Photo-induced halide redistribution in organic-inorganic perovskite films

Organic-Inorganic Hybrid Halide Perovskites for Memories, Transistors, and Artificial Synapses

Fascinating characteristics of halide perovskites (HPs), which cannot be seen in conventional semiconductors and metal oxides, have boosted the application of HPs in electronic devices beyond optoelectronics such as solar cells, photodetectors, and light-emitting diodes. Here, recent advances in HP-based memory and logic devices such as resistive-switching memories (i.e., resistive random access memory (RRAM) or memristors), transistors, and artificial synapses are reviewed, focusing on inherently exotic properties of HPs: i) tunable bandgap, ii) facile majority carrier control, iii) fast ion migration, and iv) superflexibility. Various fabrication techniques of HP thin films from solution-based methods to vacuum processes are introduced. Up-to-date work in the field, emphasizing the compositional flexibility of HPs, suggest that HPs are promising candidates for next-generation electronic devices. Taking advantages of their unique electrical properties, low-cost and low-temperature synthesis, and compositional and mechanical flexibility, HPs have enormous potential to provide a new platform for future electronic devices and explosively intensive studies will pave the way in finding new HP materials beyond conventional silicon-based semiconductors to keep up with "More-than-Moore" times.

Role of Surface Recombination in Halide Perovskite Nanoplatelets

Halide perovskites are an extremely promising material platform for solar cells and photonic devices. The role of surface carrier recombination-well known to detrimentally affect the performance of devices-is still not well understood for thin samples where the thickness is comparable to or less than the carrier diffusion length. Here, using time-resolved microspectroscopy along with modeling, we investigate charge-carrier recombination dynamics in halide perovskite CH₃NH₃PbI₃ nanoplatelets with thicknesses from ∼20 to 200 nm, ranging from much lesser than to comparable to the carrier diffusion length. We show that surface recombination plays a stronger role in thin perovskite nanoplatelets, significantly decreasing photoluminescence (PL) efficiency, PL decay lifetime, and photostability. Interestingly, we find that both thick and thin nanoplatelets exhibit a similar increase in PL efficiency with increasing excitation fluence, well described by our excitation saturation model. We also find that the excited carrier distribution along the depth impacts the surface recombination. Using the diffusion-surface recombination model, we determine the surface recombination velocity. This work provides a comprehensive understanding of the role of surface recombination and charge-carrier dynamics in thin perovskite platelets and reveals valuable insights useful for applications in photovoltaics and photonics.

Low-Temperature Plasma-Assisted Atomic-Layer-Deposited SnO2 as an Electron Transport Layer in Planar Perovskite Solar Cells

In this work, we present an extensive characterization of plasma-assisted atomic-layer-deposited SnO₂ layers, with the aim of identifying key material properties of SnO₂ to serve as an efficient electron transport layer in perovskite solar cells (PSCs). Electrically resistive SnO₂ films are fabricated at 50 °C, while a SnO₂ film with a low electrical resistivity of 1.8 × 10^-3 Ω cm, a carrier density of 9.6 × 10¹⁹ cm^-3, and a high mobility of 36.0 cm²/V s is deposited at 200 °C. Ultraviolet photoelectron spectroscopy indicates a conduction band offset of ∼0.69 eV at the 50 °C SnO₂/Cs_0.05(MA_0.17FA_0.83)_0.95Pb(I_2.7Br_0.3) interface. In contrast, a negligible conduction band offset is found between the 200 °C SnO₂ and the perovskite. Surprisingly, comparable initial power conversion efficiencies (PCEs) of 17.5 and 17.8% are demonstrated for the champion cells using 15 nm thick SnO₂ deposited at 50 and 200 °C, respectively. The latter gains in fill factor but loses in open-circuit voltage. Markedly, PSCs using the 200 °C compact SnO₂ retain their initial performance at the maximum power point over 16 h under continuous one-sun illumination in inert atmosphere. Instead, the cell with the 50 °C SnO₂ shows a decrease in PCE of approximately 50%.

Water-Repellent Low-Dimensional Fluorous Perovskite as Interfacial Coating for 20% Efficient Solar Cells

Hybrid perovskite solar cells have been capturing an enormous research interest in the energy sector due to their extraordinary performances and ease of fabrication. However, low device lifetime, mainly due to material and device degradation upon water exposure, challenges their near-future commercialization. Here, we synthesized a new fluorous organic cation used as organic spacer to form a low-dimensional perovskite (LDP) with an enhanced water-resistant character. The LDP is integrated with three-dimensional (3D) perovskite absorbers in the form of MA_0.9FA_0.1PbI₃ (FA = NH₂CH = NH₂⁺, MA = CH₃NH₃⁺) and Cs_0.1FA_0.74MA_0.13PbI_2.48Br_0.39. In both cases, a LDP layer self-assembles as a thin capping layer on the top of the 3D bulk, making the perovskite surface hydrophobic. Our easy and robust approach, validated for different perovskite compositions, limits the interface deterioration in perovskite solar cells yielding to >20% power conversion efficient solar cells with improved stability, especially pronounced in the first hours of functioning under environmental conditions. As a consequence, single and multijunction perovskite devices, such as tandem solar cells, can benefit from the use of the waterproof stabilization here demonstrated, a concept which can be further expanded in the perovskite optoelectronic industry beyond photovoltaics.

Giant Zero-Drift Electronic Behaviors in Methylammonium Lead Halide Perovskite Diodes by Doping Iodine Ions

Methylammonium lead halide perovskites have attracted extensive attention for optoelectronic applications. Carrier transport in perovskites is obscured by vacancy-mediated ion migration, resulting in anomalous electronic behavior and deteriorated reliability of the devices. In this communication, we demonstrate that ion migration can be significantly enhanced by doping additional mobile I⁻ ions into the perovskite bulk. Ionic confinement structures of vertical metal oxide semiconductor (MOS) and lateral metal semiconductor metal (MSM) diodes designed to decouple ion-migration/accumulation and electronic transport are fabricated and characterized. Measurement conditions (electric-field history, scan rate and sweep frequency) are shown to affect the electronic transport in perovskite films, through a mechanism involving ion migration and accumulation at the block interfaces. Prominent zero-point drifts of dark current-voltage curves in both vertical and lateral diode are presented, and further varied with the perovskite film containingthe different iodine-lead atomic ratio. The doped perovskite has a large ion current at grain boundaries, offering a large ion hysteresis loopand zero drift value. The results confirmthat the intrinsic behavior of perovskite film is responsible for the hysteresisof the optoelectronic devices, but also paves the way for potential applications in many types of devices including memristors and solid electrolyte batteries by doping the native species (I^- ions) in perovskite film.

