Solid-State Ionics of Hybrid Halide Perovskites.

Many exciting "anomalies" affecting long-time and low-frequency phenomena in the photoactive halide perovskites that are presently in the focus of the field of photovoltaics turn out to be rather expected from the point of view of solid-state ionics. This Perspective discusses such issues based on the mixed conducting nature of these materials and indicates how the solid-state ionics toolbox can be used to condition and potentially improve these solids. In addition to equilibrium bulk properties, interfacial effects and light effects on the mixed conductivity are considered.

Introduction: The Significance of Ion Conduction

Ion transport is crucial for various functions, mostly prominent for the field of energy research. Devices utilizing such functions include batteries, fuel cells, electrochemical sensors, and memristors. Of general relevance is the occurrence of mixed conductivity, where ionic and electronic conductivities are both appreciable. Mixed ionic–electronic conductors have been intensively studied in the field of solid-state ionics, with particular regard dedicated to the important material class of oxide perovskites. It will be shown here that many parallelisms exist with halide perovskites, which are presently heavily investigated for their potential use as efficient light-harvesters in photovoltaic devices.

Since the first observations of anomalous polarization phenomena in halide perovskite-based solar cells under operation,[1−7] and their clear attribution to ion transport,[8] a great deal of attention has been devoted to the investigation of the mixed conductivity in these materials.[9−29] The relevance of ion conduction for halide perovskites and devices is also due to its significance for degradation kinetics and for reaction processes shortening the lifetime of devices.[30−32] Moreover, ion transport is necessarily involved in the interaction of the materials with the surrounding atmosphere.[33] Last, but not least, ionic charge carriers are of great significance for space charge potentials building up at the interface with selective contact materials[34,35] (irrespective if these are generated under bias or already present in equilibrium) and are thus expected to affect carrier extraction and device performance.[36]

In this Perspective, we will focus on halide perovskite materials rather than devices and on reversible bulk ion (and electron) transport, which is inherently related to charge transport in devices. We will start out by describing the fundamentals of defect thermodynamics and kinetics, and by introducing solid-state ionics techniques commonly used to study mixed conductors. Here the mixed conducting oxide perovskite SrTiO3 serves as a model material. This basis will help us understand the results presented later for halide perovskites, which in many ways behave similarly to their oxide counterparts. We will pay particular attention to the archetypal material MAPI (methylammonium lead iodide, CH3NH3PbI3). We first describe the situation in the dark and then use the understanding gained there to extend the study to conditions under illumination. The peculiar light effects on ion transport observed in these materials will also be discussed.[37]

Solid-State Ionics Approaches To Study Mixed Conductors

In this section, first the general point defect thermodynamics underlying the compositional variation and transport properties of any ionic solid will be discussed. Second the defect kinetics will be addressed, which contains local changes in bulk defect concentrations as a function of time (i.e., transport and chemical diffusion theory) but also surface kinetics. In this context we also discuss techniques to separate ionic and electronic conductivities. To build the bridge between the well-understood oxide perovskites to the less-understood halide perovskites we will start out with oxide defect chemistry.

Defect Thermodynamics (Defect Chemical Modeling)

It is a thermodynamic necessity that, at T > 0 K, any given material contains a certain quantity of point defects, due to the configurational entropy gain obtained upon deviation from the perfect crystal.[38−40] The concentrations of all these ionic and electronic point defects (hence including the relevant charge carriers) are functions of temperature, stoichiometry (δ), and dopant content.[39−41] Increasing temperature typically enhances defect concentrations and widens the stable stoichiometry range (Figure a). Notwithstanding the typically small variations in δ, the consequences for the defect concentrations are enormous, as these typically vary by orders of magnitude within such tiny window.[42] Consequently, while stoichiometry variations are usually negligible for properties such as volume, mass, or even phase energetics, they may massively influence functional features such as electrical, thermal, and optical properties.

Figure 1

(a) Stability range of a binary oxide MO. The stable variations in stoichiometry the material can undergo (both in excess and in deficiency) are represented by the green window increasing with temperature. Within this window lies the entire defect diagram of the material, as given in detail in panel (b). (b, c) Double-logarithmic defect diagrams of a binary oxide MO, with Schottky-type intrinsic disorder as a function of (b) stoichiometry and (c) dopant content. Slopes are given on the figure. (d) Conductivity of slightly acceptor doped SrTiO3 at different temperatures as a function of P(O2) showing p- and n-type electronic conduction at low and high P(O2), respectively, and predominant ionic transport in the intermediate region. Note that the experimental observation is entirely captured by the defect chemical modeling of panel (b). Panel (d) adapted with permission from ref (43). Copyright 2008 Wiley-VCH Verlag.

Considering a model oxide MO, the oxygen partial pressure can be conveniently used as a parameter to vary stoichiometry. Qualitatively, the following can be stated: an increase in P(O2) enhances the concentrations of all the defects that increase the O-to-M ratio (i.e., δ), namely oxygen interstitials and metal vacancies. In addition, all defects decreasing the O-to-M ratio, such as oxygen vacancies and metal interstitials, will be suppressed. Increasing P(O2) also simultaneously enhances the electron hole concentration and decreases the conduction electron concentration. The effect of a dopant can also be easily qualified. If the dopant is effectively negatively charged (interstitial foreign anions, substitutional cations of lower valence, substitutional anions of higher negative charge), the concentrations of negatively charged defects are depressed while the ones of positively charged defects are augmented. The opposite is true for effectively positively charged dopants (interstitial foreign cations, substitutional cations of higher valence, substitutional anions of lower negative charge). Doping necessarily affects all ionic and electronic defect concentrations, provided these are sufficiently mobile to be equilibrated.

