Pressure-Induced Void and Crack Closure Improves the Photoconversion Eciency and Stability of Perovskite Solar Cells

One route to a brighter global energy future may be through enhancing the eciency and stability of perovskite solar cells (PSCs), which depends on the level of defects in the photoactive absorber and along the interfaces of the multilayered structure. Here, we use a combined experimental and theoretical approach to study the effects of pressure-induced compaction of microvoids and closure of cracks on the power conversion eciency (PCEs) and stability of formamidinium-rich PSCs. A range of mechanical pressures was applied to the PSCs to reduce pre-existing grain-boundary voids and interfacial cracks within the devices. The PCEs of the PSCs increased from ~19.5% to ~ 23.5% for applied pressures between ~ (0 – 7) MPa. Unlaminated device stability increased by 33%, falling to 80% of initial PCE in 1800 hrs without compression, as compared to 2400 hrs with compression. The implications of this study are discussed in light of possible future manufacturing processes.


Introduction
Photovoltaics could contribute as much as 10 TW of power to the global energy grid by 2030 1 . A candidate photovoltaic device to ful ll global demand is based on pervoskites materials. Perovskites have tunable optoelectronic properties 2,3 , and are inexpensive to manufacture 4 . Reported power conversion e ciencies (PCEs) of perovskite solar cells (PSCs) now exceed 25% 5 . Further improvement in both the performance characteristics and the stability of PSCs is essential for their applications in power generation 6,7 .
Most of the world-record high e ciencies of PSCs are based on formamidinium (FA) 8 . This is due to their high energy absorption over a wide spectral range 8 . So far, the improvements in the e ciencies of FAbased PSCs are a result of continuous efforts in tuning optoelectronic properties 9,10 , lm passivation 11,12 , improving processing conditions 13,14 , tandem technology 15 , and the doping of materials in electron-and hole-transporting layers 16,17 .
The use of pressure has been shown to improve optoelectronic properties of perovskite lms [18][19][20][21] . In particular, the application of moderate pressure, during the fabrication of PSCs, has also been shown to improve interfacial surface contacts in multilayered structures of mixed-halide methylammonium perovskite solar cells, leading to enhanced e ciencies 22 .
In this work, we investigate the reasons for the improved performance that is observed when moderate pressures are applied to FA-rich PSCs during their fabrication. The effects of pressure application (on defects in the multilayered structures) are characterized along with their optoelectronic properties. We nd that intergrain microvoids and interfacial cracks are compacted and closed due to moderate pressure application.
Thus we achieve signi cant improvement in the e ciencies of the pressure-assisted devices from ~ 19.5-23.5% for applied pressures between ~ 0-7 MPa, as well as markedly increased solar cell stability.
The results are discussed with the objective of manufacturing highly e cient and stable perovskite solar cells, within the context of pressures applied during lamination and roll-to-roll processing.