Transformation from crystalline precursor to perovskite in PbCl2-derived MAPbI3

Understanding the formation chemistry of metal halide perovskites is key to optimizing processing conditions and realizing enhanced optoelectronic properties. Here, we reveal the structure of the crystalline precursor in the formation of methylammonium lead iodide (MAPbI₃) from the single-step deposition of lead chloride and three equivalents of methylammonium iodide (PbCl₂ + 3MAI) (MA = CH₃NH₃). The as-spun film consists of crystalline MA₂PbI₃Cl, which is composed of one-dimensional chains of lead halide octahedra, coexisting with disordered MACl. We show that the transformation of precursor into perovskite is not favored in the presence of MACl, and thus the gradual evaporation of MACl acts as a self-regulating mechanism to slow the conversion. We propose the stable precursor phase enables dense film coverage and the slow transformation may lead to improved crystal quality. This enhanced chemical understanding is paramount for the rational control of film deposition and the fabrication of superior optoelectronic devices.

Efficient Perovskite Solar Cells Fabricated Through CsCl-Enhanced PbI2 Precursor via Sequential Deposition

The fabrication of high-quality perovskite film highly relies on chemical composition and the synthesis method of perovskite. So far, sequentially deposited MA0.03 FA0.97 Pb(I0.97 Br0.03 )3 polycrystalline film is adopted to produce high-performance perovskite solar cells with record power conversion efficiency (PCE). Fewer grain boundaries and incorporation of inorganic cation (e.g., cesium) would further increase device performance via sequential deposition. Here, cesium chloride (CsCl) is introduced into lead iodide (PbI2 ) precursor solution that beneficially modulates the property of PbI2 film, leading to larger grains with cesium incorporation in the resulting perovskite film. The enlarged crystal grains originate from a slower nucleation process for CsCl-containing PbI2 film when reacting with formamidine iodide, confirmed by in situ confocal photoluminescence imaging. Photovoltaic devices based on CsCl-containing PbI2 film demonstrate a higher averaging efficiency of 21.3% than 20.3% of the devices without CsCl additives for reverse scan. More importantly, the device stability is improved by CsCl additives that retain over 90% of their initial PCE value after 4000 min tracking at maximum power point under 1-sun illumination. This work paves a way to further improve the photovoltaic performance of mixed-cation-halide perovskite solar cells via a sequential deposition method.

Maximizing and stabilizing luminescence from halide perovskites with potassium passivation

Metal halide perovskites are of great interest for various high-performance optoelectronic applications. The ability to tune the perovskite bandgap continuously by modifying the chemical composition opens up applications for perovskites as coloured emitters, in building-integrated photovoltaics, and as components of tandem photovoltaics to increase the power conversion efficiency. Nevertheless, performance is limited by non-radiative losses, with luminescence yields in state-of-the-art perovskite solar cells still far from 100 per cent under standard solar illumination conditions. Furthermore, in mixed halide perovskite systems designed for continuous bandgap tunability (bandgaps of approximately 1.7 to 1.9 electronvolts), photoinduced ion segregation leads to bandgap instabilities. Here we demonstrate substantial mitigation of both non-radiative losses and photoinduced ion migration in perovskite films and interfaces by decorating the surfaces and grain boundaries with passivating potassium halide layers. We demonstrate external photoluminescence quantum yields of 66 per cent, which translate to internal yields that exceed 95 per cent. The high luminescence yields are achieved while maintaining high mobilities of more than 40 square centimetres per volt per second, providing the elusive combination of both high luminescence and excellent charge transport. When interfaced with electrodes in a solar cell device stack, the external luminescence yield-a quantity that must be maximized to obtain high efficiency-remains as high as 15 per cent, indicating very clean interfaces. We also demonstrate the inhibition of transient photoinduced ion-migration processes across a wide range of mixed halide perovskite bandgaps in materials that exhibit bandgap instabilities when unpassivated. We validate these results in fully operating solar cells. Our work represents an important advance in the construction of tunable metal halide perovskite films and interfaces that can approach the efficiency limits in tandem solar cells, coloured-light-emitting diodes and other optoelectronic applications.

Dipolar cations confer defect tolerance in wide-bandgap metal halide perovskites

Efficient wide-bandgap perovskite solar cells (PSCs) enable high-efficiency tandem photovoltaics when combined with crystalline silicon and other low-bandgap absorbers. However, wide-bandgap PSCs today exhibit performance far inferior to that of sub-1.6-eV bandgap PSCs due to their tendency to form a high density of deep traps. Here, we show that healing the deep traps in wide-bandgap perovskites-in effect, increasing the defect tolerance via cation engineering-enables further performance improvements in PSCs. We achieve a stabilized power conversion efficiency of 20.7% for 1.65-eV bandgap PSCs by incorporating dipolar cations, with a high open-circuit voltage of 1.22 V and a fill factor exceeding 80%. We also obtain a stabilized efficiency of 19.1% for 1.74-eV bandgap PSCs with a high open-circuit voltage of 1.25 V. From density functional theory calculations, we find that the presence and reorientation of the dipolar cation in mixed cation-halide perovskites heals the defects that introduce deep trap states.

Phonon Coupling with Excitons and Free Carriers in Formamidinium Lead Bromide Perovskite Nanocrystals

Organometal halide perovskites in the form of nanocrystals (NCs) have attracted enormous attention due to their unique optoelectronic and photoluminescence (PL) properties. Here, we examine the phase composition and the temperature dependence of emission line width broadening in formamidinium lead bromide (FAPbBr₃) perovskite nanocrystals (NCs) for light-emitting applications and identify different charge-carrier scattering mechanisms. Our results show most of the emission is from the orthorhombic phase. The PL line width broadening at high temperature is dominated by the Fröhlich interaction between the free charge carriers and the optical phonons. At low temperatures, the peak of the PL spectrum exhibits a continuous red shift indicating an increase of excitons contribution at lower temperatures, and concurrently the line width also narrows down due to the inhibition of the optical phonons. From the temperature-dependent measurements, the coupling strength of both the charge phonon interaction and the exciton phonon interaction have been determined. The obtained results indicate that the charge phonon coupling strengths are higher compared to the exciton phonon coupling.

