The Impedance spectroscopy analysis of perovskite solar cells is a challenging task as lead halide perovskites present many simultaneous phenomena that complicate the modeling and even the way we measure.

One of the great properties of perovskite is its ability to transport electrons and holes with a reasonably good conductivity what, combined with relatively low non radiative recombination, yields to good enough diffusion lengths, allowing an efficient extraction of the charges generated within the device.¹ Another key effect is the ability to equilibrate Fermi levels of these electronic carriers at the interfaces at positions very close to conduction and valence band of the perovskite what allows to produce open circuit potentials very close to thermodynamic limits.

At the same time, lead halide perovskites have shown to be good ionic conductors.^{1, 2} This point helps to explain some of the excellent properties of the material but also complicates the analysis of impedance, the description of the response of the devices at long times and eventually compromises long term stability of the device as the strong internal electrochemical potential attracts ions (or vacancies) towards the interfaces.

In this work some of the effects that ionic interactions have in the impedance and performance of perovskite solar cells will be described, paying special attention to interfacial effects, changes in recombination and their effect on solar cell performance.^{3, 4}  

References

(1)         Garcia-Fernandez, A.;  Moradi, Z.;  Manuel Bermudez-Garcia, J.;  Sanchez-Andujar, M.;  Gimeno, V. A.;  Castro-Garcia, S.;  Antonia Senaris-Rodriguez, M.;  Mas-Marza, E.;  Garcia-Belmonte, G.; Fabregat-Santiago, F., Effect of Environmental Humidity on the Electrical Properties of Lead Halide Perovskites. Journal of Physical Chemistry C 2019, 123 (4), 2011-2018.

(2)         Li, C.;  Guerrero, A.;  Huettner, S.; Bisquert, J., Unravelling the role of vacancies in lead halide perovskite through electrical switching of photoluminescence. Nature Communications 2018, 9 (1), 5113.

(3)         Alvarez, A. O.;  Arcas, R.;  Aranda, C. A.;  Bethencourt, L.;  Mas-Marzá, E.;  Saliba, M.; Fabregat-Santiago, F., Negative Capacitance and Inverted Hysteresis: Matching Features in Perovskite Solar Cells. The Journal of Physical Chemistry Letters 2020, 11 (19), 8417-8423.

(4)         Fabregat-Santiago, F.;  Kulbak, M.;  Zohar, A.;  Valles-Pelarda, M.;  Hodes, G.;  Cahen, D.; Mora-Sero, I., Deleterious Effect of Negative Capacitance on the Performance of Halide Perovskite Solar Cells. ACS Energy Letters 2017, 2 (9), 2007-2013.

Electrochemical impedance spectroscopy (EIS) and related analysis have successfully guided efforts for the improvement of many electrochemical and photoelectrochemical systems. For perovskite solar cells (PSC), EIS analysis has shown some complications due to stability issues and particular shapes of the obtained spectra that cannot be explained by standard models.

Here, I will present results showing a fully validated series of impedance spectra that represents a reproducible EIS timeseries at open circuit voltage (V_OC) for more than 20 hours, with a total of 150 analysed spectra. Significant changes in resistance and capacitance are observed and will be discussed, with the additional observation that these changes are almost 100% reversible if the devices are kept in the dark for only one day. The tested devices are full PSC devices that have proven to be stable over more than 500 hours. We compare those results to our latest generation of PSC that feature a self-assembled monolayer (SAM) of a fullerene derivative that have shown less than 1% of degradation over 1000 hours under light.

The second part of this talk will focus on the low frequency hook that is frequently encountered in EIS measurements on PSC. This feature has been called: (low-frequency) inductive loop, curl-back or negative loop and is also found in Lithium Ion batteries, proton exchange fuel cells (PEFC), organic light emitting diodes (OLED), thin film model electrodes, and in the field of corrosion, for example. The hook will be explained from a systems theory perspective, and a very basic explanation on the basis of a change in resistance (ΔR) of a main process will be given, considering the respective timescales. The most common equivalent circuit model (ECM) for such a low frequency hook is reviewed and the relation to a general empirical low-pass filter type model is highlighted. Thereby, a new viewpoint on the low frequency hook in EIS is presented that can facilitate the understanding and the parameter identification for the impedance analysis of spectra with such features.

In sum, this talk is designed to help researchers to get a better understanding and to create an awareness of the important aspects for an accurate, meaningful, and conclusive impedance analysis on PSC.