Moderate pressure improves device e ciency and stability
We fabricated formamidinium-rich PSC devices and applied different pressure values to compact intergrain microvoids and to close interfacial cracks. The schematics of the device architecture and procedures for pressure application are presented in Fig. 1a-c, which shows the device and polydimethyl siloxane (PDMS) anvil before pressure application (Fig. 1a), as well as during a cycle of press, hold, and lift using the PDMS anvil (Fig. 1b). The pressure -time curves are also presented in Fig. 1c for the different applied pressures.
We see an improvement in the performance characteristics of the devices as we increased the applied pressure. Figure 2a presents the current density -voltage (J-V) curves of the devices for different applied pressures. The current density signi cantly increased from 25.7 (23.1 ± 1.4) mA cm − 2 to 28.3 (26.4 ± 0.9) mA cm − 2 for applied pressures between 0 MPa and 7 MPa. Note that the data are reported in the format Best (Average ± Standard Deviation). We also observed a decrease in the current density to 24.5 (22.7 ± 1.7) mA cm − 2 when higher pressures of 10 MPa were applied to the devices.
The PCEs of the devices also increased from 19.5 (17.7 ± 1.6) % to 23.5 (21.6 ± 2.0) % (Fig. 2b), as we increased the applied pressures from 0 MPa to 7 MPa. At a pressure of 10 MPa, the PCE decreased to 18.8 (16.1 ± 1.7) %. Figure 2c shows the histograms of the PCEs for pressures between 0 MPa and 7 MPa, while Table 1 summarizes the results obtained from perovskite solar cells that were subjected to different applied pressures during their fabrication. To understand the mechanisms that drive the enhanced performace of the devices with increased pressure, we carried out cross-sectional SEM imaging of the devices before and after pressure application. Figure 2d-f presents the cross-sectional SEM images of the devices for the following conditions: no pressure (Fig. 2d); moderate pressure at 7 MPa (Fig. 2e), and too much of pressure at 10 MPa (Fig. 2f).
In the case of as-prepared devices (fabricated with no pressure application), a signi cant number of grain-boundary voids and some intergranular cracks were observed across the photoactive perovskite layer (Fig. 2d). However, after compaction, most of the voids and the integranular cracks were fully closed in the SEM cross-sections of the devices that were fabricated with pressures of 7 MPa (Fig. 2e). However, for devices fabricated with an applied pressure of 10 MPa, we observed both interfacial cracking (at the interface between the perovskite layer and the mesoporous TiO 2 layer and the interface between the perovskite layer and the Spiro-OMeTAD layer), and grain-boundary cracking in the photoactive layer (Fig. 2f).
To explore the in uence of pressure on the device stability over time, PCEs were measured under continuous 1-sun illumination for devices without pressure and those that were assisted with the optimum pressure of 7 MPa. We also studied their long-term stability by storing the devices in a desiccator (at room temperature 22-25 o C and relative humidity 20-60%). We measured their performance at different times over a period of ve months.
The PCEs of the devices under continuous illumination and the evolution of PCEs over the period of ve months are presented in Figs. 2g and 2 h, respectively. While the optimum pressure-assisted devices have longer stability before degrading to 80% of the initial PCEs (~ 2400 h), the as-prepared devices degrade faster to 80% of their initial PCEs within ~ 1800 h.
The histograms and Weibull distribution curves of the device PCEs are presented in Fig. 3a-e for different applied pressures. The estimated values of the PCEs, that correspond to the peaks of the Weibull curves, increased with increasing pressure (Fig. 3f). We also see an increase in the current density of the devices with increased applied pressures between 0 MPa -7 MPa (Fig. 4a), while the Fill Factor (FF) also increased with increasing pressure (Fig. 4b). However, there is no signi cant increase in the open circuit voltage (Fig. 4c). We attribute the improved performance of the devices to compaction of grain-boundary voids and closure of interfacial cracks for pressures between 0 MPa to 7 MPa.

Moderate pressure closes voids and cracks
To gain more insight into the mechanics involving closing of grain-boundary voids and interfacial defects that occur during pressure application, we used the ABAQUS software package (ABAQUS, Dassault Systemes, Pawtucket, RI, USA) to simulate the effects of pressure application on multilayered PSCs structures with pre-existing interfacial defects. The models assume that, in a model PSC structure, there are pre-existing grain-boundary cracks and voids 11,12,21,23,24 , as well as interfacial defects (voids and interfacial cracks) before pressure application (Fig. 5a). Our hypothesis is that these defects can be closed by applying moderate pressure (Fig. 5b). A representative axisymmetric model of the interfacial defects between the perovskite layer and the mesoporous-TiO 2 along with the boundary conditions is shown in Fig. 5c.
We assumed that the parts of the device that are farther from the pre-existing interfacial defects have no signi cant effect on the mechanics around the defect. All parts were created in Abaqus while the mechanical properties of the different materials [25][26][27][28] were incorporated into the created sections to run the simulations. All the materials were assumed to exhibit isotropic elastic behavior.
All the parts of the model were meshed using four-node bilinear axisymmetric quadrilateral elements. We ensured that the mesh sizes were identical and dense in the regions near the pre-existing interfacial defects for convergence in the simulation. While an axisymmetric boundary condition was applied at the symmetry axis (Fig. 5c), the device substrate was xed to have no displacements and no rotations. We also xed the outer edge of the model to have no lateral movement for continuity. Different pressures were then applied to the device to close up interfacial defects.
We see improved interfacial contact from the devices assisted with little or no pressure (10 − 5 MPa) to high pressure of 10 MPa (Fig. 5d-f). A detailed evolution of the stress distribution in the layered structure for different applied pressures (Fig. 6) shows that the stress distribution increases with applied pressure. We nd that the induced stresses along the interface and within the layered structure are more than the pressures applied remotely. The stresses are concentrated within gold and perovskite layers which are shown in Fig. 6 insets. At higher pressures, cracks can initiate from the region of high stress concentration which is evident in the cross section SEM image at higher pressure (Fig. 2f). The results of the simulation are consistent with void and crack closure due to moderate external pressure.

