Impedance Spectroscopy of Metal Halide Perovskite Solar Cells from the Perspective of Equivalent Circuits.

Impedance spectroscopy (IS) provides a detailed understanding of the dynamic phenomena underlying the operation of photovoltaic and optoelectronic devices. Here we provide a broad summary of the application of IS to metal halide perovskite materials, solar cells, electrooptic and memory devices. IS has been widely used to characterize perovskite solar cells, but the variability of samples and the presence of coupled ionic-electronic effects form a complex problem that has not been fully solved yet. We summarize the understanding that has been obtained so far, the basic methods and models, as well as the challenging points still present in this research field. Our approach emphasizes the importance of the equivalent circuit for monitoring the parameters that describe the response and providing a physical interpretation. We discuss the possibilities of models from the general perspective of solar cell behavior, and we describe the specific aspects and properties of the metal halide perovskites. We analyze the impact of the ionic effects and the memory effects, and we describe the combination of light-modulated techniques such as intensity modulated photocurrent spectroscopy (IMPS) for obtaining more detailed information in complex cases. The transformation of the frequency to time domain is discussed for the consistent interpretation of time transient techniques and the prediction of features of current-voltage hysteresis. We discuss in detail the stability issues and the occurrence of transformations of the sample coupled to the measurements.

Mechanisms of charge accumulation in the dark operation of perovskite solar cells.

In this work, a new current peak at forward bias in the dark current-voltage curves has been identified for standard mesoscopic perovskite solar cells. This characteristic peak appears only under some specific conditions, mainly in the reverse scan (RS) direction and when the solar cells were kept for several seconds under short-circuit conditions before starting the RS measurement. This peak disappears when the above experimental conditions are not applied. It is considered that this uncommon diode shape is obtained because shallow and/or deep trap states located at the interface between either perovskite/p-type or perovskite/n-type transport materials are dynamically filled during the RS voltage scan. To corroborate this hypothesis, the response of hole transport materials (HTMs), small molecule spiro-OMeTAD and polymer P3HT, as well as both HTMs with additives, was compared. Also perovskite absorbers such as CH3NH3PbI3 and all-inorganic perovskite based on cesium (CsPbI3) were also analyzed, achieving in all cases similar trends.

Classification of solar cells according to mechanisms of charge separation and charge collection.

In the last decade, photovoltaics (PV) has experienced an important transformation. Traditional solar cells formed by compact semiconductor layers have been joined by new kinds of cells that are constituted by a complex mixture of organic, inorganic and solid or liquid electrolyte materials, and rely on charge separation at the nanoscale. Recently, metal organic halide perovskites have appeared in the photovoltaic landscape showing large conversion efficiencies, and they may share characteristics of the two former types. In this paper we provide a general description of the photovoltaic mechanisms of the single absorber solar cell types, combining all-inorganic, hybrid and organic cells into a single framework. The operation of the solar cell relies on a number of internal processes that exploit internal charge separation and overall charge collection minimizing recombination. There are two main effects to achieve the required efficiency, first to exploit kinetics at interfaces, favouring the required forward process, and second to take advantage of internal electrical fields caused by a built-in voltage and by the distribution of photogenerated charges. These principles represented by selective contacts, interfaces and the main energy diagram, form a solid base for the discussion of the operation of future types of solar cells. Additional effects based on ferroelectric polarization and ionic drift provide interesting prospects for investigating new PV effects mainly in the perovskite materials.

Germanium coating boosts lithium uptake in Si nanotube battery anodes.

Si nanotubes for reversible alloying reaction with lithium are able to accommodate large volume changes and offer improved cycle retention and reliable response when incorporated into battery anodes. However, Si nanotube electrodes exhibit poor rate capability because of their inherently low electron conductivity and Li ion diffusivity. Si/Ge double-layered nanotube electrodes show promise to improve structural stability and electrochemical kinetics, as compared to homogeneous Si nanotube arrays. The mechanism explaining the enhancement in the rate capabilities is revealed here by means of electrochemical impedance methods. The Ge shell efficiently provides electrons to the active materials, which increase the semiconductor conductivity thereby assisting Li(+) ion incorporation. The charge transfer resistance which accounts for the interfacial Li(+) ion intake from the electrolyte is reduced by two orders of magnitude, indicating the key role of the Ge layer as an electron supplier. Other resistive processes hindering the electrode charge-discharge process are observed to show comparable values for Si and Si/Ge array electrodes.