To quantify the above considerations, the mass action laws for the defect reactions have to be addressed, together with the electroneutrality equation.[39−41] This assumes the establishment of a thermodynamic equilibrium between the point defects and the surrounding atmosphere and, in the simplest approach, considers dilute and randomly distributed point defects (defect interactions ignored). We consider again an oxide MO, for which we assume Schottky disorder (stoichiometric generation of metal ion and oxygen ion vacancies, VM″ and VO••) to be the most relevant intrinsic defect reaction (point defects are here represented in the Kröger–Vink notation). The intrinsic ionic defect situation can thus be described by the following reaction and, for dilute conditions, by the related mass-action law:MMx and OOx represent a metal ion occupying a regular metal site (oxide ion on oxygen site) with neutral effective charge. Considering the electronic side, the intrinsic electronic disorder reaction is the band-to-band transition:Let us now consider a variation in the stoichiometry of MO upon changing the oxygen partial pressure. The corresponding reaction (and mass-action law) describing the effect on the defect concentrations is

Combining eq with the electroneutrality condition, we can predict the dependencies of the defect concentrations upon stoichiometry changes. The same approach can be used to quantify the effects of doping. The obtained defect concentrations are then usually plotted in double-logarithmic diagrams (known as Kröger–Vink diagrams), such as the ones given in Figure b,c for our model oxide MO.

In a ternary compound such as SrTiO3, at not too high temperatures, the Sr/Ti ratio is fixed by the sample’s history (synthetic conditions, previous high-temperature treatments), and as such cationic defects can be effectively considered as frozen dopants. As a consequence, defect diagrams similar to the MO case can be obtained, which have been directly experimentally observed (Figure d). More detailed considerations on this aspect are given in refs (44 and 45).

Analogous diagrams can then be obtained for MAPI (reported below in Figure ), where changes in stoichiometry are given by variations of the halogen partial pressure. The relevant defect equations (assuming frozen-in Pb defects) read as follows:Note that MAMAx and IIx describe the occupancy of regular site by MA and I ions, respectively. This approach has also been successfully used to model the effects of doping[46] and of oxygen exposure[33] in MAPI. Note that in MAPI oxygen is an extrinsic—but still exchangeable—component. It is important to stress that, due to low temperatures normally used for MAPI, a relevant role may also be played by impurities or frozen-in native defects as compensating majority defects (this is also the case for SrTiO3 at low temperatures). These aspects (even replacing Schottky by anti-Frenkel disorder), do not affect the general picture. The direct correspondence with experiments attests that defect chemical modeling is a very powerful tool for the identification of the dominant charge carriers.[33,46] We will discuss these aspects further below.

Figure 10

(a–c) Defect chemical modeling applied to MAPI to reveal the defect concentrations dependences as a function of (a) stoichiometry (iodine partial pressure), (b) acceptor and donor doping content, and (c) oxygen partial pressure. (d–f) Ionic and electronic conductivity of MAPI as a function of (d) iodine partial pressure (Ar as carrier gas), (e) acceptor (Na) dopant content (under Ar and 2 × 10–7 bar I2), and (f) oxygen partial pressure (Ar as carrier). The P(O2) dependence is measured in a thin film kept at 333 K under weak illumination (0.5 mW/cm2) to accelerate the incorporation kinetics.[33] All the other samples are pellets measured using d.c. galvanostatic polarization at 343 K in the dark. Figures taken from refs (33, 46, and 72), all published under Creative Commons licenses.

Defect Kinetics

While the thermodynamics is of great importance in determining how a material behaves upon changes in composition, in reality kinetic aspects play a decisive role. Most important is the kinetics of stoichiometry change (chemical process), which dictates the compositional changes effectively taking place and thus governs a material’s kinetic stability as well. In order to connect with the detailed experience in the field of oxides, let us consider again SrTiO3, equilibrated at a certain oxygen partial pressure. An increase (or decrease) in the outer P(O2) will provide the driving force for an oxygen flux directed inside (outside) the material. Though highly complex, the process can be viewed as a series of a surface step and a diffusion process. If the surface step is rate-limiting, the flux will—at least in proximity to equilibrium—depend on the inverse of a chemical resistance (Λ) and on the variation of the oxygen chemical potential (μ0) at the surface:

Referring to δcO as a driving force, is an effective surface rate constant, which depends on the underlying mechanism of the surface reaction. The terms δμO and δcO refer to the first bulk layer counted from the gas–solid interface, and they represent the difference between actual and final values (at t = ∞). In this limiting case, the stoichiometry will be homogeneous within the sample, as shown in Figure a, and the amount of oxygen incorporated will be a function only of surface rate constant and time. Atomistically, a surface incorporation reaction is composed of several steps, which include, for O2, at least adsorption, electron transfer, O–O bond dissociation, and incorporation of atomic oxygen ions into the material. With the knowledge of the chemical reactions involved in the various steps, it is possible to relate them to experimentally accessible quantities such as the surface rate constant or the exchange rate. For more details the reader is referred to refs (41, 43, and 47). The other limiting case of interest is the one where the surface exchange rate is fast with respect to the bulk diffusion. In this situation, we can assume that the outer oxygen chemical potential will be established rapidly in the surface layer. As shown in Figure b, the concentration profiles obtained differ significantly from the previous case.

Figure 2

Limiting cases for oxygen incorporation in SrTiO3: (a) surface-limited exchange and (b) diffusion-limited incorporation. Figure taken with permission from ref (43). Copyright 2008 Wiley-VCH Verlag.

