Mesoporous Electron-Selective Contacts Enhance the Tolerance to

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Mesoporous Electron Selective Contacts Enhance the Tolerance to Interfacial Ions Accumulation in Perovskite Solar Cells Alessio Gagliardi, and Antonio Abate ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.7b01101 • Publication Date (Web): 15 Dec 2017 Downloaded from http://pubs.acs.org on December 15, 2017

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ACS Energy Letters

Mesoporous Electron Selective Contacts Enhance the Tolerance to Interfacial Ions Accumulation in Perovskite Solar Cells Alessio Gagliardi,*a Antonio Abate,*b a

b

Technische Universitaet Muenchen, Arcisstrasse 21, 80333, Munich (Germany)

Helmholtz-Zentrum Berlin für Materialien und Energie, Kekuléstraße 5, 12489 Berlin,

Germany

*Corresponding authors: A.G. [email protected]; A.A. [email protected]

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Abstract Perovskite-based solar cells are emerging as a potential new leading photovoltaic technology. However, several fundamental aspects of the stability remain unclear. In this paper, we combine experimental measurements and numerical simulations to show that a mesoporous interface between the perovskite and the electron collection layer mitigates the reversible performance loss associated with the ion migration. We argue that larger interfacial area dilutes the concentration of defects that accumulate as result of the ion migration within the perovskite under working conditions. Our investigation provides a quantitative description of the mechanism, identifying a critical defect concentration that devices can tolerate without reporting reduced performances.

TOC Graphic

Electron density distribution at the mesoporous interface between the mesoporous electron selective contact and perovskite


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Introduction Perovskite solar cells are emerging as a leading technology thanks to the remarkable increase in efficiency in the last few years and great improvements in device fabrication.1 For perovskite devices with metal oxide based electron selective contact, two architectures are mainly used: planar perovskite solar cells (pPSC) and mesoscopic perovskite solar cells (mPSC).2 In the first case, the cell is made by an electron transport layer (ETL), usually a compact layer of TiO2, capped by the perovskite and surmounted by an organic semiconductor hole transport layer (HTL). In the second architecture, the electron transport layer is mesoporous and characterised by an intermixing between the perovskite and the metal oxide. Despite the successful development of PSCs on a laboratory scale, their intrinsic stability under working conditions remains open and under debate. The initial device power conversion efficiency (PCE) can be altered by preconditioning the cell applying an external bias, both in the dark or under illumination,3-4 by light soaking5 and by voltage scanning.6 Maintaining a constant illumination and bias, the PCE stabilises after few seconds to several minutes.7-8 The stabilisation time and the stabilised PCE depend on the materials used to fabricate the device, in particular, the interface between perovskite and electron transport layer plays a key role.4-5,

9-12

So far four

fundamental physical mechanisms have been considered to explain this transient behaviour, which includes an internal polarisation with modulation of the permittivity,3,

13

trapping/detrapping mechanism,2, 9, 14 especially at the interface, ferroelectric polarization15 and band bending induced by ion defects migration.16 Systematic investigations have been carried out by many authors.7 Tress, and co-workers17 pointed out that charge carrier trapping/detrapping at the interface cannot fully explain this transient behaviour, which has often been visualised by the hysteresis of the current-voltage curves. More recently, several theoretical works18-19 have investigated the same problem using a drift-diffusion model. Van Reenen and co-workers18 used a 1D p-i-n model for investigating the combined effects of mobile ion defects and free charges. The model used a simplified planar geometry of the cell. Moving ion vacancies, as well as interfacial trap states with an associated recombination, were necessary to reproduce experimental data. The model showed that the trap states are for electrons and located near the ETL/Perovskite interface or on the contrary, they are hole traps located at the Perovskite/HTL interface. Anyway, the most relevant feature is that both trap states and ion defects are required to reproduce the transient behaviour. Richardson and coPage 3 of 20 ACS Paragon Plus Environment


