electrodes. According to our simulations (not shown here) both work in the right direction, but their impact is not as strong as the strategies proposed above.
Conclusions
We presented our analysis of ion effects on current losses in perovskite solar cells. Mobile ions cause a screening of the built-in potential leading to measurable short-circuit-current losses for lead- and tin-based perovskite absorbers. The analysis was carried out with the simulation software Setfos and inspired by the paper of Thiesbrummel J. et al.
Assuming that mobile ions are an intrinsic characteristic of perovskite solar cells, the solution to limit the current loss involves counteracting the screening effect of the mobile ions. An increase in electron mobilities in the perovskite layer and donor doping of the electron transporting layer are two viable and effective strategies to avoid the current losses.