Moderate pressure lowers defect density
Knowing that moderate pressure can improve interfacial contacts, we deposited the perovskite multilayer lms onto FTO-coated glass slides to further study defect density as a function of applied pressure. Figure 7a-e presents the cross-sectional SEM images of the perovskite multilayers for applied pressures between 0 MPa and 10 MPa. We observed a signi cant decrease in grain-boundary defects or voids as the applied pressures increased from 0 MPa to 10 MPa, leading to closely packed grains that can improve both e ciency and stability of PSCs 19,22,29 . However, we observed patches of damaged grains at the top of the perovskite lms at 10 MPa (Fig. 7e). Figure 7f presents grain-boundary void areas, as determined by analysis of the SEM images using ImageJ software. The results show a signi cant decrease in the areas of the voids as it can be physically observed on the cross section SEM images ( Fig. 7a-e).
The above results of pressure-effects on defects have signi cant implications for charge carrier dynamics in PSCs. Both grain-boundary and interfacial defects in PSCs can acts as charge carrier traps 30 and recombination sites 31,32 . Carrier trapping and defect-mediated recombination can signi cantly affect the optical properties of the perovskite lms, which we have investigated as a function of applied pressure, using optical absorbance and photoluminescence (PL) spectra.
Both the optical absorbance and PL spectra are presented in Fig. 7g. The photon absorption increased with increasing pressure from 0 MPa to 7 MPa (Fig. 7g), and then decreased in the perovskite lms prepared with applied pressures above 7 MPa (Fig. 7g inset). The increase in the peaks of the PL spectra for pressures between 0-7 MPa (Fig. 7g) is evidence of defect density reduction in the lms, as the number of voids decreases with the increasing pressure. For the applied pressures beyond 7 MPa (i.e. pressure of 10 MPa), the PL intensity is reduced due to lm damage (Fig. 7e). The initiation of cracking at an applied pressure of 10 MPa mitigates the transport of charge carriers within the multilayered structures of PSCs, which results ultimately in the decrease of the PCEs obtained for the devices fabricated with a pressure of 10 MPa.
Beyond examining PL spectra, Time-Resolved Photo-Luminescence (TRPL) provides an additional insights into the radiative lifetimes of the photoexcited charge carriers. TRPL decays taken at the peak of emission for early times (< 40 ns) (Fig. 8a) were analyzed by tting them to a bimolecular function (Eq. 1).
where I, I o , α and t are the intensity, peak magnitude, bimolecular rate and time, respectively.
We nd that application of pressure up to 7 MPa dramatically increases peak photoluminescence (Fig. 8b) while simultaneously increasing bimolecular rate (Fig. 8c). Increase in both of these parameters is indicative of the reduction in the density of deleterious defects. In agreement with structural studies that showed that increasing the pressure beyond 7 MPa to 10 MPa results in structural damage and an accompanying increase in the defect concentration, both the PL intensity and the bimolecular recombination rate exhibit a dramatic decrease in the lm prepared with 10 MPa. We conclude that moderate pressure improves the carrier dynamics of multilayer perovskite lms, but too much pressure is detrimental.