Impedance spectroscopy has been widely applied over the last decades to study electrochemical systems and solid-state devices. In the field of photovoltaics, impedance spectroscopy enables the possibility to perform in-situ characterisation under relevant operating conditions, and as function of illumination conditions, applied voltage, and ageing. It can, therefore, offer valuable insights into key loss mechanisms related to material properties and device design. However, performing impedance spectroscopy on emerging photovoltaics presents many challenges due to the ubiquitous use of multiple thin films with different physical and chemical properties, and their corresponding interfaces. As a result, the individual signatures in the impedance spectra are often difficult to interpret. In this talk, I willl discuss practical guidelines for performing impedance measurements and analysing impedance spectra. I will begin by reviewing the mathematical basics, and then discuss different strategies for choosing measurement conditions and performing data analysis. The first step is to ensure data integrity, and this depends on the measurement conditions as well as the sample itself. Impedance measurements are time-consuming, and a major source of artefacts in impedance spectra is due to sample instability. Further, knowledge of the relevant timescales of physical processes in the device, such as transport, trapping, recombination, and electron transfer at material interfaces, is a prerequisite for data analysis. I will review case studies for equivalent circuit modelling, analysis of the capacitance-frequency spectra, and performing carrier mobility measurements. 

Impedance spectroscopy has been a key technique to unveil the working mechanism of new generation photovoltaics, from sensitized to bulk heterojunction solar cells. One of the main reasons for its success was the use of equivalent circuits which gave access to important device information, such as charge recombination or transport, in a semi-direct way. 

However, an unambiguous impedance spectroscopy model for perovskite solar cells with a straightforward equivalent circuit has remained elusive, often resulting in contradictory interpretations of the results.  

We present an equivalent circuit derived from the study of a series of model systems: from a dye-sensitized configuration, where all the impedance features are well-known, to a state-of-the art perovskite solar cell [1]. This approach identifies the main impedance attributes in the perovskite-based devices, and explains the particularities including the Nyquist arcs coupling and the role of the low frequency capacitance. Concurrently, it can characterize the main physical processes determining the photovoltaic performance in a pragmatical way. The model shows its perks when applied to otherwise unintelligible cases, as a tool to unveil recombination or transport limitations. The potential and current limitations will be discussed.

The perovskite materials with ABX3 structure, where A = organic cation, B = inorganic cation and X = halides, are commonly known as Organic-Inorganic Hybrid Perovskite. In this regard, FAPbI3 and MAPbI3 (FA = NH2CHNH2 cation and MA = CH3NH3 cation) with perovskite structures are excellent solar absorber materials and potential candidates for the future photovoltaic applications. However, at ambient temperature the stability is a matter of concern for these materials as FAPbI3 transforms to a non-perovskite phase which is a bad solar absorbent and MAPbI3 decomposes with time. In this connection, it is found that the solid solutions of FAPbI3 and MAPbI3 are more stable in comparison to their individual phases. Thus, we have carried out a thorough investigation of the crystal phases of the solid solution i.e. MA(1-x)_FA(x)_PbI3 system for various x values at different temperatures covering 300 K down to 15 K by using variable temperature powder X-ray diffraction (XRD) measurement. The obtained space groups at different crystal phases are confirmed by temperature dependent single crystal XRD. In total, four crystallographic phases exist for this solid solution series namely, cubic, tetragonal, large-cell cubic and orthorhombic. By performing variable temperature dielectric measurement in impedance spectrometer, we have also seen that the dielectric constant correlates strongly with the structure. Therefore, properties of such doped systems, known to be essential for high efficiency together with stability, will have to be understood in terms of their crystallographic phases, which will be discussed in detail in the present work.

The correct interpretation of capacitance data in perovskite solar cells is very important to obtain several fundamental parameters of the material, such as doping densities and built-in voltage values from Mott-Schottky plots or the spatial distribution of trap densities from capacitance-voltage (CV) measurements or drive-level capacitance profiling (DLCP). This has been difficult so far due to apparent ionic contributions to the spectra. However, I will show that even in a p-i-n perovskite solar cell devoid of mobile ions, the apparent Mott-Schottky profile is generated not by a space charge layer related to band bending but by charge injection and transitions between the geometric capacitances of the different layers of the perovskite solar cell. These effects also yield a fundamental minimum charge density that will be observed in spatial charge density profiles from capacitance measurements that should not be mistaken as defect/doping densities. 