Due to the constraints set by the electroneutrality condition, this bulk diffusion of oxygen (and, in general, the diffusion of any component inside/outside a material) necessarily corresponds to the concentration change of a neutral component. The process is named chemical diffusion and occurs via coupled ionic and electronic transport processes. Considering the situation in which oxygen is mobile in MO, the transport from x to x′ can be described as follows:

These neutral compositional variations are governed by a chemical diffusion coefficient and thus by a chemical capacitance (Cδ) and by a chemical resistance (Rδ). The latter can be given asand can be understood in terms of an effective mass transport for which both ionic and electronic diffusions are necessary. Similarly, the chemical capacitance can be described (for ionic and electronic defects of single charge) aswith cion and ceon being the respective charge carrier concentrations. Equations and 10 can be generalized to the presence of multiple carriers and internal reactions (trapping), as discussed in detail in refs (48 and 49). In general, Cδ represents the ability of a material to change its stoichiometry. These very important parameters also determine the characteristic time scale (τδ) of the chemical diffusion process, which can be given asNote that τδ is proportional to the square of the sample thickness (L). This is characteristic for such a diffusion process and comes from Rδ and Cδ both being proportional to L. Another characteristic feature of the diffusion process is that the time dependence follows a law for short times and an exponential law for long times. The chemical diffusion coefficient can be generally expressed asNote that Dion and Deon are defect diffusivities and are proportional to the mobilities of the dominant defects, while tion and teon are the ionic and electronic transport numbers (e.g., tion = σion/σtot). χ represents the differential trapping factors that are unity in the absence of internal defect interactions, as assumed in eq . Such kinetics of stoichiometry change takes place in every mixed conductor upon the application of an electrical or chemical potential difference and underlies fundamental processes such as mass storage. Importantly, the bulk diffusion does not only describe incorporation/excorporation of exchangeable components, but also internal compositional changes that can be generated by applying current or voltage across a mixed conducting material. We will pay particular attention to this latter case from now on, as it can be directly connected to experimental methods used to characterize mixed ionic-electronic transport.

When an electrical potential difference is applied across a sample sandwiched between two electrodes that are reversible for the electrons but not for the ions, a chemical diffusion process (as the one described above) will take place, with the potential difference as the driving force. The consequence is the progressive formation of a compositional gradient involving the entire bulk of the material.[50−52] In the steady state, ∇μion ∝ ∇ϕ, and to a first approximation a linear δ profile occurs. Note that this is a bulk effect that does not generate excess charge locally. As schematized in Figure a, the stoichiometry of the material is, in these conditions, a function of the position between the electrodes. The case of symmetric boundary conditions (both electrodes reversible only for one of the carriers) has been described by Yokota,[52] while the case where on one side the electrode is reversible for both carriers by Wagner and Hebb.[50,51] This phenomenon (known as stoichiometric polarization) happens alongside space charge polarization, but on a completely different length (and time) scale. We will briefly mention this issue in the next section, but the interested reader is referred to the literature for more information.[34,35]

Figure 3

(a) Composition of a non-stoichiometric MO sample as a function of position with respect to ion-blocking partially reversible electrodes, with (right) or without (left) a d.c. current (or voltage). Note that, for perovskite structures, δ is typically negative. The corresponding bulk stoichiometric polarization affects the composition in the entire bulk. Space charge effects at the boundaries are indicated with dashed lines. (b) Galvanostatic and (c) potentiostatic polarization measurements, obtained by applying a constant current and a constant voltage, respectively. (d) Simplified equivalent circuit describing the chemical diffusion under galvanostatic conditions. For more precise evaluations, the circuit discussed in ref (53) has to be used.

A stoichiometric polarization can be induced by applying a d.c. current or voltage, and we thus refer to a galvanostatic or potentiostatic measurement, respectively.[41] The typical electrical responses of a mixed conductor in these two experiments are reported in Figure b,c. Initially, both ionic and electronic charge carriers respond simultaneously to the electrical potential difference, yielding the sharp increase denoted as Vinit or Iinit. Subsequently, the blocking of the ionic species by the electrodes is progressively perceived, and via coupling with electronic species a stoichiometric gradient forms. This steady-state situation, in which only the electronic carriers flow is represented by the reaching of a saturation current or voltage (VS or IS, see Figure b,c). Alternatively, the potential difference can be applied in a.c., and here we refer to high frequencies (bulk dielectric relaxation) or low frequencies (chemical diffusion). We will not discuss these measurement here, but more information on the impedance of mixed conductor can be found elsewhere.[53−55] Moreover, this situation also takes place when the electrical stimuli are triangular, as used in i–V experiments. As there is no resting phase at the turning point of an i–V curve, the stoichiometric polarization appears in the form of a hysteresis.[56] The comparison of the steady-state situation with the short time behavior (or with the high frequency response in impedance) allows one to separate the ionic and electronic resistances. This follows from the application of an equivalent circuit representing the mixed conductivity, which for galvanostatic conditions can be simplified to yield the circuit of Figure d. The generalized equivalent circuit that includes chemical effects can be found in the literature.[53] More information on the underlying chemical diffusion process can be extracted from the characteristic time scale of the polarization, which was previously described in eq . As already mentioned, the occurrence of the “square-root regime” is a typical signature of a chemical diffusion process. Nevertheless, in addition to these measurements it is well advised to use complementary evidence from electromotive force (emf) experiments, Faradaic reaction cells, permeation cells, chemical pumps, or similar to conclude on the presence of mixed ionic electronic transport.[41]

Significant complications may occur due to the presence of internal defect reactions (e.g., defect association/trapping), but also by strong deviation from equilibrium. For the former case, we refer the reader to the literature for a complete treatment of the problem and of its consequences on the electrical measurements described above.[49,57] The latter situation is realized in the case of high applied voltages/currents during a polarization experiment, but also for abrupt variations of stoichiometry. In these cases, the chemical diffusion coefficient ceases to be independent of the potential gradient (electrical or chemical). This leads to sharp concentration variations such as the ones shown in Figure a,[58] and even to the appearance of a proper diffusion front (Figure b).[59]