Charge separation at disordered semiconductor heterojunctions from random walk numerical simulations.

Many recent advances in novel solar cell technologies are based on charge separation in disordered semiconductor heterojunctions. In this work we use the Random Walk Numerical Simulation (RWNS) method to model the dynamics of electrons and holes in two disordered semiconductors in contact. Miller-Abrahams hopping rates and a tunnelling distance-dependent electron-hole annihilation mechanism are used to model transport and recombination, respectively. To test the validity of the model, three numerical "experiments" have been devised: (1) in the absence of constant illumination, charge separation has been quantified by computing surface photovoltage (SPV) transients. (2) By applying a continuous generation of electron-hole pairs, the model can be used to simulate a solar cell under steady-state conditions. This has been exploited to calculate open-circuit voltages and recombination currents for an archetypical bulk heterojunction solar cell (BHJ). (3) The calculations have been extended to nanostructured solar cells with inorganic sensitizers to study, specifically, non-ideality in the recombination rate. The RWNS model in combination with exponential disorder and an activated tunnelling mechanism for transport and recombination is shown to reproduce correctly charge separation parameters in these three "experiments". This provides a theoretical basis to study relevant features of novel solar cell technologies.

Solution-processed small molecule:fullerene bulk-heterojunction solar cells: impedance spectroscopy deduced bulk and interfacial limits to fill-factors.

Using impedance spectroscopy, we demonstrate that the low fill factor (FF) typically observed in small molecule solar cells is due to hindered carrier transport through the active layer and hindered charge transfer through the anode interfacial layer (IFL). By carefully tuning the active layer thickness and anode IFL in BDT(TDPP)2 solar cells, the FF is increased from 33 to 55% and the PCE from 1.9 to 3.8%. These results underscore the importance of simultaneously optimizing active layer thickness and IFL in small molecule solar cells.

Ionic Field Screening in MAPbBr3 Crystals Revealed from Remnant Sensitivity in X-ray Detection.

Research on metal halide perovskites as absorbers for X-ray detection is an attractive subject due to the optimal optoelectronic properties of these materials for high-sensitivity applications. However, the contact degradation and the long-term instability of the current limit the performance of the devices, in close causality with the dual electronic-ionic conductivity of these perovskites. Herein, millimeter-thick methylammonium-lead bromide (MAPbBr3) single and polycrystalline samples are approached by characterizing their long-term dark current and photocurrent under X-ray incidence. It is shown how both the dark current and the sensitivity of the detectors follow similar trends at short-circuit (V = 0 V) after biasing. By performing drift-diffusion numerical simulations, it is revealed how large ionic-related built-in fields not only produce relaxations to equilibrium lasting up to tens of hours but also continue to affect the charge kinetics under homogeneous low photogeneration rates. Furthermore, a method is suggested for estimating the ionic mobility and concentration by analyzing the initial current at short-circuit and the characteristic diffusion times.

Surface versus Bulk Currents and Ionic Space-Charge Effects in CsPbBr3 Single Crystals.

CsPbBr3 single crystals have potential for application in ionizing-radiation detection devices due to their optimal optoelectronic properties. Yet, their mixed ionic-electronic conductivity produces instability and hysteretic artifacts hindering the long-term device operation. Herein, we report an electrical characterization of CsPbBr3 single crystals operating up to the time scale of hours. Our fast time-of-flight measurements reveal bulk mobilities of 13-26 cm2 V-1 s-1 with a negative voltage bias dependency. By means of a guard ring (GR) configuration, we separate bulk and surface mobilities showing significant qualitative and quantitative transport differences. Our experiments of current transients and impedance spectroscopy indicate the formation of several regimes of space-charge-limited current (SCLC) associated with mechanisms similar to the Poole-Frenkel ionized-trap-assisted transport. We show that the ionic-SCLC seems to be an operational mode in this lead halide perovskite, despite the fact that experiments can be designed where the contribution of mobile ions to transport is negligible.

