Scan-Rate Dependence of Hysteresis in Planar Perovskite Solar Cells: A Reproducibility Study

Keywords: perovskite solar cells; hysteresis; scan rate; reproducibility; stabilised power output

¹ Department of Physics, Example University, Example City, Country (fictional). ² Institute of Materials, Sample Research Centre, Sample City, Country (fictional). ^* Corresponding author: author.one@example.org

1. Introduction

Hysteresis between the forward and reverse J–V scans of perovskite solar cells has been linked to ion migration, trap filling and capacitive effects [1–3]. Reported efficiencies depend on the scan direction, the scan rate and the pre-bias history, so a single number is not comparable between laboratories [4]. We therefore ask a narrow question: how large is the scan-rate dependence in devices made by one reproducible recipe?

The PCE is defined by Equation (1),

$$PCE = \frac{J_{sc}\, V_{oc}\,\mathit{F}\mathit{F}}{P_{in}} \times 100\,\%\quad\quad(1)$$

where $J_{sc}$ is the short-circuit current density, $V_{oc}$ the open-circuit voltage, $\mathit{F}\mathit{F}$ the fill factor and $P_{in} = 100$ mW cm⁻² the incident power density. We quantify hysteresis with the index $HI = \left( {PCE}_{rev} - {PCE}_{fwd} \right)/{PCE}_{rev}$.

2. Methods

2.1 Device fabrication

Devices had the stack glass/ITO/SnO₂/CH₃NH₃PbI₃/Spiro-OMeTAD/Au (Figure 1). Substrates (15 × 15 mm²) were cleaned in three solvents and treated with UV–ozone for 15 min at 25 °C. The absorber was spin-coated at 4000 rpm for 30 s and annealed at 100 °C for 10 min. The layer thickness was 450 ± 20 nm (profilometer, n = 12). The active area was 0.09 cm², defined by a metal mask.

2.2 Measurement protocol

Measurements followed these steps:

1. Illuminate the device for 60 s at open circuit (preconditioning; omitted for the “no preconditioning” group).
2. Scan from 1.2 V to 0 V (reverse), then from 0 V to 1.2 V (forward).
3. Repeat at scan rates of 10, 25, 50, 100, 250 and 500 mV s⁻¹.
4. Hold the device at $V_{mpp}$ for 300 s and record the stabilised power output.

The diode behaviour used for the fits is given by Equation (2) and the aligned relations that follow:

$$J(V) = J_{L} - J_{0}\left\lbrack \exp\left( \frac{qV}{nk_{B}T} \right) - 1 \right\rbrack\quad\quad(2)$$

$$\begin{matrix} V_{oc} & = \frac{nk_{B}T}{q}\ln\left( \frac{J_{L}}{J_{0}} + 1 \right) \\ \mathit{F}\mathit{F} & = \frac{J_{mpp}V_{mpp}}{J_{sc}V_{oc}} \end{matrix}\quad\quad(3)$$

Charge collected during a scan can be estimated from $Q = \int_{0}^{V_{\max}}C(V)\, dV$, and the mean of $N$ devices with standard deviation is $\bar{x} = \frac{1}{N}\sum_{i = 1}^{N}x_{i}$, $\sigma = \sqrt{\frac{1}{N - 1}\sum_{i = 1}^{N}\left( x_{i} - \bar{x} \right)^{2}}$.

3. Results and discussion

3.1 Effect of scan direction

Figure 2 shows representative curves. The reverse scan gives $V_{oc}$ = 1.12 V and $J_{sc}$ = 22.4 mA cm⁻²; the forward scan gives 1.09 V and 22.3 mA cm⁻².

Table 1 summarises the champion and mean device parameters.

3.2 Effect of scan rate

Figure 3 shows that the reverse-scan PCE decreased monotonically with scan rate (panel a), whereas the forward scan passed through a maximum. The hysteresis index is distributed around 0.09 (panel b).

Table 2 groups the results by preconditioning, with merged header cells and a footnote marker.

The stabilised power output at $V_{mpp}$ was 18.2 % after 300 s, consistent with the slow reverse scan.¹

Table 3 is deliberately wide to test horizontal scrolling on phones.

3.3 Failed devices

Nine devices (15 %) were excluded because of shunts ($R_{sh} < 500\ \Omega\,{cm}^{2}$) or because the Au contact delaminated. They are listed in the supplementary data so that the yield is not overstated. The trap density estimated by space-charge-limited current was about 2 × 10¹⁵ cm⁻³ and the film thickness varied by ±20 nm. A bold claim such as “no hysteresis” is therefore not supported; a modest statement is: hysteresis was small (HI < 0.05) only for slow, preconditioned scans.

A short excerpt of the analysis script:

hi = (pce_rev - pce_fwd) / pce_rev
print(f"mean HI = {hi.mean():.3f} +/- {hi.std(ddof=1):.3f}")

4. Conclusions

• The reverse-scan PCE depends on scan rate, falling from 18.9 % to 16.5 %.
• Hysteresis is small only for slow, preconditioned scans (HI < 0.05).
• Reporting scan rate, direction and pre-bias history is necessary for comparable efficiencies.

Acknowledgements

The authors thank the technical staff of the fictional Example University cleanroom.

Funding

Example Research Council, grant ERC-0000 (fictional).

Data availability

The raw J–V files for all 60 devices are available from the corresponding author on request. (Fictional statement.)

Competing interests

The authors declare no competing interests.

References

1. H. J. Snaith, A. Abate, J. M. Ball et al., “Anomalous hysteresis in perovskite solar cells,” J. Phys. Chem. Lett. 5, 1511 (2014). doi:10.1021/jz500113x
2. W. Tress, N. Marinova, T. Moehl et al., “Understanding the rate-dependent J–V hysteresis, slow time component, and aging in CH₃NH₃PbI₃ perovskite solar cells,” Energy Environ. Sci. 8, 995 (2015). doi:10.1039/C4EE03664F
3. E. L. Unger, E. T. Hoke, C. D. Bailie et al., “Hysteresis and transient behavior in current–voltage measurements of hybrid-perovskite absorber solar cells,” Energy Environ. Sci. 7, 3690 (2014). doi:10.1039/C4EE02465F
4. E. Zimmermann, P. Ehrenreich, T. Pfadler et al., “Erroneous efficiency reports harm organic solar cell research,” Nat. Photonics 8, 669 (2014). doi:10.1038/nphoton.2014.210

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