Figure 4

(a) Conductivity profile measured perpendicularly by microelectrodes after applying 300 V across a Fe-doped SrTiO3 single crystal (electrodes placed at 0 and 3000 μm) for 90 min at 493 K. The analysis shows that the regimes of n-, vacancy-, and p-type conductivity are traversed. Panel (a) adapted with permission from ref (58). Copyright 2002 Kluwer Academic Publishers. (b) Oxygen vacancy concentration profiles in Fe-doped SrTiO3 after abruptly changing P(O2) from 1 bar to 10–30 bar at 800 K. Snapshot of the quenched samples as a function of time, showing the moving of a diffusion front (oxygen loss takes place from the top). Panel (b) taken with permission from ref (43). Copyright 2008 Wiley-VCH Verlag.

Defect Thermodynamics and Kinetics Involving Interfaces

The thermodynamic and kinetic situations described so far only apply to the bulk of the material under consideration. A further relevant field of study deals with ionic/electronic phenomena taking place at interfaces such as solid–solid (grain boundary, heterogeneous contacts) and solid–gas (material surface) interfaces. At the distance of the screening length (or below), distinct deviations from electroneutrality occur, and field effects determine the carrier concentrations. Figure a,b shows the correspondence of such field effects with concentration variations of electronic and ionic carriers. In fact in many materials, such as SrTiO3, it is the ionic point defects which determine the field, while the electrons follow such field undergoing a “fellow traveler” effect. These phenomena are described in detail in ref (36). The deliberate introduction of interfaces (or more generally charged higher-dimensional defects) can be used as a materials design strategy in a similar way as the classic (zero-dimensional) doping. We speak then of heterogeneous (or higher-dimensional) doping. Such effects can lead to large variations in ionic and electronic charge carrier concentrations and can thus determine the macroscopic functional properties of a material given a high enough density of heterogeneities (e.g., in mesoscopic structures, see Figure c). The promising field that investigates these systems is called nano-ionics, and its general relevance for electronics and information technology is discussed elsewhere.[60] Interfaces of interest in our context are homophase boundaries (grain boundaries) but also heterophase boundaries such as oxide/halide interfaces.[36,61]

Figure 5

(a) Energy level diagram for ionic and electronic carriers at an interface in the case of predominant Frenkel disorder. Panel (a) taken with permission from ref (41). Copyright 2004 Wiley-VCH Verlag. (b) Defect concentration changes as a function of distance from a positively charged interface. All positive defects are suppressed, and all negative defects are enhanced close to the boundary. Panel (b) adapted with permission from ref (62). Copyright 1995 Elsevier Science Ltd. (c) Strong size effects on the conductivity of SrTiO3 when entering the mesoscopic regime. Grain sizes of polycrystalline samples are given in the figure. Panel (c) adapted with permission from ref (63). Copyright 2010 Wiley-VCH Verlag.

The intrinsic situation is more complex if deviations from equilibrium are allowed. Then kinetic space charges can build up even in the absence of equilibrium charges. The most important issue here is space charge polarization, which complements the stoichiometric polarization discussed before. In contrast to the latter, the relaxation time of space charge polarization is typically much shorter and can be given aswhere ε is the dielectric constant and λ is the screening length. It is worthy of mention that, in the literature dealing with halide perovskites, the effect of ion conduction is typically ascribed to space charge polarization, instead of the above-described bulk polarization, disregarding the different time constants (cf. eqs and 13).

Defect Thermodynamics and Kinetics under Light

So far, we have not considered light effects. Under illumination with light of energy above bandgap, the continuity condition has to be complemented by generation/annihilation terms for the electronic carriers. Here we are considering the steady-state situation under uniform and constant illumination, where the large photogeneration of electrons and holes, after deducting rapid recombination processes, yields an effectively increased concentration of electronic carriers. The defect chemical considerations given previously approximately apply to the steady state, but only if the radiation effects are sufficiently quick. Interesting light effects on the ionic defect concentrations could be imagined in the case where electrons and holes are kinetically decoupled. We will show below that indeed light effects on ionic transport are not only perceptible, but very substantial in MAPI.

Ion Conduction in Hybrid Halide Perovskites

In the following part we will explicitly refer to hybrid halide perovskites and show that their properties, at least under dark conditions, are very similar to the ones established for oxide mixed conductors.

First Indications

First indications of the presence of mobile ionic species in hybrid halide perovskites came from the observation of “anomalous” polarization phenomena in perovskite solar cells under operation. These behaviors appeared at long times (or low a.c. frequencies) in the form of hysteretic i–V curves,[1−4] high apparent dielectric constants,[5,6] and field-switchable photovoltaic effects.[7] While initially some of these phenomena were attributed to ferroelectricity stemming from the organic cation dipoles,[64,65] this assessment was later revised due to the highly disordered nature of these dipoles at room temperature.[66−69] In fact the reported phenomena are strikingly similar to the stoichiometric polarization effects described in section .

An observation of ion migration in hybrid perovskites was already given in ref (7), albeit the changes reported appeared irreversible (or not clearly reversible). Similar evidence was later reported in refs (70 and 71). We find it important to stress here that these results have been observed under degradation conditions (see section ), and as such are not directly representative of equilibrium properties (e.g., bulk ion conduction).