Coupling between Ion Drift and Kinetics of Electronic Current Transients in MAPbBr3 Single Crystals.

The optoelectronic properties of halide perovskite materials have fostered their utilization in many applications. Unravelling their working mechanisms remains challenging because of their mixed ionic-electronic conductive nature. By registering, with high reproducibility, the long-time current transients of a set of single-crystal methylammonium lead tribromide samples, the ion migration process was proved. Sample biasing experiments (ionic drift), with characteristic times exhibiting voltage dependence as ∝ V -3/2, is interpreted with an ionic migration model obeying a ballistic-like voltage-dependent mobility (BVM) regime of space-charge-limited current. Ionic kinetics effectively modify the long-time electronic current, while the steady-state electronic currents' behavior is nearly ohmic. Using the ionic dynamic doping model (IDD) for the recovering current at zero bias (ion diffusion), the ionic mobility is estimated to be ∼10-6 cm2 V-1 s-1. Our findings suggest that ionic currents are negligible in comparison to the electronic currents; however, they influence them via changes in the charge density profile.

Characterization of nanostructured hybrid and organic solar cells by impedance spectroscopy.

We review the application of impedance spectroscopy in dye-sensitized solar cells, quantum dot-sensitized solar cells and organic bulk heterojunction solar cells. We emphasize the interpretation of the impedance parameters for determining the internal features of the device, concerning the carrier distribution, materials properties such as the density of states and/or doping of the semiconductors, and the match of energy levels for photoinduced charge generation and separation. Another central task is the determination of recombination mechanisms from the measured resistances, and the factors governing the device performance by combined analysis of resistances as a function of voltage and current-voltage curves.

Mobile Ion-Driven Modulation of Electronic Conductivity Explains Long-Timescale Electrical Response in Lead Iodide Perovskite Thick Pellets.

The favorable optoelectronic properties of metal halide perovskites have been used for X- and γ-ray detection, solar energy, and optoelectronics. Large electronic mobility, reduced recombination losses of the electron-hole pairs, and high sensitivity upon ionizing irradiation have fostered great attention on technological realizations. Nevertheless, the recognized mixed ionic-electronic transport properties of hybrid perovskites possess severe limitations as far as long-timescale instabilities and degradation issues are faced. Several effects are attributed to the presence of mobile ions such as shielding of the internal electrical field upon biasing and chemical interaction between intrinsic moving defects and electrode materials. Ion-originated modulations of electronic properties constitute an essential peace of knowledge to further progress into the halide perovskite device physics and operating modes. Here, ionic current and electronic impedance of lead methylammonium iodide perovskite thick pellets are independently monitored, showing self-consistent patterns. Our findings point to a coupling of ionic and electronic properties as a dynamic doping effect caused by moving ions that act as mobile dopants. The electronic doping profile changes within the bulk as a function of the actual ion inner distribution, then producing a specific time dependence in the electronic conductivity that reproduces time patterns of the type ∝t, a clear fingerprint of diffusive transport. Values for the iodine-related defect diffusivity in the range of Dion ∼ 10-8 cm2 s-1, which corresponds to ionic mobilities of about µion ∼ 10-6 cm2 V-1 s-1, are encountered. Technological realizations based on thick perovskite layers would benefit from this fundamental information, as far as long-timescale current stabilization is concerned.

Utilization of Temperature-Sweeping Capacitive Techniques to Evaluate Band Gap Defect Densities in Photovoltaic Perovskites.

Capacitive techniques, routinely used for solar cell parameter extraction, probe the voltage-modulation of the depletion layer capacitance isothermally as well as under varying temperature. In addition, defect states within the semiconductor band gap respond to such stimuli. Although extensively used, capacitive methods have found difficulties when applied to elucidating bulk defect bands in photovoltaic perovskites. This is because perovskite solar cells (PSCs) actually exhibit some intriguing capacitive features hardly connected to electronic defect dynamics. The commonly reported excess capacitance observed at low frequencies is originated by outer interface mechanisms and has a direct repercussion on the evaluation of band gap defect levels. Starting by updating previous observations on Mott-Schottky analysis in PSCs, it is discussed how the thermal admittance spectroscopy and the deep level transient spectroscopy characterization techniques present spectra with overlapping or even "fake" peaks caused by the mobile ion-related, interfacial excess capacitance. These capacitive techniques, when used uncritically, may be misleading and produce wrong outcomes.