Ion-Migration Inhibition by the Cation-π Interaction in Perovskite Materials for Efficient and Stable Perovskite Solar Cells

Migration of ions can lead to photoinduced phase separation, degradation, and current-voltage hysteresis in perovskite solar cells (PSCs), and has become a serious drawback for the organic-inorganic hybrid perovskite materials (OIPs). Here, the inhibition of ion migration is realized by the supramolecular cation-π interaction between aromatic rubrene and organic cations in OIPs. The energy of the cation-π interaction between rubrene and perovskite is found to be as strong as 1.5 eV, which is enough to immobilize the organic cations in OIPs; this will thus will lead to the obvious reduction of defects in perovskite films and outstanding stability in devices. By employing the cation-immobilized OIPs to fabricate perovskite solar cells (PSCs), a champion efficiency of 20.86% and certified efficiency of 20.80% with negligible hysteresis are acquired. In addition, the long-term stability of cation-immobilized PSCs is improved definitely (98% of the initial efficiency after 720 h operation), which is assigned to the inhibition of ionic diffusions in cation-immobilized OIPs. This cation-π interaction between cations and the supramolecular π system enhances the stability and the performance of PSCs efficiently and would be a potential universal approach to get the more stable perovskite devices.

Statistics of the Auger Recombination of Electrons and Holes via Defect Levels in the Band Gap-Application to Lead-Halide Perovskites

Recent evidence for bimolecular nonradiative recombination in lead-halide perovskites poses the question for a mechanistic origin of such a recombination term. A possible mechanism is Auger recombination involving two free charge carriers and a trapped charge-carrier. To study the influence of trap-assisted Auger recombination on bimolecular recombination in lead-halide perovskites, we combine estimates of the transition rates with a detailed balance compatible approach of calculating the occupation statistics of defect levels using a similar approach as for the well-known Shockley-Read-Hall recombination statistics. We find that the kinetics resulting from trap-assisted Auger recombination encompasses three different regimes: low injection, high injection, and saturation. Although the saturation regime with a recombination rate proportional to the square of free carrier concentration might explain the nonradiative bimolecular recombination in general, we show that the necessary trap density is higher than reported. Thus, we conclude that Auger recombination via traps is most likely not the explanation for the observed nonradiative bimolecular recombination in CH₃NH₃PbI₃ and related materials.

The Role of Metal Halide Perovskites in Next-Generation Lighting Devices

The development of smart illumination sources represents a central challenge for current technology. In this context, the quest for novel materials that enable efficient light generation is essential. Metal halide compounds with perovskite crystalline structure (ABX₃) have gained tremendous interest in the last five years since they come as easy-to-prepare high performance semiconductors. Perovskite absorbers are driving the power-conversion-efficiencies of thin film photovoltaics to unprecedented values. Nowadays, mixed-cation, mixed-halide lead perovskite solar cells reach efficiencies consistently over 20% and promise to get close to 30% in multijunction devices when combined with silicon cells at no surcharge. Nonetheless, perovskites' fame extends further since extensive research on these novel semiconductors has also revealed their brightest side. Soon after their irruption in the photovoltaic scenario, demonstration of efficient color tunable-with high color purity-perovskite emitters has opened new avenues for light generation applications that are timely to discuss herein.

Tunable Polaron Distortions Control the Extent of Halide Demixing in Lead Halide Perovskites

Photoinduced phase separation in mixed halide perovskites emerges from their electro-mechanical properties and high ionic conductivities, resulting in photoinduced I^--rich charge carrier traps that diminish photovoltaic performance. Whether photoinduced phase separation stems from the polycrystalline microstructure or is an intrinsic material property has been an open question. We investigate the nanoscale photoinduced behavior of single-crystal mixed Br^-/I^- methylammonium (MA⁺) lead halide perovskite (MAPb(Br _xI_{1- x})₃) nanoplates, eliminating effects from extended structural defects. Even in these nanoplates, we find that phase separation occurs, resulting in I^--rich clusters that are nucleated stochastically and stabilized by polarons. Upon lowering the electron-phonon coupling strength by partially exchanging MA⁺ for Cs⁺, a phase-separated steady state is not reached, nevertheless transient I^- clustering still occurs. Our results, supported by multiscale modeling, demonstrate that photoinduced phase separation is an intrinsic property of mixed halide perovskites, the extent and dynamics of which depends on the electron-phonon coupling strength.

Origin of Light-Induced Photophysical Effects in Organic Metal Halide Perovskites in the Presence of Oxygen

Herein we present a combined study of the evolution of both the photoluminescence (PL) and the surface chemical structure of organic metal halide perovskites as the environmental oxygen pressure rises from ultrahigh vacuum up to a few thousandths of an atmosphere. Analyzing the changes occurring at the semiconductor surface upon photoexcitation under a controlled oxygen atmosphere in an X-ray photoelectron spectroscopy (XPS) chamber, we can rationalize the rich variety of photophysical phenomena observed and provide a plausible explanation for light-induced ion migration, one of the most conspicuous and debated concomitant effects detected during photoexcitation. We find direct evidence of the formation of a superficial layer of negatively charged oxygen species capable of repelling the halide anions away from the surface and toward the bulk. The reported PL transient dynamics, the partial recovery of the initial state when photoexcitation stops, and the eventual degradation after intense exposure times can thus be rationalized.

Conjugated Polyelectrolytes as Efficient Hole Transport Layers in Perovskite Light-Emitting Diodes

Perovskite-based optoelectronic devices have been rapidly developing in the past 5 years. Since the first report, the external quantum efficiency (EQE) of perovskite light-emitting diodes (PeLEDs) has increased rapidly through the control of morphology and structure from 0.1% to more than 11%. Here, we report the use of various conjugated polyelectrolytes (CPEs) as the hole injection layer in PeLEDs. In particular, we find that poly[2,6-(4,4-bis-potassium butanylsulfonate)-4 H-cyclopenta-[2,1- b;3,4- b']-dithiophene)] (PCPDT-K) transfers holes effectively, blocks electron transport from the perovskite to the underlying ITO layer, and reduces luminescence quenching at the perovskite/PCPDT-K interface. Our optimized PeLEDs with PCPDT-K show enhanced EQE by a factor of approximately 4 compared to control PeLEDs with PEDOT:PSS, reaching EQE values of 5.66%, and exhibit improved device stability.