A direct measurement of reversible bulk ion conduction in MAPI, and its separation from the electronic response, was first reported in ref (8) using d.c. galvanostatic polarization and emf measurements under equilibrium conditions. This was later complemented by ref (72). It is also worth noting that several halide perovskites, both hybrid and fully inorganic, were already assessed as mixed conductors long before their application in photovoltaic devices.[73−76] Alongside these first experimental reports, consistent supporting evidence came from computational works indicating the ease of formation (and, in some cases, high mobility) of ionic defects in hybrid halide perovskites (in particular in MAPI).[77−82] Nonetheless, there is no good agreement on the predicted formation energies,[77,79] nor on the extracted activation energies for mobility (e.g., migration energy for iodine vacancy motion in MAPI ranges between 0.08 and 0.58 eV).[80−82]

Points of Concern in Electrochemical Characterizations

Here we discuss a few key aspects in the study of halide perovskites and of their ionic motion that we feel have not received adequate attention. These refer to the thermodynamic definition of the materials, the impact of voltage on stability as well as on ion diffusion, and the difficulty in measuring and evaluating activation energies.

As already mentioned, many experiments (usually electrical or electrochemical) aimed at clarifying ion motion in halide perovskites are not performed under reversible and defined conditions, casting doubts on the conclusions. First of all, the charge carrier thermodynamics requires (beside definition of pressure and temperature) definition of stoichiometry and doping content. A crucial role in this context is played by the halogen partial pressure (stoichiometry) and by the oxygen partial pressure (acceptor doping), which severely influence the charge carrier concentrations (section 2.1). Moreover, halide perovskites suffer from severe stability problems, which can be induced by temperature, water/humidity, oxygen, high-intensity light, or a combination thereof. Lack of control over these parameters can lead to rapid degradation and to the irreversible loss of volatile components, affecting the measurements.

Another very important—and almost entirely overlooked—source of instability can be voltage. In several experiments, a voltage is applied across two terminals to induce ion movement, while the migration is monitored by different methods. The reported voltages applied were usually very high, in the range of tens to hundreds of volts, and as such above the thermodynamically expected decomposition voltage. It is straightforward to connect this with the stoichiometric polarization discussed in section . Irrespective of the resulting electric field, the voltage—if applied by electrodes that block the ions—induces in the steady state (SS) a difference in the chemical potential of the components which may easily exceed the stability limit (USS = −ΔμX/F, as = 0; see Figure a). Of particular relevance for halide perovskites is the chemical potential difference of the halogen (ΔμX), as this is the most mobile species (Figure ). Already a voltage of 1.4 V suffices to drive MAPbI3, MAPbBr3, and MAPbCl3 out of their stability range and to decompose them in methylamine, lead halides, and hydrogen halides even under standard conditions (standard Gibbs formation energies for this reaction are −125, −130, and −113 kJ/mol, respectively).[83] A voltage of 5.1 V is even enough to decompose MAPbI3, MAPbBr3, and MAPbCl3 into elements (standard Gibbs energy of formation for this reaction are −260, −400, and −490 kJ/mol, respectively).[83] Under these conditions, eventually degradation will occur, starting from the electrode interfaces. In halide perovskites, the kinetics of these processes is rather quick, in particular under illumination, and as such a metastable situation is not expected (as it may be the case for materials with very low ionic conductivities).

Figure 6

(a) Consequence of the application of a voltage to a mixed conductor with ion-blocking electrodes. Due to the nature of the contacts, in the steady state the chemical potential of the halide ions () is constant, while the electron and neutral halogen chemical potentials ( and μX) follow the voltage and give rise to a stoichiometric polarization. (b) Stability window of a binary metal halide MX as a function of temperature, representing tolerable changes in stoichiometry (δ). Application of a voltage induces a variation in μX*, which establishes on the two sides of a material chemical potential values which may exceed the stability window (red line). Depending on the initial position of the sample within the stability window, only one of the two chemical potential values may fall outside the window (blue line), but this occurrence still leads to degradation.

Let us now discuss the effect of voltage on the ionic transport. As the migration thresholds for ion transport are usually of the order of 0.1 eV or higher, hopping kinetics show that the local ion conductivities are not affected by the voltage, unless the resulting electric field is relevant at the hopping distance, i.e. in the order of 0.1 V/nm.[41] Even with micrometer-size electrode spacing, the voltages required to reach such electric fields will exceed the decomposition voltage. A different question is the influence of voltage on local defect concentrations (mentioned in section ), which stems from the bulk concentration polarization based on the coupling between voltage and chemical potential. As shown in Figure for SrTiO3, for voltages on the order of a few hundred volts (which is insufficient to induce the above-mentioned effect) the concentration variations can be sharp, but still describable by a (spatially dependent) chemical diffusion coefficient. While these voltages exceed the decomposition voltage, the very sluggish cation diffusion in this material, combined with the short application times of the voltage, allow for a metastable situation.

The last issue worth discussing here concerns activation energy measurements, which have been heavily used to characterize ionic mobility in halide perovskites and are often based on Arrhenius-type plots of the conductivity. Four points are worth mentioning: (i) In mixed conductors, it is not adequate to speak of an activation energy for the total conductivity. Rather, the T-dependences for the various species have to be considered separately, as the materials can be equally ionically and electronically conducting, especially under equilibrium conditions.[8,72] (ii) It cannot be assumed that, upon varying temperature, the charge carrier concentrations will remain constant. This stems not only from possible irreversibility effects such as loss of extrinsic (oxygen, residual solvent molecules, etc.) or even intrinsic components (methylamine, halogen), but also from the fact that the conductivity activation energy contains a defect formation term alongside the mobility term. (iii) At the expected relatively high defect concentrations and low temperatures, defect association may heavily impact the activation energy value. Upon heating, dissociation of defect complexes (ionic–ionic or ionic–electronic) would give rise to an effectively enhanced free carrier concentration, yielding even higher activation energies. A further complication, as discussed in ref (84), deals with the simultaneous presence of intrinsic and extrinsic defect regimes which can be crossed as a function of temperature. (iv) The best defined situation as far as measurement and evaluation are concerned is when the T-dependence is studied at constant halide partial pressure (EP). This requires reversible electrodes and possibly very long equilibration times. The alternative is to measure at constant stoichiometry (i.e., in a sealed system), so to assess a different—but related—value of the activation energy (Eδ). According to σ(δ,T) = σ(PX(δ,T), T), Eδ can then be related to EP through the following equation:[85]If these conditions are not guaranteed, then the meaning of the temperature dependence is complex.