New approaches to the lithiation kinetics in reaction-limited battery electrodes through electrochemical impedance spectroscopy.

Electrochemical impedance spectroscopy is a widely employed technique probing kinetic limitations in the charging of battery electrodes. Hindrance mechanisms locate at the interfaces between the active material and the electrolyte, and in the bulk of the reacting compound. Rate-limiting mechanisms are viewed as resistive circuit elements and can be extracted using standard impedance analyzers. Classical impedance models consider charge transport, mainly ion diffusion as slower carrier, as the principal kinetic limitation impeding full electrode charging. This is indeed the case for many technologically relevant battery compounds. In other instances, instead of being diffusion-limited, electrodes may undergo charging limitation caused by the kinetics of the reduction reaction itself. Specific impedance models for reaction-limited mechanisms are summarized here and proved for relevant electrode compounds, in particular for conversion or alloying electrodes in which Li+ intake produces a full rearrangement of the lattice structure with significant atomic displacement.

Effects of Frequency Dependence of the External Quantum Efficiency of Perovskite Solar Cells.

Perovskite solar cells are known to show very long response time scales, on the order of milliseconds to seconds. This generates considerable doubt over the validity of the measured external quantum efficiency (EQE) and consequently the estimation of the short-circuit current density. We observe a variation as high as 10% in the values of the EQE of perovskite solar cells for different optical chopper frequencies between 10 and 500 Hz, indicating a need to establish well-defined protocols of EQE measurement. We also corroborate these values and obtain new insights regarding the working mechanisms of perovskite solar cells from intensity-modulated photocurrent spectroscopy measurements, identifying the evolution of the EQE over a range of frequencies, displaying a singular reduction at very low frequencies. This reduction in EQE is ascribed to additional resistive contributions hindering charge extraction in the perovskite solar cell at short-circuit conditions, which are delayed because of the concomitant large low-frequency capacitance.

Recent Advances to Understand Morphology Stability of Organic Photovoltaics.

Organic photovoltaic devices are on the verge of commercialization with power conversion efficiencies exceeding 10 % in laboratory cells and above 8.5 % in modules. However, one of the main limitations hindering their mass scale production is the debatable inferior stability of organic photovoltaic devices in comparison to other technologies. Adequate donor/acceptor morphology of the active layer is required to provide carrier separation and transport to the electrodes. Unfortunately, the beneficial morphology for device performance is usually a kinetically frozen state which has not reached thermodynamic equilibrium. During the last 5 years, special efforts have been dedicated to isolate the effects related to morphology changes taking place within the active layer and compare to those affecting the interfaces with the external electrodes. The current review discusses some of the factors affecting the donor/acceptor morphology evolution as one of the major intrinsic degradation pathways. Special attention is paid to factors in the nano- and microscale domain. For example, phase segregation of the polymer and fullerene domains due to Ostwald ripening is a major factor in the microscale domain and is affected by the presence of additives, glass transition temperature of the polymers or use of crosslinkers in the active layer. Alternatively, the role of vertical segregation profile toward the external electrodes is key for device operation, being a clear case of nanoscale morphology evolution. For example, donor and acceptor molecules actually present at the external interfaces will determine the leakage current of the device, energy-level alignment, and interfacial recombination processes. Different techniques have been developed over the last few years to understand its relationship with the device efficiency. Of special interest are those techniques which enable in situ analysis being non-destructive as they can be used to study accelerated degradation experiments and some will be discussed here.

Methylammonium Lead Bromide Perovskite Battery Anodes Reversibly Host High Li-Ion Concentrations.