Cation-Dependent Light-Induced Halide Demixing in Hybrid Organic-Inorganic Perovskites

Mixed cation metal halide perovskites with increased power conversion efficiency, negligible hysteresis, and improved long-term stability under illumination, moisture, and thermal stressing have emerged as promising compounds for photovoltaic and optoelectronic applications. Here, we shed light on photoinduced halide demixing using in situ photoluminescence spectroscopy and in situ synchrotron X-ray diffraction (XRD) to directly compare the evolution of composition and phase changes in CH(NH₂)₂CsPb-halide (FACsPb-) and CH₃NH₃Pb-halide (MAPb-) perovskites upon illumination, thereby providing insights into why FACs-perovskites are less prone to halide demixing than MA-perovskites. We find that halide demixing occurs in both materials. However, the I-rich domains formed during demixing accumulate strain in FACsPb-perovskites but readily relax in MA-perovskites. The accumulated strain energy is expected to act as a stabilizing force against halide demixing and may explain the higher Br composition threshold for demixing to occur in FACsPb-halides. In addition, we find that while halide demixing leads to a quenching of the high-energy photoluminescence emission from MA-perovskites, the emission is enhanced from FACs-perovskites. This behavior points to a reduction of nonradiative recombination centers in FACs-perovskites arising from the demixing process and buildup of strain. FACsPb-halide perovskites exhibit excellent intrinsic material properties with photoluminescence quantum yields that are comparable to MA-perovskites. Because improved stability is achieved without sacrificing electronic properties, these compositions are better candidates for photovoltaic applications, especially as wide bandgap absorbers in tandem cells.

Perovskite Solar Cells with Inorganic Electron- and Hole-Transport Layers Exhibiting Long-Term (≈500 h) Stability at 85 °C under Continuous 1 Sun Illumination in Ambient Air

Despite the high power conversion efficiency (PCE) of perovskite solar cells (PSCs), poor long-term stability is one of the main obstacles preventing their commercialization. Several approaches to enhance the stability of PSCs have been proposed. However, an accelerating stability test of PSCs at high temperature under the operating conditions in ambient air remains still to be demonstrated. Herein, interface-engineered stable PSCs with inorganic charge-transport layers are shown. The highly conductive Al-doped ZnO films act as efficient electron-transporting layers as well as dense passivation layers. This layer prevents underneath perovskite from moisture contact, evaporation of components, and reaction with a metal electrode. Finally, inverted-type PSCs with inorganic charge-transport layers exhibit a PCE of 18.45% and retain 86.7% of the initial efficiency for 500 h under continuous 1 Sun illumination at 85 °C in ambient air with electrical biases (at maximum power point tracking).

Photochemical Control of Exciton Superradiance in Light-Harvesting Nanotubes

Photosynthetic antennae and organic electronic materials use topological, structural, and molecular control of delocalized excitons to enhance and direct energy transfer. Interactions between the transition dipoles of individual chromophore units allow for coherent delocalization across multiple molecular sites. This delocalization, for specific geometries, greatly enhances the transition dipole moment of the lowest energy excitonic state relative to the chromophore and increases its radiative rate, a phenomenon known as superradiance. In this study, we show that ordered, self-assembled light-harvesting nanotubes (LHNs) display excitation-induced photobrightening and photodarkening. These changes in quantum yield arise due to changes in energetic disorder, which in turn increases/decreases excitonic superradiance. Through a combination of experiment and modeling, we show that intense illumination induces different types of chemical change in LHNs that reproducibly alter absorption and fluorescence properties, indicating control over excitonic delocalization. We also show that changes in spectral width and shift can be sensitive measures of system dimensionality, illustrating the mixed 1-2D nature of LHN excitons. Our results demonstrate a path forward for mastery of energetic disorder in an excitonic antenna, with implications for fundamental studies of coherent energy transport.

Large tunable photoeffect on ion conduction in halide perovskites and implications for photodecomposition

In the same way as electron transport is crucial for information technology, ion transport is a key phenomenon in the context of energy research. To be able to tune ion conduction by light would open up opportunities for a wide realm of new applications, but it has been challenging to provide clear evidence for such an effect. Here we show through various techniques, such as transference-number measurements, permeation studies, stoichiometric variations, Hall effect experiments and the use of blocking electrodes, that light excitation enhances by several orders of magnitude the ionic conductivity of methylammonium lead iodide, the archetypal metal halide photovoltaic material. We provide a rationale for this unexpected phenomenon and show that it straightforwardly leads to a hitherto unconsidered photodecomposition path of the perovskite.

The Role of Excitation Energy in Photobrightening and Photodegradation of Halide Perovskite Thin Films

We study the impact of excitation energy on the photostability of methylammonium lead triiodide (CH₃NH₃PbI₃ or MAPI) perovskite thin films. Light soaking leads to a transient increase of the photoluminescence efficiency at excitation wavelengths longer than 520 nm, whereas light-induced degradation occurs when exciting the films with wavelengths shorter than 520 nm. X-ray diffraction and extinction measurements reveal the light-induced decomposition of CH₃NH₃PbI₃ to lead iodide (PbI₂) for the high-energy excitation regime. We propose a model explaining the energy dependence of the photostability that involves the photoexcitation of residual PbI₂ species in the perovskite triggering the decomposition of CH₃NH₃PbI₃.

Revealing the Self-Degradation Mechanisms in Methylammonium Lead Iodide Perovskites in Dark and Vacuum

Organic-inorganic lead halide perovskite phases segregate (and their structures degrade) under illumination, exhibiting a poor stability with hysteresis and producing halide accumulation at the surface.In this work, we observed structural and interfacial dissociation in methylammonium lead iodide (CH₃ NH₃ PbI₃ ) perovskites even under dark and vacuum conditions. Here, we investigate the origin and consequences of self-degradation in CH₃ NH₃ PbI₃ perovskites stored in the dark under vacuum. Diffraction and photoelectron spectroscopic studies reveal the structural dissociation of perovskites into PbI₂ , which further dissociates into metallic lead (Pb⁰ ) and I₂^- ions, collectively degrading the perovskite stability. Using TOF-SIMS analysis, AuI₂^- formation was directly observed, and it was found that an interplay between CH₃ NH₃⁺ , I₃^- , and mobile I^- ions continuously regenerates more I₂^- ions, which diffuse to the surface even in the absence of light. Besides, halide diffusion causes a concentration gradient between Pb⁰ and I₂^- and creates other ionic traps (PbI₂^- , PbI^- ) that segregate as clusters at the perovskite/gold interface. A shift of the onset of the absorption band edge towards shorter wavelengths was also observed by absorption spectroscopy, indicating the formation of defect species upon aging in the dark under vacuum.