Small perturbation techniques have been widely used for the investigation of perovskite solar cells and have helped understand important aspects of their operation. An adequate interpretation of the spectra given by impedance spectroscopy (IS), intensity-modulated photocurrent spectroscopy (IMPS) and intensitymodulated photovoltage spectroscopy (IMVS) is key for the understanding of device operation. The utilization of a correct equivalent circuit to fit the spectra and extract real parameters is needed to get this information and provide a proper interpretation. In this work, we present an equivalent circuit based on previous studies [1],[2] which is able both to reproduce the most general features and also the exotic behaviours found in impedance spectra. From the measurements, we demonstrate that the mid-frequency features that appear in IS spectra clearly depend on the active layer thickness and we prove the spectral correlation of the three techniques that has been suggested theoretically.[3]

Engineering two-dimensional (2D) / three-dimensional (3D) perovskites has emerged as an attractive route to efficient and stable perovskite solar cells. Beyond improving the surface stability of the 3D layer and acting as a trap passivation agent, the exact function of 2D/3D device interface remains vague.

Understanding the optoelectornic processes at the interface is therefore crucial.

In our work we provide the exact knowledge on the interface processes and energetics in 2D/3D perovskite interfaces. By combining different time resolved technicques such as optical pumop probe spectroscopy, time resolved microwave conductivity and novel ultraviolet photoelectron spectroscopy (UPS) depth-profiling technique, we show the 2D/3D interface properties and how the interface function is influenced by the nature of the 2D overlayer. As a result, the 2D/3D perovskite interface can form a p-njunction able of reducing the electron density at the hole transport layer interface, but also that the optimized 2D/3D suppresses the interfacial recombination losses, leading to open-circuit voltage (VOC) which approaches the potential internal Quasi-Fermi Level Splitting (QFLS) of the perovskite absorber [1,2].

We thus identify the essential parameters and energetic alignment scenario required for 2D/3D perovskite systems in order to surpass the current limitations of hybrid perovskite solar cell performances and advance in device optimization.

We report a novel photocurrent frequency modulation mapping technique, which enables us to achieve micrometer spatial and sub-microsecond temporal resolution of photocurrent transients. We employ our technique to report charge carrier recombination dynamics in hybrid perovskite bulk and selectively at interfaces with electrodes. We isolate and identify material-specific loss channels for device operation by characterizing the charge dynamics at interfaces with individual electrodes and charge selective layers. We further find a bulk charge trapping length for bulk hole traps of 21 μm with an associated trapping timescale of 2 μs, demonstrating that bulk trapping is not a major limiting factor for long-distance charge transport in perovskite-based devices. We determine the length and timescales of carrier transport via diffusion and photon recycling. We find significant photocurrent losses on and near gold electrodes due to the formation of a reduced charge carrier mobility region near the perovskite-gold interface with an associated trapping timescale of 0.7 μs. Our ability to expand the steady-state mechanisms of interface processes in space and time has potential to characterize a wide range of processes, which provides novel insights into device operation for high throughput optimization of optoelectronic and related energy applications.

We report the in-operando charge carrier recombination dynamics in perovskite bulk and at interfaces with electrodes by employing a novel photocurrent modulation technique, which enables us to achieve micrometre spatial and sub-microsecond temporal resolution of photocurrent transients. Our capacity to identify and isolate significant loss channels for device operation, by characterizing the performance of individual electrodes and charge selective layers, has previously only been achieved via indirect techniques. We find a charge trapping length for bulk hole traps of 21 μm with an associated trapping timescale of 2 μs, demonstrating that bulk trapping is not a major limiting factor for long-distance charge transport in perovskite-based devices. We observe significant photocurrent losses on and near gold electrodes due to the formation of a reduced charge carrier mobility region near the perovskite-gold interface with an associated trapping timescale of 0.7 μs. We further determine the length and timescales of carrier transport via diffusion and photon recycling. Our novel ability to expand the steady-state operation of the device in space and time allows us to characterise a broad range of processes in-operando with crucial insights into device operation, and paves the way for high throughput optimisation of interfaces for high-efficiency optoelectronics.

The ultrafast polarization response to incident light and ensuing electronic excitations are essential to the outstanding optoelectronic properties of lead halide perovskites (LHPs). In recent studies, a dynamically disordered structure and anharmonic crystal lattice was suggested to be a key component for LHPs’ complex polarization dynamics [1], [2]. In this work, we develop a novel type of two-dimensional (2D) spectroscopy to spectrally resolve and disentangle contributions to the ultrafast optical Kerr-effect (OKE) in MAPbBr3 and its all-inorganic counterpart CsPbBr3. This technique allows us to energetically dissect broadband light propagation and dispersive polarization responses in the vicinity of the electronic bandgap. Light propagation in LHPs is in particular technologically relevant for solar cell, light modulation and LED applications due to stimulated emission, polariton condensation and photon recycling which may take place in the investigated spectral region [3], [4].  

