To begin our analysis we address the suggestion that hysteresis in PSCs cannot be attributed to mobile ions alone, but is due to a specific combination of mobile ions and interfacial traps or recombination centres [10]. In that study it was argued that whilst purely bulk recombination is capable of accounting for standard hysteresis behaviour, the required rate constants are un- physically high. We also find that surface recombination is an apparently necessary feature, but for different reasons which play an essential role in the results to follow.
(c) (d) (a) (b) + + + + + + + - - - - - - - no accumulation +ve accumulation HTL ETL HTL ETL -ve accumulation HTL ETL + + + + + + + - - - - - - - + + + + + + + - - - - - - - - - - - - - - + + + + + + + HTL ETL HTL ETL HTL ETL Vb = 0V Vb = 1V h+ e- e- h+ e- Eb Eb ≈ 0 Eb h+ e- h+ e- h+
Figure 2.3: (a) Simulated rapid-scan characteristics (at instantaneous speed) for cells with high (solid) and low (dotted) rates of surface recombination corresponding to different pre-biasing voltages (equivalently degrees of negative ionic accumulation). The effect of surface recombina- tion is most obvious in the forward scan open-circuit voltage which may be either enhanced or diminished compared to the reverse scan depending on the interfacial defect density. (b) Simu- lated trends in instantaneous open-circuit voltage versus pre-bias voltage showing qualitatively different behaviour depending on the interface defect density (labels correspond to defect den- sities at the HTL/ABS and ABS/ETL interfaces respectively). (c,d) Simulated band diagrams at 0 V (c) and 1V (d) bias demonstrating the effects of positive (left) and negative (right) ionic accumulation, as compared with no accumulation (middle). Negative accumulation (right) in- duces an unfavourable electric field that increases bulk SRH recombination at low bias voltages, but can lower it above the built-in voltage (e.g. near open-circuit) due to a reduced overlap in the carrier profiles relative to unaccumulated case (compare the middle and right panels in (d)). This effect explains the increased open-circuit voltage under negative accumulation seen in mod- els with predominantly bulk-recombination (e.g. the topmost line in (b)). In (c,d,left), regions of reversed electric field or unfavourable band bending trap carriers near the wrong interface, causing increased surface recombination and hence reduced Jsc under positive accumulation.
Examples of simulated rapid-scan I-V measurements are shown in Fig. 2.3a subject to differ- ent degrees of surface recombination. From these results it is clear that surface recombination has a strong influence on the forward scan at high forward bias, and particularly affects its intercept or open-circuit voltage (Voc). Without surface recombination the predicted forward
scan voltage often exceeds that of the reverse scan, as shown in Fig. 2.3a (dotted lines), which contradicts the experimental trend represented in Fig. 2.1a. With added surface recombina- tion (solid lines) the correct trends result, particularly in terms of the voltage, which is then drastically diminished in rapid scans following negative pre-biasing, as in experiment. The dis- crepancy between experiment and our simulated result with only bulk recombination in Fig. 2.3a suggests that the effect of surface recombination is apparently vital. In the following we will rationalize this observation by arguing that there are two competing effects of ion accumu- lation which influence the instantaneous open-circuit voltage: enhanced surface recombination due to the compensated field, and suppressed bulk recombination. Under certain circumstances this competition can lead to higher open-circuit voltages under ionic accumulation, a somewhat surprising prediction which we confirm in our transient Voc measurements discussed later (Fig.
2.7).
For the remainder of this chapter it is helpful to introduce some terminology: here and in the following “negative ionic accumulation” is used to denote the state in which ions are distributed with positive ions located on the HTL side and negative ions on the ETL side of the absorber layer (we delay considering the opposite state of positive accumulation until sec. 2.4.3). Neg- ative accumulation is to be expected if a cell is left to equilibrate at negative “internal bias” (V −Vbuilt−in) <0.4 Since a good cell should have Vbuilt−in ≈ 1 V , most bias voltages in the
power-generating quadrant of the I-V plane will cause negative ionic accumulation at equilib- rium. Negative accumulation usually has a negative impact on cell performance, manifesting as instantaneously lower current extraction for cells pre-biased at 0 V as compared to those pre- biased at Voc (e.g. Fig. 2.1a). This comes about because ions in negative accumulation screen
the built-in field that would normally sweep photo-generated carriers out of the cell (compare Figs. 2.3(c,middle) and 2.3(c,right)). However, there are also circumstances under which neg- ative accumulation can act to reduce recombination. Pertinent to the current discussion is the situation where a cell is measured above its built-in voltage, for instance atVoc: here the electric
field induced by ions under negative accumulation can instead act to reduce SRH recombination in the bulk. This occurs because the ion-induced field acts to reduce the overlap between the density of electrons and holes (Figs. 2.3(c,d)), thereby reducing the SRH recombination rate relative to homogeneous electron/hole distributions with an equal np product. This effect ex-
4
asV refers to the potential difference across the perovskite layer the contribution of series resistances occurring elsewhere in the cell is not included.
plains why the model in Fig. 2.3a, having only bulk SRH recombination, fails to show a reduced open-circuit voltage under negative accumulation despite having reduced current over the rest of the I-V curve (which is below the built-in voltage).
Different instances of the competition between surface and bulk recombination under nega- tive accumulation are demonstrated in Fig. 2.3b which shows the rapid-scan or instantaneous
Voc versus pre-bias voltage for cells with varying interfacial defect densities. These calculations
show explicitly that without a significant density of interfacial defects there is a increasing trend in instantaneous open-circuit voltage with decreasing pre-bias voltage (equivalent to increasing negative ionic accumulation), whereas with high defect densities the trend is reversed. Interest- ingly, at intermediate densities a non-monotonic trend emerges which can be invoked to explain our measurement of non-monotonic transient open-circuit voltage (Fig. 2.7) discussed below. In summary, the inclusion of surface recombination seems indeed necessary to reproduce our experimental I-V curves, however, for a different reason than that stated in ref. [?] which simply invoked the relative sensitivity of recombination to bulk versus interfacial defects.