Having developed an understanding of two potentially important factors in the appearance of inverted hysteresis, namely band bending and bulk ionic accumulation, we now return to interpreting the different behaviours exhibited by our one and two-step cells in Fig. 2.12. A common prediction across all models considered above is that the current loss following forward biasing originates from diffusion-limited regions localized on one side of the cell. In the DLM the size of these regions is pre-set, whereas in the drift-diffusion model the size and shape are determined by many factors including the ion density, the charge of the mobile species, band offsets, contact layer doping and relative dielectric constants. Nonetheless both models
Figure 2.16: Measurements showing the effect of the illuminating wavelength on the current loss in a two-step cell. Cells illuminated with shorter wavelengths experience a larger Jsc loss
after forward-biasing at 1.2 V expressed as a fraction of Jsc following biasing at 0.6 V instead.
Both Jsc values were measured using rapid 10 V s−1 reverse scans starting at 1.2 V as shown in
the inset. Filled and empty circles correspond to separate repeats of the same measurement (taken in different order) demonstrating that the effect is essentially reproducible. We note that expressing the current as a fraction limits the possible influence of variable light intensity, which was in any case observed to have little to no effect on the relative current loss (Fig. S5 in [33]).
predict that the current loss should increase when generation is concentrated in any one of these regions, such as when shorter wavelength light with a smaller absorption depth is used to probe the region near either interface. We have tested this prediction on our two-step MAPbI3 cells
using varying wavelength illumination shining in from the TiO2 front-side. The results in Fig.
2.16 show that the recombination losses following forward-biasing increase dramatically with shorter-wavelength illumination. This is compelling evidence that there is indeed a region of high recombination forming at the MAPbI3-TiO2 interface after forward biasing. In Fig. 2.16
theJscmeasured on a rapid reverse scan following 1.2 V pre-biasing is expressed as a ratio ofJsc
measured in the same manner after biasing the cell at a smaller forward voltage of 0.6 V. The ratio of these two currents J1sc.2V/J0sc.6V cancels out the main factors related to external quantum efficiency and light intensity and therefore expresses differences due only to the pre-biasing voltage (including the effects of ion accumulation). A simple attempt at predicting this ratio is to assume that the J0.6V
sc value is close to the illuminating photocurrent, and that J1sc.2Vis reduced
by an amount proportional to the quantity of generation occurring inside the diffusion-limited zones. The quantity 1−J1sc.2V/J0sc.6V should therefore be proportional (by an unknown factor
depending on recombination probabilities within the diffusion-limited zone) to the fraction of generation occurring within the diffusion-limited zones at short-circuit. Denoting the width of the the MAPbI3-TiO2 zone at 0 V bywand absorption depth at the illuminating wavelengthλ
by δp, one then expects the following rough scaling of the current loss
1−J1.2V sc /J0sc.6V|λ1 1−J1.2V sc /J0sc.6V|λ2 = 1−exp(−w/δp1) 1−exp(−w/δp2) . (2.1)
Predictions of this simplified model for different values of whave been added to the data of Fig. 2.16 by adjusting to the value of the measured current loss at 450 nm, and using absorption depths calculated from published optical data for MAPbI3 [44]. Although the fit is not highly
accurate, it can clearly be seen that smaller values ofwpredict a larger variation with wavelength. A minimum value of w = 15 nm is used since smaller widths would require a recombination probability greater than one within the diffusion-limited zone to account for the ≈25% current loss measured at 450 nm. The measurements of Fig. 2.16 are therefore apparently more in favour of small regions (with a minimum width of 15 nm) having high recombination probability, possibly corresponding to regions of reversed electric field and high surface recombination as depicted in Fig. 2.13b and 2.14a, than the generically larger diffusion-limited regions of Figs. 2.14(b,c) predicted by bulk ion accumulation. We note that the minimum width of 15 nm should be interpreted as an effective width in a planar approximation of our mesoporous cells, and that the actual width could be significantly smaller due to the high surface area of the mesoporous scaffold. The application of these measurements to a planar cell archicture could be used to obtain a genuine lower bound on the widths of the ionic space charge layer, complementary to the upper bounds derived recently [42].
Band-bending of the kind shown in Fig. 2.13b seems to be the most likely explanation for the large wavelength-variation of J1sc.2V in our two-step cells. Given this, we consider variations in the degree of band-bending as being a likely candidate to explain the difference between our one and two step cells (Fig. 2.12). As the band bending changes with the interfacial band offset, in the sense of diminishing with larger electron affinity, a slightly larger electron affinity in the one-step perovskite could be responsible for a smaller current loss (the simulations of Fig. 2.16 indicate that required variations would be less than 1 eV). Whilst the electronic band gap of MAPbI3 is consistently reported in the range of 1.5 eV-1.6 eV, a wide variety of
values have been assigned to the electron affinity, with reported values ranging from 3.6 eV to 4.8 eV [45, 46, 40]. Although ambiguity in determining the absolute values of these quantities from UV and X-ray photoelectron spectroscopy (XPS) measurements may explain some of this variability, a similarly large range of values has been recently obtained using a single protocol by varying the perovskite precursor stoichiometry and film deposition method [40]. In that work
Figure 2.17: Measurements of Jscafter forward-biasing at 1 V showing a dependence on the film
preparation. Values are expressed as a fraction of their values after biasing at a lower voltage (0.6 V). One-step cells prepared with a 5% MAI-rich precursor ratio were found to exhibit a large current loss after forward biasing (≈ 7%), at a level comparable to the two-step cells (≈8%), whose preparation includes a post-treatement step with a highly concentrated MAI. In this case the one-step cell exhibited an almost negligible Jsc loss of≈1%. Composition (right
axis) expresses the Pb4f to N1s ratio measured via XPS in the case of the two-step cell and the precursor ratios in the case of the one-step cells, which was independently verified to closely match the XPS result.
a correlation was found between the precursor ratio and the resulting film’s binding energies, with MAI rich precursors tending to produce films of generally lower electron affinity. As the two-step procedure employed here for depositing perovksite films included a post-treatment with a highly concentrated solution of MAI, the perovskite layer in those cells is expected to be relatively MAI rich relative to that in the one-step cells. Consequently, the two-step cells are expected to feature lower values of χMAPbI3, and therefore a greater interfacial band offset in
the sense ofχTiO2−χMAPbI3 being larger. This increased offset, and the concomitant increase in
band-bending following forward biasing, plausibly explains the appearance of strongly inverted hysteresis in our two step cells.