In both LHPs, we find intense nonlinear mixing of anistropically propagating light fields, resulting in an oscillatory polarization response, which strongly depends on the crystallographic phase and the position of the electronic bandgap. Our findings moreover raise the awareness for anisotropic and nonlinear light propagation, complicating conventional time-resolved methods, such as transient absorption, two-dimensional electronic spectroscopy and (1D) OKE near resonances of the dielectric function. We further demonstrate the power of two-dimensional optical Kerr-effect (2D-OKE) and its temperature-dependent fingerprint to quantify the dispersion anisotropy of LHPs’ orthorhombic phase. In addition to revealing highly dispersive anisotropic light propagation and its nonlinear mixing, this study finally establishes a unified origin of ultrafast Kerr responses in single crystal LHPs near the optical bandgap.

The perovskite solar cells have been extensively developed since 2009 but still the ultrafast and fast processes occurring at the interfaces in this system are not fully understood. We focused on the investigation of electron transport paths: after light absorption, an electron is promoted from the valence to the conduction band, and then several processes can occur. First few hundreds of femtosecond after light absorption are governed by cooling of the hot carriers. When the process is finished, sharp bleach due to the band filling phenomena occurs at absorption edge in the transient absorption measurements. Its decay correlates with photoluminescence kinetics and represents the excited carrier lifetime [1,2]. That decay proceeds by several paths such as the recombination (first-, second- and third-order) and the charge injection to an electron transporting material (ETM) or a hole transporting material (HTM).       

In this work we focused on a triple cation perovskite FA_0.76MA_0.19Cs_0.05(I_0.81Br_0.19)₃ sandwiched between a spiro-OMeTAD (HTM) and mesoporous TiO₂ (ETM) layers prepared under ambient (in the presence of oxygen and ambient room humidity) conditions. The studies were based on femtosecond to nanosecond transient absorption, picosecond to nanosecond time-resolved emission, electrochemical impedance spectroscopy and x-ray diffraction measurements of the prepared cells. By properly tuning the excitation wavelength, changing the excitation side and grazing angles we were able to selectively probe the titania/perovskite or perovskite/spiro-OMeTAD interfaces of the cells.

Difference in PbI₂ content as well as difference in charge dynamics on the ETM and HTM interface were detected. The transient bleach and stationary emission band maximum was also shifted when HTM or ETM side was investigated. We also checked influence of DMSO content in the precursor solution on the cell parameters. We found that higher DMSO concentration causes an increase of the ideality factor in electrochemical impedance studies [3].

Mobile ions in metal halide perovskites are causing current-voltage hysteresis in solar cells, and promote degradation and non-radiative recombination. We want to contribute to the understanding of the fundamental properties of ionic transport and its relationship to processing parameters. Therefore, we characterised the ionic defect landscape of methylammonium lead triiodide (MAPbI₃) perovskites with fractionally changed precursor stoichiometry [1] by impedance spectroscopy and deep-level transient spectroscopy (DLTS). I will briefly introduce these experimental methods, and how the latter allows to distinguish between electronic traps and ionic defects. With IS, we observed three different ionic defects in MAPbI₃ and their migration rates and activation energies. To gain more insight, we applied a newly developed algorithm for performing inverse Laplace transform to evaluate the DLTS capacitance transients. The result reveals a broad distribution of migration rates for each of the observed ionic defect [2]. Our findings show a major impact of the precursor stoichiometry on the defect landscape, with direct consequences for the electronic properties such as the measured built-in potential and the open-circuit voltage. I will also show how we applied the Meyer-Neldel rule to categorise the migration rates of the different ionic defects and discuss where it comes from [3].

[1] P. Fassl, V. Lami, A. Bausch, Z. Wang, M.T. Klug, H.J. Snaith, and Y. Vaynzof, Fractional deviations in precursor stoichiometry dictate the properties, performance and stability of perovskite photovoltaic devices. Energy & Environmental Science 11, 3380 (2018).
[2] S. Reichert, J. Flemming, Q. An, Y. Vaynzof, J.-F. Pietschmann, and C. Deibel, Ionic-Defect Distribution Revealed by Improved Evaluation of Deep-Level Transient Spectroscopy on Perovskite Solar Cells. Phys. Rev. Applied 13, 034018 (2020).
[3] S. Reichert, Q. An, Y.-W. Woo, A. Walsh, Y. Vaynzof, and C. Deibel, Probing the ionic defect landscape in halide perovskite solar cells. arXiv 2005.06942v1 (2020).