The Nature of Ion Conduction under Equilibrium Conditions

A significant amount of work has been dedicated to unraveling the nature of ion conduction in hybrid halide perovskites. Unsurprisingly, most of the works focused on MAPI. In general, almost all the contributions identify either iodide ions[8,12,15,86−90] and/or methylammonium ions[70,71,89−92] to be mobile. Extrinsic ion migration (Li, Au) has been studied as well.[93−95] Unfortunately, many of the reports lacked unambiguous and/or direct experimental evidence (see also previous section), causing the question on the nature of ion conduction in these materials to remain open for a surprisingly long time.

Direct experimental evidence comes from reaction cell experiments, where a significant iodine diffusion in MAPI is observed in the form of secondary phase formation (Figure ).[8,72] While these experiments cannot rule out a parallel minor diffusion of the cations, they clearly demonstrate iodine motion as a major contribution. This occurrence is entirely unsurprising, as fast and reversible halide exchange (for which halide diffusion is necessary) was observed for halide perovskites,[96−98] in agreement with earlier works reporting halide conduction in several halide perovskites.[73−76] Note also that the perovskite structure favors anion transport, as extensively shown for oxide ion conduction in oxide perovskites.

Figure 7

Faradaic reaction cell experiments in the dark. (a) Schematics of the cell +M|MAPI|AgI|Ag–, with M = Cu or Pb. (b) XRD analysis of the interfaces of the reaction cell with M = Pb, after flowing 50 nA/cm2 of current for 1 week at 343 K under Ar atmosphere. Note the formation of PbI2 at the Pb|MAPI contact. No other secondary phases were present at any other interface, and no PbI2 formation was observed in the absence of current flow.[8,72] (c) XRD analysis of the interfaces of the reaction cell with M = Cu, after flowing 25 nA/cm2 of current for 1 week at 323 K under Ar atmosphere. Note the formation of CuI at the Cu|MAPI contact. No other secondary phases were present at any other interface, and no CuI formation was observed in the absence of current flow.[8,72] Figure taken from ref (72), published 2017 under a Creative Commons license.

As far as the cation diffusion is concerned, all previous observations are either indirect or irreversible (often simultaneous with phase degradation). An example is reported in Figure , where MA ions in MAPI migrate under illumination and bias, leading to phase degradation close to the electrodes. While this process is surely relevant for the material (and device) stability, it is not the one we are interested in when it comes to bulk charge transport in materials and devices.

Figure 8

Photothermal induced resonance (PTIR) microscopy of MAPI thin film under 80 V (1.6 V/μm) of bias: (a) before applying bias, (b) after 100 s, and (c) after 200 s. Scale bars are 20 μm. Bright area represents MA accumulation. Adapted with permission from ref (70).

To reliably determine whether cation diffusion contributes to bulk charge transport, non-destructive and direct methods are required. Powerful tools in this respect are NMR and tracer diffusion experiments. As shown in Figure , 1H NMR spectra present a large, almost invariant line width as a function of temperature, which indicate absence of significant MA diffusion.[72]14N spectra, given in Figure a, consistently show a typical quadrupolar splitting in the tetragonal phase of MAPI that could only exist without significant isotropic motion (e.g., diffusion). The results are in agreement with tracer diffusion experiments, where only a negligible MA diffusion is observed (orders of magnitude below the iodine transport).[72,99] Similar conclusions can be drawn for Pb cations based on the quasi-invariance of the 207Pb line width with temperature (Figure c). Based on the above evidence it is clear that, at least for equilibrium conditions, only iodide ions are sufficiently mobile as to be relevant for the macroscopic charge transport. Nonetheless, a minor diffusivity of the cations (as directly observed for MA)[72,99] is still expected to be of importance for decomposition processes and cation exchange reactions.[100,101]

Figure 9

NMR analysis of cation diffusion in MAPI. (a) 14N spectra displaying a quadrupolar splitting at T < 323 K (tetragonal phase). The existence of such splitting necessarily indicates absence of significant isotropic motion in this phase. (b) Full width at half-maximum of 1H NMR spectra as a function of temperature. The line width does not significantly vary with T and remains large even at 500 K, indicating lack of cation diffusion (this motion would average the intermolecular dipole–dipole interaction composing the line width that are not averaged by internal rotation).[69,72] (c) Full width at half-maximum of 207Pb NMR spectra as a function of temperature. The same arguments used for the proton case of panel (b) are valid here. Figure taken from ref (72), published 2017 under a Creative Commons license.