Ions migrate through the hybrid halide perovskite lattice, allowing for a variety of electrochemical applications as perovskite-based electrodes for batteries. It is still unknown how extrinsic defects such as lithium ions interact with the hybrid perovskite structure during the charging process. It is shown here that Li+ intake/release proceeds by topotactic insertion into the hybrid perovskite host, without drastic structural alterations or rearrangement. Even the perovskite electronic band structure remains basically unaltered upon cycling. The occurrence of conversion or alloying reactions producing metallic lead is discarded. Stable specific capacity ∼200 mA h g-1 is delivered, which entails outstanding Li-ion molar concentration, x in LixCH3NH3PbBr3, approaching 3. Slight distortions of the perovskite lattice upon cycling explain the highly reversible Li+ intercalation reaction that also exhibits an excellent rate capability.

Surface Polarization Model for the Dynamic Hysteresis of Perovskite Solar Cells.

The dynamic hysteresis of perovskite solar cells consists of the occurrence of significant deviations of the current density-voltage curve shapes depending on the specific conditions of measurement such as starting voltage, waiting time, scan rate, and other factors. Dynamic hysteresis is a serious impediment to stabilized and reliable measurement and operation of the perovskite solar cells. In this Letter, we formulate a model for the dynamic hysteresis based on the idea that the cell accumulates a huge quantity of surface electronic charge at forward bias that is released on voltage sweeping, causing extra current over the normal response. The charge shows a retarded dynamics due to the slow relaxation of the accompanying ionic charge, that produces variable shapes depending on scan rate or poling value and time. We show that the quantitative model provides a consistent description of experimental results and allows us to determine significant parameters of the perovskite solar cell for both the transient and steady-state performance.

Operating Mechanisms of Mesoscopic Perovskite Solar Cells through Impedance Spectroscopy and J-V Modeling.

The performance of perovskite solar cell (PSC) is highly sensitive to deposition conditions, the substrate, humidity, and the efficiency of solvent extraction. However, the physical mechanism involved in the observed changes of efficiency with different deposition conditions has not been elucidated yet. In this work, PSCs were fabricated by the antisolvent deposition (AD) and recently proposed air-extraction antisolvent (AAD) process. Impedance analysis and J-V curve fitting were used to analyze the photogeneration, charge transportation, recombination, and leakage properties of PSCs. It can be elucidated that the improvement in morphology of perovskite film promoted by AAD method leads to increase in light absorption, reduction in recombination sites, and interstitial defects, thus enhancing the short-circuit current density, open-circuit voltage, and fill factor. This study will open up doors for further improvement of device and help in understanding its physical mechanism and its relation to the deposition methods.

Correlation between volume change and cell voltage variation with composition for lithium intercalated amorphous films.

Interactions between the intercalant and the host have been studied in homogeneous amorphous Li(x)WO3 prepared by electron beam evaporation, using electrochemical experiments with films of different thickness (100-400 nm). We have related the intercalation thermodynamics, described previously by us [Solid State Ionics 2005, 176, 1701] with other models that take into account film volume dilatation along the intercalation. A distinct behavior of cell voltage variation with composition and volume change is observed for the thinnest (100 nm) films: cell voltage follows ideal insertion thermodynamics and no deformation was detected using profilometry techniques. In contrast, thicker films exhibited both volume changes and, correspondingly, cell voltage departs from ideality due to contributions to the chemical potential arising from elastic distortions of the host matrix.

Light-Induced Space-Charge Accumulation Zone as Photovoltaic Mechanism in Perovskite Solar Cells.

We fabricated formamidinium lead iodide perovskite solar cell for analysis of the photovoltaic mechanism based on the interpretation of the capacitance variation under illumination. It was shown that the low-frequency capacitance increases proportional to incident light intensity, and in addition it increases proportional to absorber thickness. Furthermore, the voltage dependence of capacitance is exponential with slope 1/2 (thermal energy). We conclude that the large photovoltage and capacitance are associated with electronic accumulation zone at the interface with the metal oxide contact. While this type of accumulation capacitance is common in many devices as transistors, the perovskite solar cell shows a singular behavior in that under light the electronic carrier accumulation grows unlimited by another series capacitance, reaching values as large as 10 mF cm(-2) at one sun illumination.