The existence of slow dynamic processes in perovskite solar cells is well-known. This is most commonly observed as hysteresis in the current-voltage curve during device efficiency measurements. Slow processes have also been observed in a range of frequency and time domain measurements. Whilst there is considerable evidence linking the origins of these observed processes to the migration of ions within the perovskite, the exact nature of their interaction with the electronic structure of the device is still unclear.

We have employed a range of complimentary frequency and time domain characterization techniques in an attempt to understand these complex interactions. These techniques include impedance (EIS), intensity modulated photovoltage/photocurrent (IMVS/IMPS) and transient photovoltage/photocurrent spectroscopies (TPV/TPC). We have also studied a range of cell architectures from planar to triple-mesoporous perovskite devices. Unusual behaviours such as the negative transient photovoltage/photocurrent response appear to have analogous behaviours in the frequency domain in the form of multiple arcs and loops. It is our hope that by combining the use of both of these techniques it may help our interpretation of device operation.

For example, our previous findings from temperature dependent EIS measurements allowed us to establish a clear link between ionic redistribution and changing recombination rates. This process has also been identified in TPV measurements during the slow V_oc rise under illumination. We employed this understanding to measurements performed on triple-mesoporous perovskite devices containing the additive 5-AVAI, which revealed the inhibition of ionic movement due to the presence of the additive. This property is related to the exceptionally slow response time of these devices, and also their improved stability.

A major hurdle for commercialization of perovskite solar cells remains, the degradation of this class of materials under a range of environmental factors. Ion migration has been identified as one of the main drivers for degradation, decreasing the power conversion efficiency of the devices over time.

It was shown that MAPbBr3 is more stable under environmental conditions when compared to MAPbI3. Using transient ion drift, we show that this stems from key changes in ion migration when going from MAPbI3 to MAPbBr3: methylammonium migration is suppressed, while bromide migration is reduced. Composition engineering can thus be used as a tool to mitigate ion migration. We extend our investigation to the evolution of ion migration in different MAPbBr3 solar cells as a function of the grain size of the active perovskite film. We show that beyond composition engineering, crystallinity can be another effective tool to control ion migration.

Ruddlesden-Popper (RP) halide perovskites are the new kids on the block for high-performance perovskite photovoltaics with excellent ambient stability. The layered nature of these perovskites offers an exciting possibility of harnessing their optoelectronic properties for various applications. However, ion migration, one origin of current-voltage hysteresis in halide perovskites, unlocks new opportunities for resistive switching for different applications such as data storage, synaptic devices, neuromorphic electronics, logic gates, etc. Herein, we show the strong relationship between the resistive switching mechanism in random access memory (RAM) devices with the number of octahedral layers present in RP perovskites. The ON/OFF ratio of RP-based devices peaks at n̅ = 5, demonstrating the highest ON/OFF ratio of ∼10⁴ and minimal operation voltage in 1.0 mm² device. Long data retention even in 60% relative humidity and stable write/ erase capabilities exemplify their potential for memory applications. The in-depth impedance spectroscopy findings reveal formation of conducting silver iodide layer via chemical reaction between migrating ions and the external contacts and accumulation of iodine vacancies are the underlying cause to control the resistive switching. Furthermore, the absence of current-switching on replacement of Ag top electrode with chemically non-reactive Au validate our findings and confirm the necessity of the interfacial reaction.     

The bandgap tunability of mixed-halide perovskites makes them promising candidates for light emitting diodes and tandem solar cells. However, illuminating mixed-halide perovskites results in the formation of segregated phases enriched in a single-halide. This segregation occurs through ion migration, which is also observed in single-halide compositions, and whose control is thus essential to enhance the lifetime and stability of the devices. Using pressure-dependent transient absorption spectroscopy, we find that the formation rates of both iodide- and bromide-rich phases in MAPb(BrxI_1-x)₃ reduce by two orders of magnitude on increasing the pressure to 0.3 GPa. We explain this reduction from a compression-induced increase of the activation energy for halide migration, which is supported by first-principle calculations. A similar mechanism occurs when the unit cell volume is reduced by incorporating a smaller cation. These findings reveal that stability with respect to halide segregation can be achieved either physically through compressive stress or chemically through compositional engineering.