Discussion
Our study provides some new insights into the effects of pressure on the microvoid compaction and crack closure that can occur during the pressure-assisted fabrication of perovskite solar cells. Such remotely applied moderate pressures (between 0 and 7 MPa) close up cracks and voids. The closing up of the defects also reduces carrier recombination, as is evident in the photoluminescence results 33 . The defect reduction in the photoactive perovskite layers and along interfaces promotes light absorption that generates more charge carriers.
Although the remote application of moderate pressure induces high stresses around grains, as established by our simulation results, it can also induce the closure of the integranular cracks in the active perovskite layers (Fig. 2d-f). Such closure can enhance charge and light transport within the perovskite layers. It can also reduce the transport of water vapor within grain boundary and porous sections of the multilayered PSC structures.
Since such moisture can absorb to, or react with layers in the PSC structures to cause device degradation, the observed closure of grain boundary cracks (pathways for grain boundary diffusion), porosity/microvoids and interfacial cracks (pathways for enhanced internal diffusion), should lead to improved PSC stability for devices fabricated with pressures up to 7 MPa. However, for devices fabricated with pressures of 10 MPa, the induced cracks at these higher pressure levels reduce the overall levels of charge transport, while enabling enhanced charge recombination. Hence, the PCEs of the PSCs produced with applied pressures of 10 MPa are lower than those produced with applied pressures of 7 MPa.
The above insights are important for the design of pressure-assisted processes for the fabrication of perovskite solar cells. These may include: lamination processes 34 or roll-to-roll-processing 35,36 that can be used to fabricate PSCs under well controlled pressure application. These fabrication processes may also be combined with encapsulation processes that limit the percolation of water vapor into the PSCs under potential service conditions. They may, therfore, enhance the stability of the PSCs, while providing future opportunity to enhance the photoconversion e ciencies that can be achieved in future pressureassisted perovskite solar cells.

Conclusions
In summary, the photoconversion e ciencies of perovskite solar cells can be enhanced by applying moderate remote pressures (up to 7 MPa) during solar cell fabrication. Such pressure application leads to void compaction and crack closure. However, higher pressures degrade the device performance due to structural damage by cracking. Furthermore, devices with lower defect densities live longer under ambient conditions without any encapsulation. The bene ts of moderate applied pressure can be exploited for future lamination and roll-to-roll processes in the manufacture of perovskite solar cells -for a brighter energy future.
Fabrication of Layered PSCs. FTO-coated glass and bare glass substrates were cut into dimensions 25 mm x 25 mm and sonicated successively (each for 15 min) in decon-90 detergent, deionized water, acetone (Sigma Aldrich), and IPA (Sigma Aldrich). The cleaned substrates were then blow-dried in nitrogen gas, prior to UV-Ozone cleaning (Novascan, Main Street, Ames, IA, USA) for 20 minutes to remove organic residuals. An electron transport layer (ETL) (that comprises compact and mesoporous layers of titanium oxide) was deposited onto FTOcoated glass, following a previous protocol 22 . The PDMS anvil was then cut out into the dimensions of the device's glass substrate and attached to the crosshead of the Instron machine with the surface that was cured against the polished silicon facing down. A schematic of the set-up before the ramping of the head of Instron is shown in Fig. 1a. The Instron was set to ramp in compression at a displacement rate of 1.0 mm min − 1 to press and hold down the device (Fig. 1b)  Characterization of Layered PSCs.
The optical absorbances of the multilayer lms were measured using an Avantes UV-Vis spectrophotometer (AvaSpec-2048, Avantes, BV, USA). The PL and TRPL measurements were obtained by exciting the lms with a 405 nm picosecond laser source (Aura Technology PIXEA) using 270 nW incident power, 2 kHz repetition rate and 50% of tuning. The excitation signal was sent to a Horiba MicOS microscope optical spectrometer system that consists of a Horiba iHR550 spectrometer, a luminescence microscope with a 50X Edmund Optics Plan Apo NIR Mitutoyo objective, and a Horiba Synapse EM CCD camera. The PL spectra and TRPL measurements were then obtained using a single photon counter module (SPD-OEM-VIS, Aurea Technology) and an acquisition software interface.
The microstructures of perovskite lms and the cross section of PSCs were obtained using a eldemission scanning electron microscope (SEM) (JEOL JSM-700F, Hollingsworth & Vose, MA, USA) with an SEM working distance of 10-11 mm at a low accelerating voltage of 5 kV. Current density against voltage (J-V) were measured (before and after the pressure treatment) using a Keithley source meter unit (SMU2400) (Keithley, Tektronix, Newark, NJ, USA) that was connected to an Oriel solar simulator (Oriel, Newport Corporation, Irvine, CA, USA) under AM1.5G illumination of 90 mW cm − 2 . The SMU was operated using a KickStart instrument control software. The solar simulator was calibrated using a 918D high performance calibrated photodiode sensor (Newport). The device was masked to expose an area of 0.13 cm 2 to illumination.

Data availability
The authors declare that the data supporting the ndings of this study are available within the paper     voids, which are compacted by moderate pressure. Too much pressure, however, creates cracks.