workers19 investigated the same problem. The proposed model allows for a more refined mesh as well as the possibility to include the correct transient of the system. It includes mobile ion vacancies, and the diffusion constant for ion defects is kept consistent with experimental analysis and ab-initio calculations.16 Moreover, the model allows capturing the details of the Debye layer where most of the charge accumulation occurs. According to this model, there is no need for trap states to reproduce experimental results. This overture on numerical models concludes that there is a strong indication, also supported by experimental evidence, that both interfacial trap states, as well as ion migration, play a fundamental role in the transient behaviour of PSCs. Thus, interface engineering, and better crystallisation can overcome or strongly reduce this problem.9 Literature data also indicates that the transient behaviour of mPSCs comprising a TiO2 as metal oxide ETL20 is less pronounced than in pPSCs.21-22 This difference correlates directly to the long-debated question of the exact effect of the mesoporous TiO2 electrode on the device performance. The difference between mPSC and pPSCs are in part due to the different crystallinity of the perovskite layer when deposited on top of the porous or flat layer. However, there are clear differences even when the morphology of the perovskite layer, including the grain size distribution and pinholes density, is comparable between the two architectures21. In any case, the common expectation should be that planar architecture must show better results than the mesoporous one since the smaller size of the perovskite grains within the mesoporous scaffold and the consequent increase in the density of defects and grain boundaries pointing to this conclusion. Thus, the fact that the mesoporous has better performance than a planar ETL-perovskite interface is unexpected and unexplained. In this work, we analyse the effect of having a planar or a mesoporous interface between the metal oxide ETL and the perovskite. In line with previous literature, we show that a mesoporous interface is beneficial to stabilise the initial performance under the maximum power point tracking and that partial losses of the initial performance are a reversible process23 induced by charge accumulation at the metal oxide/perovskite interface. The benefit induced by the mesoporous interface is fundamentally due to a large surface area that dilutes the ionic defects accumulating at the ETL during the device operational. We calculated that a surface concentration of defects above a threshold density of about 5 x 1018 cm-3 might reduce the stabilised maximum power output with a significant increase in degradation with a density above 1019 cm-3. An accumulation density in this range means a bulk density before accumulation in the range of 1016 - 1017 cm-3 for a 500 nm thick perovskite layer. Thus, we demonstrate that devices prepared with TiO2 and SnO2 as metal oxide ETL are more resilient to the defects accumulation in a mesoporous than in a planar configuration. Page 4 of 20 ACS Paragon Plus Environment

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Experimental Results In this section, we show that indeed a mesoporous stabilises the power output more than a planar ETL. We prepared TiO2-based mPSCs and pPSCs as described in the experimental section. The stabilised power conversion efficiency was estimated tracking the device maximum power point (MPP) over few cycles of several minutes (see Figure 1a). After reaching a maximum, the MPP traces decay with the similar rate for the meso and the planar device within the first cycle of 600s of tracking. On longer times, the MPP of the mPSC tends to stabilise 15-20% below the maximum efficiency, while the pPSC continues to lose at a large rate. We have recently demonstrated that negatively charged ionic defects migration and accumulation at the mesoporous electron contact over minutes to hours abates the initial efficiency before the MPP trace stabilises 15-20% below the maximum efficiency.23 Given that the ion vacancies migration is the dominating degradation mechanism within the timescale of the experiment, the data in Figure 1a shows that mPSCs are more resilient than the pPSCs to the ion defects migration.