Light-induced lattice expansion leads to high-efficiency perovskite solar cells

Light-induced structural dynamics plays a vital role in the physical properties, device performance, and stability of hybrid perovskite-based optoelectronic devices. We report that continuous light illumination leads to a uniform lattice expansion in hybrid perovskite thin films, which is critical for obtaining high-efficiency photovoltaic devices. Correlated, in situ structural and device characterizations reveal that light-induced lattice expansion benefits the performances of a mixed-cation pure-halide planar device, boosting the power conversion efficiency from 18.5 to 20.5%. The lattice expansion leads to the relaxation of local lattice strain, which lowers the energetic barriers at the perovskite-contact interfaces, thus improving the open circuit voltage and fill factor. The light-induced lattice expansion did not compromise the stability of these high-efficiency photovoltaic devices under continuous operation at full-spectrum 1-sun (100 milliwatts per square centimeter) illumination for more than 1500 hours.

The Impact of Atmosphere on the Local Luminescence Properties of Metal Halide Perovskite Grains

Metal halide perovskites are exceptional candidates for inexpensive yet high-performing optoelectronic devices. Nevertheless, polycrystalline perovskite films are still limited by nonradiative losses due to charge carrier trap states that can be affected by illumination. Here, in situ microphotoluminescence measurements are used to elucidate the impact of light-soaking individual methylammonium lead iodide grains in high-quality polycrystalline films while immersing them with different atmospheric environments. It is shown that emission from each grain depends sensitively on both the environment and the nature of the specific grain, i.e., whether it shows good (bright grain) or poor (dark grain) luminescence properties. It is found that the dark grains show substantial rises in emission, while the bright grain emission is steady when illuminated in the presence of oxygen and/or water molecules. The results are explained using density functional theory calculations, which reveal strong adsorption energies of the molecules to the perovskite surfaces. It is also found that oxygen molecules bind particularly strongly to surface iodide vacancies which, in the presence of photoexcited electrons, lead to efficient passivation of the carrier trap states that arise from these vacancies. The work reveals a unique insight into the nature of nonradiative decay and the impact of atmospheric passivation on the microscale properties of perovskite films.

Local Observation of Phase Segregation in Mixed-Halide Perovskite

Mixed-halide perovskites have emerged as promising materials for optoelectronics due to their tunable band gap in the entire visible region. A challenge remains, however, in the photoinduced phase segregation, narrowing the band gap of mixed-halide perovskites under illumination thus restricting applications. Here, we use a combination of spatially resolved and bulk measurements to give an in-depth insight into this important yet unclear phenomenon. We demonstrate that photoinduced phase segregation in mixed-halide perovskites selectively occurs at the grain boundaries rather than within the grain centers by using shear-force scanning probe microscopy in combination with confocal optical spectroscopy. Such difference is further evidenced by light-biased bulk Fourier-transform photocurrent spectroscopy, which shows the iodine-rich domain as a minority phase coexisting with the homogeneously mixed phase during illumination. By mapping the surface potential of mixed-halide perovskites, we evidence the higher concentration of positive space charge near the grain boundary possibly provides the initial driving force for phase segregation, while entropic mixing dominates the reverse process. Our work offers detailed insight into the microscopic processes occurring at the boundary of crystalline perovskite grains and will support the development of better passivation strategies, ultimately allowing the processing of more environmentally stable perovskite films.

Imaging Heterogeneously Distributed Photo-Active Traps in Perovskite Single Crystals

Organic-inorganic halide perovskites (OIHPs) have demonstrated outstanding energy conversion efficiency in solar cells and light-emitting devices. In spite of intensive developments in both materials and devices, electronic traps and defects that significantly affect their device properties remain under-investigated. Particularly, it remains challenging to identify and to resolve traps individually at the nanoscopic scale. Here, photo-active traps (PATs) are mapped over OIHP nanocrystal morphology of different crystallinity by means of correlative optical differential super-resolution localization microscopy (Δ-SRLM) and electron microscopy. Stochastic and monolithic photoluminescence intermittency due to individual PATs is observed on monocrystalline and polycrystalline OIHP nanocrystals. Δ-SRLM reveals a heterogeneous PAT distribution across nanocrystals and determines the PAT density to be 1.3 × 10¹⁴ and 8 × 10¹³ cm^-3 for polycrystalline and for monocrystalline nanocrystals, respectively. The higher PAT density in polycrystalline nanocrystals is likely related to an increased defect density. Moreover, monocrystalline nanocrystals that are prepared in an oxygen- and moisture-free environment show a similar PAT density as that prepared at ambient conditions, excluding oxygen or moisture as chief causes of PATs. Hence, it is concluded that the PATs come from inherent structural defects in the material, which suggests that the PAT density can be reduced by improving crystalline quality of the material.

Self-Healing Inside APbBr3 Halide Perovskite Crystals

Self-healing, where a modification in some parameter is reversed with time without any external intervention, is one of the particularly interesting properties of halide perovskites. While there are a number of studies showing such self-healing in perovskites, they all are carried out on thin films, where the interface between the perovskite and another phase (including the ambient) is often a dominating and interfering factor in the process. Here, self-healing in perovskite (methylammonium, formamidinium, and cesium lead bromide (MAPbBr₃ , FAPbBr₃ , and CsPbBr₃ )) single crystals is reported, using two-photon microscopy to create damage (photobleaching) ≈110 µm inside the crystals and to monitor the recovery of photoluminescence after the damage. Self-healing occurs in all three perovskites with FAPbBr₃ the fastest (≈1 h) and CsPbBr₃ the slowest (tens of hours) to recover. This behavior, different from surface-dominated stability trends, is typical of the bulk and is strongly dependent on the localization of degradation products not far from the site of the damage. The mechanism of self-healing is discussed with the possible participation of polybromide species. It provides a closed chemical cycle and does not necessarily involve defect or ion migration phenomena that are often proposed to explain reversible phenomena in halide perovskites.