The remaining question to be addressed is then related to the defect mechanism behind the iodine transport (vacancy- or interstitial-based). In oxide perovskites, interstitial oxide motion can be excluded owing to site and bond arguments. Most of the existing computational literature on halide perovskites also suggests that halide vacancies have lower activation energies for the motion,[80−82] but in some cases interstitials appear equally mobile.[82] Normally, due to the high density of the structure, Schottky disorder is much more common than anti-Frenkel disorder (halide displacement from a regular lattice site, forming a vacancy and an interstitial) in perovskites. Moreover, as already mentioned, many oxide perovskites are oxide-ion (or proton) conductors via oxygen vacancies. To identify the dominant ionic defects in MAPI and halide perovskites, one can apply solid-state ionic approaches such as the one described previously. As shown in Figure a–c, defect chemical modeling at the level of mass action laws (see section ) can be used to predict the effects of stoichiometry changes, doping content, and oxygen incorporation on the defect concentrations.[46] These models can be compared with experiments, where stoichiometry variations, purposeful doping, and oxygen treatments are realized (Figure d–f) and the induced changes in ionic and electronic conductivities are recorded. The strong and reversible enhancement of electronic conductivity upon increase in the iodine partial pressure unambiguously indicates electron holes as the dominant electronic carriers (cf. Figure a,d). This is consistent with the doping experiment of Figure e, where acceptor doping clearly increases the electronic conductivity (cf. Figure b). Note that, according to the defect chemical modeling, we also expect a transition from p- to n-type electronic conductivity at sufficiently low P(I2) (see N region of Figure a). This occurrence is indeed experimentally observed when exposing the samples to an I2 sink.[37] As far as the ionic conductivity is concerned, as shown in Figure d this reversibly decreases as a function of P(I2), indicating iodine vacancies as dominant ionic charge carriers, as these are annealed by iodine incorporation (see eq ). We note here that the comparable changes of σion and σeon on a logarithmic scale would also indicate not too dissimilar concentrations of the relevant charge carriers (see defect diagram of Figure a, I-to-P transition regime). This is in contrast with conductivity experiments showing comparable ionic and electronic conductivities in these samples, and as such it remains an open question. A more detailed account of this discrepancy has been given in ref (46). Nevertheless, the increase of ionic conductivity upon acceptor doping given in Figure e strongly confirms iodine vacancies to be the dominant ionic charge carriers.[46,72] In addition, as shown in Figure f, the increase in ionic and electronic conductivity upon O2 incorporation (expected to behave as acceptor dopant if incorporated sufficiently, see Figure c) provides a further confirmation of the nature of the dominant carriers. This defect chemical approach clearly reveals that, in MAPI, iodine vacancies are the dominant ionic (and electron holes the dominant electronic) charge carriers under equilibrium conditions.[33,46,72]

Nonetheless, there are reports on iodine interstitials being dominant charge carriers,[84] with experimental evidence for mobile interstitials claimed in refs (24 and 28). In ref (24), both iodide vacancies and interstitials are proposed using results of activation energy values, which are, however, debatable (see section ). In ref (28), neutron scattering experiments reveal the presence of iodine interstitials, which are claimed to form neutral I2 molecules. Changes in occupancy between regular and interstitial sites are used to infer migration, even though they are more representative of an interstitial formation process, as migration involves a jump from an interstitial site to another. The observation of interstitial neutral iodine is consistent with the much smaller size with respect to an iodide ion, and this aspect is also discussed in the mechanism of light-enhanced ionic conductivity (see section ).[37] In this respect, it is still questionable whether the dominant defect disorder in this material is of Schottky ([VMA′] = [VI•]) or anti-Frenkel ([VI•] = [Ii′]) type, as in both cases the iodide vacancy concentration would be predominant. Experimental results given in ref (28) suggest the presence of anti-Frenkel disorder, while indication of Schottky disorder is found in the observation of a perceptible (albeit minor) MA diffusion,[72,99] which is consistent with the presence of a high concentration of MA defects (e.g., vacancies). Without further evidence, none of the above can be taken as a conclusive result. Importantly, the low temperature situation in halide perovskites (e.g., around room temperature) is very likely an extrinsic situation dominated by impurities (e.g., oxygen, metal ions, etc.) compensating for VI•. This assessment is based on the comparatively low native point defect concentrations with respect to the expected impurity level (coming, e.g., from the solution-based synthesis) and also on all the experience on oxide perovskites at low temperatures. A similar evaluation was also proposed in ref (84).

As a final note, we want to stress the importance of interfacial redistribution phenomena for these materials, both at grain boundaries and at hetero-interfaces. Ongoing work already shows that equilibrium space charge polarization in halide perovskites under equilibrium is, to a significant extent, ionically controlled.[102] Such behavior could indeed be expected based on the higher concentration of ionic charge carriers. This redistribution may have important consequences for the charge-transfer and recombination phenomena taking place at the interfaces in working devices, and as such deserves a thorough investigation. A recent example of a study of the effect of ionic carrier redistribution on charge transfer in photovoltaic devices is given in ref (20).

Light Effects on Ion Conduction

Having understood the mixed conducting transport in the dark, we can now move to consider the situation under illumination. The various indications for ion transport discussed earlier were already collected under illumination and in working photovoltaic devices,[1−7] suggesting the relevance of the ionic transport even under light. Interestingly, this would imply light-induced changes of the ionic transport itself happening alongside the electronic excitation. Indeed, light effects on bulk ionic transport in freestanding halide perovskites were suggested in refs (8, 103, and 104). Figure shows such light effects on d.c. polarization curves or on the effective conductivity activation barriers. Note that the latter measurement is sensitive to the total conductivity and is also affected by defect formation and, even more importantly, defect association processes which have strong temperature dependences (see section ).

Figure 11

(a, b) Direct current polarization experiments on MAPI thin films under illumination as a function of temperature: (a) d.c. polarization curves under 1 mW/cm2 light and (b) extracted values for ionic conductivity under several light intensities (from 0 mW/cm2 in gray symbols to 20 mW/cm2 in red symbols). Adapted from ref (104). Published 2016 under a Creative Commons license. (c, d) Activation energy of the total electrical conductivity of MAPI (c) thin films and (d) single crystals as a function of temperature and illumination. Figure from ref (103), reproduced by permission of the PCCP Owner Societies. (e, f) D.c. polarization experiments on MAPI thin films as a function of light intensity at 313 K: (e) d.c. polarization curves in the dark (black) and under 1 mW/cm2 light (red) and (f) extracted values for ionic and electronic conductivity. Figures (e) and (f) first published in ref (37).