Figure 1. (a) Maximum power output tracking for a mesoporous and a planar TiO2 based perovskite solar cell measured under 1 sun equivalent white LED illumination (no UV light) and dry air. Devices were continuously kept at the maximum power point by the standard "perturb and observe" method for 3 cycles of 600 s and left in in the dark at open circuit for a minute in between the cycles. The efficiency of devices were about 16 for the mesoporous ad 13% for the planar device. Data were normalized to the maximum value. (b) Same analysis for a mesoporous and a planar SnO2-based perovskite solar cell. The device efficiencies were about 14.5 for the mesoporous and 13.5% for the planar device. Data were normalised to the maximum value of the first cycle. Page 6 of 20 ACS Paragon Plus Environment

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We have to note that the electronic properties of the TiO2 strongly depends on the deposition methods.24 It is likely that the mesoporous and the planar TiO2 electrodes have significantly different work function, which can induce the different behaviours observed in Figure 1.25 To demonstrate that the TiO2 is not playing the main role, we repeated the same experiment for SnO2-based perovskite solar cells. Similar to what observed for TiO2, Figure 1b displays that in SnO2-based devices the MPP trace of pPSC continues to decrease after reaching a maximum within the first minutes of tracking. At the same time, the trace of the mPSC tends to stabilise to slightly higher value than the initial efficiency. This improvement is due to the well-known effect of the SnO2,26 which in part masks the detrimental effect of the ion vacancies accumulation. We conclude that the MPP tracking curves for TiO2 and SnO2 PSCs provide experimental evidence that mesoporous ETLs enable perovskite solar cells more resilient towards the losses induced by ion defects migration. We are not excluding the possibility to get stable planar PSCs, as indeed demonstrated for devices prepared with both planar SnO2 and TiO2 ETL.21-22 However, the possibility to get stable planar PSCs is linked directly to the concentration of ionic defects within the perovskite, which we calculate using a drift-diffusion model as detailed in the next section.



Simulation Results The hypothesis of the present work can be summarized as the following: the difference between mesoporous and planar architecture is fundamentally related to the different surface area between the metal oxide ETLs and perovskite.27 To demonstrate this hypothesis, and explain the experimental behaviour, we first show that assuming the same material parameters, the difference between mesoporous and planar solar cells is rather small and the electron collection does not require a mesoporous interface. Thus differences cannot arise from electrostatic effects induced by the higher porosity of the TiO2 in one architecture respect to the other. To check this point, we make simulations including the real morphology for the mesoporous TiO2.

Figure 2. (a) Structure of the two perovskite cells with the different components. A thin recombination layer is added at the organic/perovskite interface to include interface recombination. (b) Left: structure of the PSC. Right: Electron current density at JSC inside the TiO2 layer. The perovskite layer is explicitly shown. The colour bar indicates the electron density across the perovskite.

The model applied is drift-diffusion solved using finite elements. The advantage of this model is its intrinsic simplicity coupled with the possibility, thanks to the use of finite elements, of solving the equations over a generic geometry.28-31 For the details and parameters of the model see the support information. The geometries of the two devices are shown in Figure 2a. For the planar architecture, it is made a simple 1D simulation, as the system is translational invariant in the plane orthogonal to the current flow, in the mesoporous case it is necessary to include the 3D morphology explicitly. The two geometries of the device are composed of a TiO2 layer (ETL), a perovskite layer and an organic capping layer (HTL) made of Spiro-OMeTAD. The size of the entire device is 290 nm. This is less than the usual thickness of real devices. In particular, the mesoporous region in mPSC solar cells is larger, in the range of 200 nm, while in our case only 50 nm thick. The thickness of the cell has been reduced to speed up the Page 8 of 20 ACS Paragon Plus Environment