Impact of Small Phonon Energies on the Charge-Carrier Lifetimes in Metal-Halide Perovskites

Metal-halide perovskite (MHP) solar cells exhibit long nonradiative lifetimes as a crucial feature enabling high efficiencies. Long nonradiative lifetimes occur if the transfer of electronic into vibrational energy is slow due to, e.g., a low trap density, weak electron-phonon coupling, or the requirement to release many phonons in the electronic transition. Here, we combine known material properties of MHPs with basic models for electron-phonon coupling and multiphonon-transition rates in polar semiconductors. We find that the low phonon energies of MAPbI₃ lead to a strong dependence of recombination rates on trap position, which we deduce from the underlying physical effects determining nonradiative transitions. This is important for nonradiative recombination in MHPs, as it implies that they are rather insensitive to defects that are not at midgap energy, which can lead to long lifetimes. Therefore, the low phonon energies of MHPs are likely an important factor for their optoelectronic performance.

Optogenetics-Inspired Tunable Synaptic Functions in Memristors

Two-terminal memristors with internal Ca²⁺-like dynamics can be used to faithfully emulate biological synaptic functions and have been intensively studied for neural network implementations. Inspired by the optogenetic technique that utilizes light to tune the Ca²⁺ dynamics and subsequently the synaptic plasticity, we develop a CH₃NH₃PbI₃ (MAPbI₃)-based memristor that exhibits light-tunable synaptic behaviors. Specifically, we show that by increasing the formation energy of iodine vacancy (V_I^·/V_I^×), light illumination can be used to control the V_I^·/V_I^× generation and annihilation dynamics, resembling light-controlled Ca²⁺ influx in biological synapses. We demonstrate that the memory formation and memory loss behaviors in the memristors can be modified by controlling the intensity and the wavelength of the illuminated light. Coincidence detection of electrical and light stimulations is also implemented in the memristive device with real-time (≤20 ms) response to light illumination. These results open options to modify the synaptic plasticity effects in memristor-based neuromorphic systems and can lead to the development of electronic systems that can faithfully emulate diverse biological processes.

In Situ Observation of Light Illumination-Induced Degradation in Organometal Mixed-Halide Perovskite Films

Organometal mixed-halide perovskite materials hold great promise for next-generation solar cells, light-emitting diodes, lasers, and photodetectors. Except for the rapid progress in the efficiency of perovskite-based devices, the stability issue over prolonged light illumination has severely hindered their practical application. The deterioration mechanism of organometal halide perovskite materials under light illumination has seldom been conducted to date, which is indispensable to the understanding and optimization of photon-harvesting process inside perovskite-based optoelectronic devices. Here, explicit degradation pathways and comprehensive microscopic understandings of white-light-induced degradation have been put forward for two organometal mixed-halide perovskite materials (e.g., MAPbI_3-xCl_x and MAPbBr_3-xCl_x) under high vacuum conditions. In situ compositional analysis and real-time film characterizations reveal that the decomposition of both mixed-halide perovskites starts at the grain boundaries, leading to the formation of hydrocarbons and ammonia gas with the residuals of PbI₂(Cl), Pb, or PbCl_xBr_2-x in the films. The degradation has been correlated to the localized trap states that induce strong coupling between photoexcited carriers and the crystal lattice.

Hysteresis phenomena in perovskite solar cells: the many and varied effects of ionic accumulation

The issue of hysteresis in perovskite solar cells has now been convincingly linked to the presence of mobile ions within the perovskite layer. Here we test the limits of the ionic theory by attempting to account for a number of exotic characterization results using a detailed numerical device model that incorporates ionic charge accumulation at the perovskite interfaces. Our experimental observations include a temporary enhancement in open-circuit voltage following prolonged periods of negative bias, dramatically S-shaped current-voltage sweeps, decreased current extraction following positive biasing or "inverted hysteresis", and non-monotonic transient behaviours in the dark and the light. Each one of these phenomena can be reproduced and ultimately explained by our models, providing further evidence for the ionic theory of hysteresis as well as valuable physical insight into the factors that coincide to bring these phenomena about. In particular we find that both interfacial recombination and carrier injection from the selective contacts are heavily affected by ionic accumulation, and are essential to explaining the non-monotonic voltage transients and S-shaped J-V curves. Inverted hysteresis is attributed to the occurrence of "positive" ionic accumulation, which may also be responsible for enhancing the stabilized open-circuit voltage in some perovskite cells.

Ionic-Electronic Ambipolar Transport in Metal Halide Perovskites: Can Electronic Conductivity Limit Ionic Diffusion?

Ambipolar transport describes the nonequilibrium, coupled motion of positively and negatively charged particles to ensure that internal electric fields remain small. It is commonly invoked in the semiconductor community where the motion of excess electrons and holes drift and diffuse together. However, the concept of ambipolar transport is not limited to semiconductor physics. Materials scientists working on ion conducting ceramics understand ambipolar transport dictates the coupled diffusion of ions and the rate is limited by the ion with the lowest diffusion coefficient. In this Perspective, we review a third application of ambipolar transport relevant to mixed ionic-electronic conducting materials for which the motion of ions is expected to be coupled to electronic carriers. In this unique situation, the ambipolar diffusion model has been successful at explaining the photoenhanced diffusion of metal ions in chalcogenide glasses and other properties of materials. Recent examples of photoenhanced phenomena in metal halide perovskites are discussed and indicate that mixed ionic-electronic ambipolar transport is similarly important for a deep understanding of these emerging materials.

In situ and real-time ToF-SIMS analysis of light-induced chemical changes in perovskite CH3NH3PbI3

A hybrid light/ToF-SIMS system was used to analyze the dynamic chemical changes of perovskite CH₃NH₃PbI₃ materials under light illumination.

Effect of Low Temperature on Charge Transport in Operational Planar and Mesoporous Perovskite Solar Cells

Low-temperature optoelectrical studies of perovskite solar cells using MAPbI₃ and mixed-perovskite absorbers implemented into planar and mesoporous architectures reveal fundamental charge transporting properties in fully assembled devices operating under light bias. Both types of devices exhibit inverse correlation of charge carrier lifetime as a function of temperature, extending carrier lifetimes upon temperature reduction, especially after exposure to high optical biases. Contribution of bimolecular channels to the overall recombination process should not be overlooked because the density of generated charge surpasses trap-filling concentration requirements. Bimolecular charge recombination coefficient in both device types is smaller than Langevin theory prediction, and its mean value is independent of the applied illumination intensity. In planar devices, charge extraction declines upon MAPbI₃ transition from a tetragonal to an orthorhombic phase, indicating a connection between the trapping/detrapping mechanism and temperature. Studies on charge extraction by linearly increasing voltage further support this assertion, as charge carrier mobility dependence on temperature follows multiple-trapping predictions for both device structures. The monotonously increasing trend following the rise in temperature opposes the behavior observed in neat perovskite films and indicates the importance of transporting layers and the effect they have on charge transport in fully assembled solar cells. Low-temperature phase transition shows no pattern of influence on thermally activated electron/hole transport.