Even though the ion conduction enhancement is strongly corroborated by the detailed analysis of the polarization transients,[37] these experiments are not sufficient to unambiguously confirm the mixed conducting nature of a sample (as already discussed in section ). To exclude electronic effects as the cause for these observations, more direct experimental methods are required, such as emf cells, permeation cells, and excorporation experiments.[37] As shown in Figure , these characterizations consistently show the presence of ionic conduction in MAPI even under illumination. Moreover, they indicate that an enhanced iodine transport is taking place.[37] To understand the nature of the dominant charge carriers under light, tracer diffusion and NMR experiments were carried out on thin films under light,[99] in addition to stoichiometric variations and Hall effect measurements.[37] The qualitative charge carrier situation turned out to be similar to the dark case, at least for low light intensities. As in the dark, electron holes and iodine vacancies appear to be the dominant ionic and electronic charge carriers.

Figure 12

(a, b) Emf cell built on a MAPI thin film. Pb/PbI2 and Ag/AgI mixtures are used as electrode and to provide a constant I2 activity: (a) schematic and (b) voltage measured across the cell with and without light. The presence of a significant voltage under light necessarily means that a substantial portion of the conductivity is still ionic. (c, d) Permeation cell obtained by depositing a MAPI thin film on a Cu substrate and exposing it to I2 vapor: (c) schematic and (d) formation of CuI on the illuminated side probed by XRD. The formation of CuI solely on the illuminated side indicates an enhanced permeation flux, consistent with higher ion conduction under light. (e, f) Excorporation experiment performed by immersing a MAPI film in toluene: (e) schematic and (f) concentration of I2 excorporated into toluene as a function of time, with and without 1 mW/cm2 illumination. The accelerated iodine loss under illumination indicates enhanced iodine transport. Figures first published in ref (37).

Based on this knowledge, a mechanism for the photoinduced enhancement of ion transport was proposed in ref (37). It relies on the interaction of electron holes with iodide ions sitting on regular iodine sites. Irrespective of the role of excess electrons, the holes can be localized neutralizing negatively charged iodide ions. These neutral atoms, due to a significantly lower size and to the tendency to interact with iodide ions in order to share the charge, can easily be displaced (e.g., interstitially), leaving an iodine vacancy behind, which is enabling the enhanced ion transport. Note that self-trapping processes involving electron holes and halide ions, and also the formation of halide dimers sharing a single negative charge (but not the increased σion) are very well known to happen in alkali halides.[105−108] This tentative mechanism would also have important implications for the photostability of MAPI (and possibly of other halide perovskites), as the enhanced ionic carrier concentration comes as a consequence of the formation of neutral iodine atoms. As such, this gives a heightened chemical potential of neutral iodine inside the perovskite material, which can act as the driving force for an irreversible loss of iodine under prolonged illumination in favor of a sink (e.g., toluene, vacuum, or the ambient gas phase).[37] As such processes would happen in bromides and iodides to a very different degree, this mechanism would also provide a straightforward explanation for the photoinduced phase separation of mixed iodide–bromide halide perovskites.[109] The different reactions of Br– and I– with electron holes would enhance the energy of the mixtures, in particular at comparable Br/I contents, favoring the formation of iodine-rich and bromine-rich domains. Lastly, as the described photoeffects are inherently connected with volume changes they may also be related to the macroscopic volume expansion observed in MAPI upon illumination.[110] At this stage, more experimental evidence is required to support these claims.

Conclusions and Outlook

So far, the equilibrium situation appears to be quite clear, and—from a solid-state ionics perspective—not at all unexpected. As in many oxide perovskites, we are dealing here with a mixed conducting material in which the majority of the ionic transport is carried by anion vacancies. Moreover, the behavior observed (particularly under equilibrium conditions) upon stoichiometry changes and the occurrence of stoichiometric polarization both conform to the expected behavior of a typical oxide perovskite. Similarities may also be expected regarding the impact of higher-dimensional defects on the point defect concentrations. Due to the soft structure of these materials, and to their practical use in contact with other phases, this latter aspect should be worth investigating in detail.

In contrast, major differences with the high temperature situation in oxide perovskites lie in (i) the expected high degree of defect association due to low temperature (and high defect concentrations), (ii) a more important role of impurities (or frozen-in native defects) as compensating majority defects, and (iii) the significant light effects on ionic transport. While the first points stem from the different temperature regimes but are not rooted in a different underlying charge carrier chemistry, the third point is surprising and can be ascribed to the less dense structure of MAPI as compared to, e.g., SrTiO3. Concerning the first point, defect concentrations and mobility values still remain to be unambiguously determined, both in the dark and under illumination. This aspect extends to the halide perovskite compositions used in devices (e.g., mixed-cation and mixed-anion) and would greatly help quantitatively understanding the charge transport in these materials. Regarding the second point, it would be important to identify and quantify the possible impurities present in these materials, so to assess their impact on the properties of materials and devices. As to the third point, the atomistic mechanism of the photoenhancement remains to be clearly proven, and the connection to the stability of the materials deserves special attention. Of particular interest may be the relation between the photoenhanced ion conduction and the halide demixing in mixed-anion compositions, as well as the potential effect on the phase volume. In the context of this Perspective, the most important issues for the future are (i) to evaluate the application of the solid-state ionics toolbox to the function of halide perovskite-based photovoltaic devices, in terms of bulk as well as interfacial defect chemistry, and (ii) to explore the consequences of the photoenhanced ion conduction regarding novel light-triggered or light-sensitive devices.