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simulation time as the mesoporous layer requires a fine meshing which results in around half a million elements. The size of the elements has been chosen 1 nm thick, thus small enough to describe the effect of the Debye layer at the interface. However, if electrical differences exist between the planar and the mesoporous architectures, it is irrelevant if the overall thickness is chosen to be of 50 or 200 nm. This scenario occurs because of the two materials under consideration, perovskite and TiO2, have a high permittivity and thus can efficiently screen any electrostatic effect. This means that interface effects are mainly local compared to for example organic semiconductors with permittivity in the range of 3-4. An immediate result of including the morphology is that it is possible to evaluate the interface area between oxide and perovskite directly. We have used two different geometries, one constructed using a Monte Carlo algorithm, the other taken from experimental measurements in previous works (see also support information for more details).32 For the constructed one we only build a 50 x 50 x 50 nm3 volume. The internal surface is around 8 times the planar surface. Considering the usual thickness of the mesoporous region in the range of 200 nm, we get a ratio between oxide/perovskite interface among planar and mesoporous of 32. Using the experimental geometry, we get a factor of 11 for 200 nm. Thus, we can assume that with 200 nm of the mesoporous layer, the internal interface between TiO2 and perovskite is at least 10 times larger compared to the planar interface. Finally, a recombination layer is added at the perovskite/organic interface. In Figure 2b the electron current density is shown. Electrons are photogenerated in the perovskite and then partially collected at the TiO2 and partially recombine at the interface with the organic layer. The figure is drawn for mPSC assuming no ion accumulation and then strong band bending at the interface, which means a good alignment between TiO2 and perovskite conduction band edges. Thus the injection of electrons, in this case, is straightforward. The perovskite region is superimposed to show the electron flux injected in the TiO2. The different colours on the perovskite layer represent the electron density at different spatial positions. A small accumulation of electrons occur just before the mesoporous region where then electrons are injected, and in fact, the density drops quickly after that.



Figure 3. Top: Conduction (blue) and valence (orange) band profiles for the pPSC (left) and the mPSC (right) at JSC. Bottom: density profile for electrons (blue) and holes (orange) at JSC for pPSC and mPSC. The profiles are plotted for two conditions: normal band alignment (continuous line), and 0.1 eV band offset (broken line).

In Figure 3 it is shown the band profile at JSC for the planar and mesoporous cells and the density profile of electrons and holes. Both are plotted considering two conditions, one where the barrier energy between TiO2 and perovskite was set to the normal alignment and the other when it was set a 0.1 eV electron injection barrier. On the left, the results of the pPSC and on the right the ones for the mPSC are plotted. Beside some differences in the mesoporous region, there are no big differences in the energy profile and charge density, with and without injection barrier, between the mPSC and the pPSC. On the right figure, mesoporous case, it is possible to note a spike in electron density at around 120 nm in the mesoporous region. This spike is due to a small TiO2 region crossed by our 1D cut of the 3D geometry. The spike is, in fact, consistent with a variation in the bandgap (right figure, top panel) at the same position (120 nm).


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Figure 4. (a) Internal interface in the mesoporous architecture. (b) Ratio (mesoporous over planar) for various physical quantities at the TiO2/perovskite interface and comparison of the JSC. (c) Same analysis at the MPP. Finally, we have calculated the interface quantity averages for the mesoporous and the planar architectures, and we have taken their ratio (mesoporous/planar), see Figure 4. The parameters took into account are all the fundamental electrical (electrostatic potential and electric field) and electronic (electron and hole densities) quantities relevant for the physics at the interface. A value of 1 means that there is no difference between the average value of a physical quantity at the TiO2/perovskite interface between planar and mesoporous geometry. Deviation from 1 means that there are differences. It was required to take the average values because, in the case of the mesoporous interface, physical quantities are not constant over the whole area. The quantities have been evaluated at JSC and MPP. At JSC we observe some deviations only for the hole density (one order of magnitude higher in average) and a slightly higher electric field intensity. This means that some charge accumulation occurs in the mPSC leading to a stronger electric field. There is also a change in the JSC value with a reduction of 10% in maximum current density. However, this reduction is due to the lower absorption in the mPSC due to the presence of the TiO2 in the mesoporous layer. The presence of the TiO2 in the mesoporous architecture changes the generation slightly, as only the fraction of volume with perovskite contributes to charge photogeneration. At MPP there is an inverted condition where the mesoporous shows a lower hole density compared to the planar and consequently a reduction in electric field intensity. However, despite these differences, the MPP of the two architectures is the same (also considering the difference in JSC) and occurs at the same voltage. Thus the result of this analysis is that given similar material properties there is fundamentally no difference between the working operation for the pPSC and the mPSC assuming that no charged ions accumulate at the two interfaces and no trap states are present.