Zero-dimensional methylammonium iodo bismuthate solar cells and synergistic interactions with silicon nanocrystals

Organometal trihalide perovskite solar cells have attracted monumental attention in recent years. Today's best devices, based on a three-dimensional perovskite structure of corner-sharing PbI₆ octahedra, are unstable, toxic, and display hysteresis in current-voltage measurements. We present zero-dimensional organic-inorganic hybrid solar cells based on methylammonium iodo bismuthate (CH₃NH₃)₃(Bi₂I₉) (MABI) comprising a Bi₂I₉ bioctahedra and observe very low hysteresis for scan rates in the broad range of 150 mV s^-1 to 1500 mV s^-1 without any interfacial layer engineering. We confirm good stability for devices produced and stored in open air without humidity control. The MABI structure can also accommodate silicon nanocrystals, leading to an enhancement in the short-circuit current. Through the material MABI, we demonstrate a promising alternative to the organometal trihalide perovskite class and present a model material for future composite third-generation photovoltaics.

Impact of Chemical Doping on Optical Responses in Bismuth-Doped CH3NH3PbBr3 Single Crystals: Carrier Lifetime and Photon Recycling

We studied the optical responses of organic-inorganic halide perovskite CH₃NH₃PbBr₃ single crystals doped with heterovalent Bi³⁺ ions (electron densities up to 2.3 × 10¹² cm^-3). The Bi doping causes no significant changes in the band gap energy but leads to an enhanced Urbach tail and photoluminescence blue shift. On the basis of the time-resolved photoluminescence measurements, we attribute the PL response to a shorter carrier lifetime induced by Bi doping, which results in a reduced photon recycling effect (i.e., the repeated emission and reabsorption of photons inside the crystal). We discuss the physical relation between Bi concentration and the optical and electric properties of Bi-doped CH₃NH₃PbBr₃ and reveal the unique nature of the Bi³⁺ ion as a dopant in halide perovskites.

Tracking Photoexcited Carriers in Hybrid Perovskite Semiconductors: Trap-Dominated Spatial Heterogeneity and Diffusion

We use correlated confocal and wide-field fluorescence microscopy to probe the interplay between local variations in charge carrier recombination and charge carrier transport in methylammonium lead triiodide perovskite thin films. We find that local photoluminescence variations present in confocal imaging are also observed in wide-field imaging, while intensity-dependent confocal measurements show that the heterogeneity in nonradiative losses observed at low excitation powers becomes less pronounced at higher excitation powers. Both confocal and wide-field images show that carriers undergo anisotropic diffusion due to differences in intergrain connectivity. These data are all qualitatively consistent with trap-dominated variations in local photoluminescence intensity and with grain boundaries that exhibit varying degrees of opacity to carrier transport. We use a two-dimensional kinetic model to simulate and compare confocal time-resolved photoluminescence decay traces with experimental data. The simulations further support the assignment of local variations in nonradiative recombination as the primary cause of photoluminescence heterogeneity in the films studied herein. These results point to surface passivation and intergrain connectivity as areas that could yield improvements in perovskite solar cells and optoelectronic device performance.

Enhancing Optoelectronic Properties of Low-Dimensional Halide Perovskite via Ultrasonic-Assisted Template Refinement

Low-dimensional halide perovskite (HP) has triggered lots of research attention in recent years due to anisotropic optoelectronic/semiconducting properties and enhanced stability. High-quality low-dimensional HPs via controllable engineering are required to fulfill the encouraging promise for device applications. Here, we introduce, for the first time, postsynthetic ultrasonic-assisted refinement of two-dimensional homologous HPs (OA₂PbBr₄, OA is octadecylamine). The solution-prepared OA₂PbBr₄, either in the form of large-sized microcrystal or nanosheet, obtains significantly enhanced crystallinity after ultrasonic treatment. We further show that OA₂PbBr₄ nanosheets can be used as a template to construct low-dimensional CsPbBr₃ with the size and morphology inherited. Importantly, we found the ultrasonic-treated OA₂PbBr₄ crystals, compared with pristine ones, lead to enhanced optoelectronic properties for the resultant low-dimensional CsPbBr₃, as demonstrated by improved photodetection performances, including prolonged charge-carrier lifetime, improved photostability, increased external quantum yield/responsivity, and faster response speed. We believe this work provides novel engineering of low-dimensional HPs beyond the reach of straightforward synthesis.

Mixed-Halide Perovskites with Stabilized Bandgaps

One merit of organic-inorganic hybrid perovskites is their tunable bandgap by adjusting the halide stoichiometry, an aspect critical to their application in tandem solar cells, wavelength-tunable light emitting diodes (LEDs), and lasers. However, the phase separation of mixed-halide perovskites caused by light or applied bias results in undesirable recombination at iodide-rich domains, meaning open-circuit voltage (V_OC) pinning in solar cells and infrared emission in LEDs. Here, we report an approach to suppress halide redistribution by self-assembled long-chain organic ammonium capping layers at nanometer-sized grain surfaces. Using the stable mixed-halide perovskite films, we are able to fabricate efficient and wavelength-tunable perovskite LEDs from infrared to green with high external quantum efficiencies of up to 5%, as well as linearly tuned V_OC from 1.05 to 1.45 V in solar cells.

Kinetic Isotope Effects Provide Experimental Evidence for Proton Tunneling in Methylammonium Lead Triiodide Perovskites

The occurrence of proton tunneling in MAPbI₃ hybrid organic inorganic perovskites is demonstrated through the effect of isotopic labeling of the methylammonium (MA) component on the dielectric permittivity response. Deuteration of the ammonium group results in the acceleration of proton migration (inverse primary isotope effect), whereas deuteration of the methyl group induces a normal secondary isotope effect. The activation energies for proton migration are calculated to be 50 and 27 meV for the tetragonal and orthorhombic phases, respectively, which decrease upon deuteration of the ammonium group. The low activation barrier and the deviation from unity of the ratio of the pre-exponential factors (A_H/A_D = 0.3-0.4) are consistent with a tunneling mechanism for proton migration. Deuteration of the PEDOT:PSS hole transport layer results in a behavior that is intermediate between that of the deuterated and undeuterated perovskite, due to extrinsic ion migration between the two materials.