Figure 5. The two different models for the ion accumulation and trap states at the perovskiteETL interface. (a) The charged ion vacancies accumulation inside the perovskite. The accumulation layer is assumed to be 2 nm thick.19 For the ions, the negative charges accumulate at the ETL interface and an equivalent positive charge density at the HTL interface to keep global charge neutrality. (b) Trap states at the oxide/perovskite interface.

In this second part, we use the planar architecture only. After having demonstrated that the mesoporous morphology is not relevant per se, we can reduce to analyse the effects of a different charge accumulation density at the ETL/perovskite interface without including the real 3D structure. This reduces the simulation to a 1D model. We reduce to the 1D model as we can show that the charge density fluctuations across the interface are not particularly large at MPP (see SI). In fact, the density across the interface fluctuates by a factor 4 only. The 1D reduction is an approximation as such variations in the local density can anyway introduce some local effects, which are neglected here. However, a factor of 4 is small compared to a variation in the interface area between planar and mesoporous in the range of 10-30. We show here that when we include electron trap states and accumulate charged ion vacancies at the interface the MPP changes are sensitive to the charge density, especially beyond a threshold value. This indicates that given the same perovskite and thus the same amount of ion vacancies, a difference in the internal interface larger than 10, as previously calculated, can make an important difference in the MPP of the device.


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Figure 6. (a) Black curve (bottom label): change in trap density of the Gaussian distribution. Red curve (top label): different band gap energy position of the Gaussian trap density expressed, as the distance is eV from the perovskite valence band edge. (b) Change in MPP for different concentration of fixed charges (ionic defects) at the interface TiO2/perovskite. The system is the same used to simulate the planar architecture in the previous section. The only difference is that now at the TiO2/perovskite interface a layer 2 nm thick has been added where a fixed density of negative charges are present (representing the charged ions) or an electron trap density (for the trap effect). For the simulations with ions, to keep a global neutrality in the perovskite film, an equivalent layer 2 nm thick was added at the HTL/perovskite interface with a fixed density of positive charges. For the simulations with traps, a density of electron traps was included in the 2 nm layer at the TiO2 interface. The trap density was not considered as recombination centres; they are only a source of space charge accumulation. The traps were modelled with a Gaussian density of states (200 meV wide) inside the perovskite bandgap. The energy position of the trap states is assumed to be 1 eV from the top of the perovskite valence band. However, we have also tried different energy position, i.e. 0.7 and 1.2 eV. The MPP of the two cases is compared with an "ideal" MPP calculated using a device where no accumulation, neither due to trapped charges or ion vacancies, forms at any interface in the device. This solar cell is our reference device. The MPP were calculated just simulating the full JV and then comparing the MPP of the different devices. In our simulations, we study interface effects only, and thus we have introduced no defects and trap states in the bulk region. We assume that all defects have migrated at the interface and there is no residual trap and defect density in bulk. In Figure 6a, black-square curve, it is shown the comparison between the reference (no traps) MPP and the effect of charged traps for different trap densities. Four different densities33-34 are Page 13 of 20 ACS Paragon Plus Environment