Real-Time Observation of Iodide Ion Migration in Methylammonium Lead Halide Perovskites

Organic-inorganic metal halide perovskites (e.g., CH₃ NH₃ PbI_3-x Cl_x ) emerge as a promising optoelectronic material. However, the Shockley-Queisser limit for the power conversion efficiency (PCE) of perovskite-based photovoltaic devices is still not reached. Nonradiative recombination pathways may play a significant role and appear as photoluminescence (PL) inactive (or dark) areas on perovskite films. Although these observations are related to the presence of ions/defects, the underlying fundamental physics and detailed microscopic processes, concerning trap/defect status, ion migration, etc., still remain poorly understood. Here correlated wide-field PL microscopy and impedance spectroscopy are utilized on perovskite films to in situ investigate both the spatial and the temporal evolution of these PL inactive areas under external electric fields. The formation of PL inactive domains is attributed to the migration and accumulation of iodide ions under external fields. Hence, we are able to characterize the kinetic processes and determine the drift velocities of these ions. In addition, it is shown that I₂ vapor directly affects the PL quenching of a perovskite film, which provides evidence that the migration/segregation of iodide ions plays an important role in the PL quenching and consequently limits the PCE of organometal halide-based perovskite photovoltaic devices.

Direct Observation of Halide Migration and its Effect on the Photoluminescence of Methylammonium Lead Bromide Perovskite Single Crystals

Optoelectronic devices based on hybrid perovskites have demonstrated outstanding performance within a few years of intense study. However, commercialization of these devices requires barriers to their development to be overcome, such as their chemical instability under operating conditions. To investigate this instability and its consequences, the electric field applied to single crystals of methylammonium lead bromide (CH₃ NH₃ PbBr₃ ) is varied, and changes are mapped in both their elemental composition and photoluminescence. Synchrotron-based nanoprobe X-ray fluorescence (nano-XRF) with 250 nm resolution reveals quasi-reversible field-assisted halide migration, with corresponding changes in photoluminescence. It is observed that higher local bromide concentration is correlated to superior optoelectronic performance in CH₃ NH₃ PbBr₃ . A lower limit on the electromigration rate is calculated from these experiments and the motion is interpreted as vacancy-mediated migration based on nudged elastic band density functional theory (DFT) simulations. The XRF mapping data provide direct evidence of field-assisted ionic migration in a model hybrid-perovskite thin single crystal, while the link with photoluminescence proves that the halide stoichiometry plays a key role in the optoelectronic properties of the perovskite.

Bright-Emitting Perovskite Films by Large-Scale Synthesis and Photoinduced Solid-State Transformation of CsPbBr3 Nanoplatelets

Lead halide perovskite nanocrystals are an emerging class of materials that have gained wide interest due to their facile color tuning and high photoluminescence quantum yield. However, the lack of techniques to translate the high performance of nanocrystals into solid films restricts the successful exploitation of such materials in optoelectronics applications. Here, we report a heat-up and large-scale synthesis of quantum-confined, blue-emitting CsPbBr₃ nanoplatelets (NPLs) that self-assemble into stacked lamellar structures. Spin-coated films fabricated from these NPLs show a stable blue emission with a photoluminescence quantum yield (PLQY) of 25%. The morphology and the optoelectronic properties of such films can be dramatically modified by UV-light irradiation under ambient conditions at a high power, which transforms the self-assembled stacks of NPLs into much larger structures, such as square-shaped disks and nanobelts. The emission from the transformed thin films falls within the green spectral region with a record PLQY of 65%, and they manifest an amplified spontaneous emission with a sharp line width of 4 nm at full-width at half-maximum under femtosecond-pulsed excitation. The transformed films show stable photocurrents with a responsivity of up to 15 mA/W and response times of tens of milliseconds and are robust under treatment with different solvents. We exploit their insolubility in ethanol to fabricate green-emitting, all-solution-processed light-emitting diodes with an external quantum efficiency of 1.1% and a luminance of 590 Cd/m².

Structural and Photophysical Properties of Methylammonium Lead Tribromide (MAPbBr3) Single Crystals

The structural and photophysical characteristics of MAPbBr₃ single crystals prepared using the inverse temperature crystallization method are evaluated using temperature-dependent X-ray diffraction (XRD) and optical spectroscopy. Contrary to previous research reports on perovskite materials, we study phase transitions in crystal lattice structures accompanied with changes in optical properties expand throughout a wide temperature range of 300–1.5 K. The XRD studies reveal several phase transitions occurred at ~210 K, ~145 K, and ~80 K, respectively. The coexistence of two different crystallographic phases was observed at a temperature below 145 K. The emission peaks in the PL spectra are all asymmetric in line shape with weak and broad shoulders near the absorption edges, which are attributed to the Br atom vacancy on the surface of the crystals. The time-resolved PL measurements reveal the effect of the desorption/adsorption of gas molecules on the crystal surface on the PL lifetimes. Raman spectroscopy results indicate the strong interplays between cations and different halide atoms. Lastly, no diamagnetic shift or split in emission peaks can be observed in the magneto-PL spectra even at an applied magnetic field up to 5 T and at a temperature as low as 1.5 K.

Pinning Down the Anomalous Light Soaking Effect toward High-Performance and Fast-Response Perovskite Solar Cells: The Ion-Migration-Induced Charge Accumulation

The light soaking effect (LSE) is widely known in perovskite solar cells (PVSCs), but its origin is still elusive. In this study, we show that in common with hysteresis, the LSE is owed to the ion migration in PVSCs. Driven by the photovoltage, the mobile ions in the perovskite materials (MA⁺/I^-) migrate to the selective contacts, forming a boosted P-i-N junction resulting in enhanced charge separation. Besides, the mobile ions (MA⁺) can soften and suture the PCBM/perovskite interface and thus reduce the trap density, in keeping with a higher open-circuit voltage. Finally, almost LSE-free PVSCs can be prepared by using 0.1 wt % MAI-doped PCBM as the electron transport material, whereas overdoping (1 wt % MAI doping) makes the LSE even more pronounced due to excess mobile ions that need time to migrate to reach a new quasi-static state.