tested, namely 5 x 1018, 1019, 1.2 x 1019 and 1.4 x 1019 cm-3. We observe a reduction in stabilised MPP of 2.5% in the first case, compared to the reference, of 6% in the second case, of 8% in the third case and around 10% in the last case. The other points in Figure 6a, red circles, shows the effect of the energy position inside the bandgap of the trap states. In this case, a density of 5 x 1018 cm-3 is kept fixed, for a broadening of 200 meV, but the energy position of the band is changed from 0.7 to 1.2 eV respect to the valence band. The trend shows how deep traps get more effective in reducing the MPP by reducing their energetic distance from the valence band. In this case the reduction in MPP are equal to 1.4% (1.2 eV), 2.5% (1 eV) and 3.4% (0.7 eV). The effect of the ion vacancies accumulation is shown in Figure 6b. In this case, the only parameter that we can change is the density of charges at the interface. We show the effect on the MPP using the same charge density as for the trap simulations. The reduction in MPP is 3.8% in the first case (5 x 1018 cm-3), 11% (1019 cm-3), 18% (1.2 x 1019 cm-3) and 26.3% (1.4 x 1019 cm-3). The ion accumulation is more effective than trapped charges in reducing the MPP. This because in the case of trap states only a fraction of them is occupied, accordingly with the electron Fermi energy in the perovskite layer near the interface. We can also notice how the reduction in the MPP becomes more and more severe beyond the critical threshold of 1019 cm-3 ionic defects. For ionic densities below 1018 cm-3, the effect is negligible. While the 1018 cm-3 may look like a relatively large value, we should remember that ionic defects within the whole perovskite layer migrate and accumulate in a narrow interfacial layer with the contacts. In nonworking conditions, (no light and voltage applied), the ions are uniformly distributed within the perovskite layer; their effective density is likely to be lower than 1018 cm-3.34 However when the device is under working conditions (light and voltage applied), the accumulation takes place. For example, assuming a density of traps in the range of 1016 -1017 cm-3 in a 500 nm thick perovskite layer, we can achieve a final accumulation in the order of 2.5 1018 -1019 cm-3 in 2 nm interface layer.


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Conclusions We studied the role of the mesoporous metal oxide electron selective contact (TiO2 and SnO2 in perovskite solar cells, combining drift-diffusion modelling and experiments. The investigation focuses on the regular architectures of a perovskite device with a metal oxide as electron transport layer, which is one of the most diffused and better-performing device architecture. We do not discuss the inverted architecture, which cannot be easily prepared using the same stack of materials and it will be the object of later studies. While it has been proven that planar contacts can effectively collect the charge generated in micrometre thick perovskite layers,35 here we not only demonstrate that mesoporous contacts help to stabilise the device power output, but we also provide for the first time a quantitative explanation of this effect. Experiments show that charged defects migrate within the perovskite layer and accumulate at the contacts on a timescale of minutes to hours. The initial device maximum power output decreases with the density of negative defects accumulating at the perovskite-electron contact interface. Modelling shows as the larger interface of the mesoporous electron contact results in up to one order of magnitude lower steady-state density of interfacial defects compared to a flat contact. In turn, this can significantly lower performance losses as observed in mesoporous devices compared to planar ones, prepared using both TiO2 and SnO2 as electron selective contacts. Notably, we found that a planar perovskite solar cell does not reach an effective steady-state power output after hours of maximum power point tracking. This finding is reinforced by the data recently reported in the literature for state-of-the-art planar PSCs,21-22 which support our conclusion that mesoporous are intrinsically more tolerant than planar metaloxide architectures towards the ion vacancies migration. Nevertheless, regular planar devices could be equally stable than meso as long as the number of defects that can accumulate at the ETL interface is below the threshold density of 5 x1018 cm-3. Such interfacial density corresponds to a pristine density of defects below 2 x 1016 cm-3 for 500 nm thick perovskite layer before accumulation. Notably, Mosconi and co-workers estimate a normal defect concentration higher than 1016 cm-3.34



Acknowledgement AG acknowledges the Nanosystems Initiative Munich (NIM) SFB 937 by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for fund.

Supporting Information Available The SI includes four sections: one about the details of the drift-diffusion model (and the used parameters), a second describing how we generate the 3D morphology for the mesoporous layer, a third about supporting the approximation to 1D simulations in the last part of the paper and a fourth about experimental details for device fabrication and characterization.


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