Memristive arrangements of nanofluidic pores.

We demonstrate that nanofluidic diodes in multipore membranes show a memristive behavior that can be controlled not only by the amplitude and frequency of the external signal but also by series and parallel arrangements of the membranes. Each memristor consists of a polymeric membrane with conical nanopores that allow current rectification due to the electrical interaction between the ionic solution and the pore surface charges. This surface charge-regulated ionic transport shows a rich nonlinear physics, including memory and inductive effects, which are characterized here by the current-voltage curves and electrical impedance spectroscopy. Also, neuromorphiclike potentiation of the membrane conductance following voltage pulses (spikes) is observed. The multipore membrane with nanofluidic diodes shows physical concepts that should have application for information processing and signal conversion in iontronics hybrid devices.

Hysteresis in memristors produces conduction inductance and conduction capacitance effects.

Memristors are devices in which the conductance state can be alternately switched between a high and a low value by means of a voltage scan. In general, systems involving a chemical inductor mechanism as solar cells, asymmetric nanopores in electrochemical cells, transistors, and solid state memristive devices, exhibit a current increase and decrease over time that generates hysteresis. By performing small signal ac impedance spectroscopy, we show that memristors, or any other system with hysteresis relying on the conductance modulation effect, display intrinsic dynamic inductor-like and capacitance-like behaviours in specific input voltage ranges. Both the conduction inductance and the conduction capacitance originate in the same delayed conduction process linked to the memristor dynamics and not in electromagnetic or polarization effects. A simple memristor model reproduces the main features of the transition from capacitive to inductive impedance spectroscopy spectra, which causes a nonzero crossing of current-voltage curves.

Accelerating the Assessment of Hysteresis in Perovskite Solar Cells.

Halide perovskite materials have reached important milestones in the photovoltaic field, positioning them as realistic alternatives to conventional solar cells. However, unavoidable kinetic phenomena have represented a major concern for reliable steady-state performance assessment from standard current-voltage measurements. In particular, the dynamic hysteresis of current-voltage curves requires relatively long stabilization to achieve a credible figure for the power conversion efficiency. Hysteresis is caused by complex current transient phenomena that become active during staircase voltammetry. Here, we address the root of this problem. We pinpoint the dynamic characteristics behind the slow transient responses to strategically predict a minimum time delay and thus estimate the power conversion efficiency under steady-state conditions. Circuit-element analysis and impedance spectroscopy confirm our predictions based on an advanced transient study. Our results fundamentally explore the possibility of reducing data time acquisition in a reliable performance assessment, providing disruptive solutions and perspectives toward systematic production of photovoltaic perovskites.

Hysteresis in Organic Electrochemical Transistors: Distinction of Capacitive and Inductive Effects.

Organic electrochemical transistors (OECTs) are effective devices for neuromorphic applications, bioelectronics, and sensors. Numerous reports in the literature show persistent dynamical hysteresis effects in the current-voltage curves, attributed to the slow ionic charging of the channel under the applied gate voltage. Here we present a model that considers the dominant electrical and electrochemical operation aspects of the device based on a thermodynamic function of ion insertion. We identify the volume capacitance as the derivative of the thermodynamic function, associated with the chemical capacitance of the ionic-electronic film. The dynamical analysis shows that the system contains both capacitive and inductive hysteresis effects. The inductor response, which can be observed in impedance spectroscopy, is associated with ionic diffusion from the surface to fill the channel up to the equilibrium value. The model reveals the multiple dynamical features associated with specific kinetic relaxations that control the transient and impedance response of the OCET.

Enhanced LED Performance by Ion Migration in Multiple Quantum Well Perovskite.

Here we study the effect of ion migration on the performance of perovskite light emitting diodes (PeLEDs). We compared aromatic and linear barrier molecules in Ruddlesden-Popper and Dion-Jacobson two-dimensional perovskites having multiple quantum well (MQW) structures. PeLED devices were fabricated by using the same conditions and architecture, while their electroluminescence properties and ion migration behavior were investigated. Impedance spectroscopy measurements were used to analyze the PeLEDs, which found a direct link between the barrier molecule type, the device efficiency, and ion migration. The best performing LEDs were based on the aromatic barriers, which present dominant inductive impedance, indicating an earlier onset voltage of radiative recombination. These findings present an approach of how to control radiative emission in perovskite LEDs which opens the way for further improvement in PeLEDs and memristors.

Synaptical Tunability of Multipore Nanofluidic Memristors.

We demonstrate a multipore nanofluidic memristor with conical pores showcasing a wide range of hysteresis and memristor properties that provide functionalities for brainlike computation in neuromorphic applications. Leveraging the interplay between the charged functional groups on the pore surfaces and the confined ionic solution, the memristor characteristics are modulated through the electrolyte type, ionic concentrations, and pH levels of the aqueous solution. The multipore membrane mimics the functional characteristics of biological ion channels and displays synaptical potentiation and depression. Furthermore, this property can be inverted in polarity by chemically varying the pH level. The ability to modulate memory effects by ionic conductivity holds promise for enhancing signal information processing capabilities.

Iontronic Nanopore Model for Artificial Neurons: The Requisites of Spiking.

Brain-inspired neuromorphic computing is currently being investigated for effective artificial intelligence (AI) systems. The development of artificial neurons and synapses is imperative to creating efficient computational biomimetic networks. Here we propose the minimal configuration of an effective iontronic spiking neuron based on a conical nanofluidic pore ionic diode. The conductance is composed of a Boltzmann open channel probability and a blocking inactivation function, forming the structure of a memristor. The presence of a negative resistance and the combination of activation-deactivation dynamics cause a Hopf bifurcation. Using the characteristic frequencies of small perturbation impedance spectroscopy, we discuss the conditions of spiking, in which the system enters a limit cycle oscillation. We arrive at the conclusion that an excitable neuron-like system can be made with a single active channel instead of the more complex combination of multiple channels that occurs in the Hodgkin-Huxley neuron model.

Electrical Charge Coupling Dominates the Hysteresis Effect of Halide Perovskite Devices.

Hysteresis effects in ionic-electronic devices are a valuable resource for the development of switching memory devices that can be used in information storage and brain-like computation. Halide perovskite devices show frequent hysteresis in current-voltage curves that can be harnessed to build effective memristors. These phenomena can be often described by a set of highly nonlinear differential equations that involve current, voltage, and internal state variables, in the style of the famous Hodgkin-Huxley model that accounts for the initiation and temporal response of action potentials in biological neurons. Here we extend the neuron-style models that lead to chemical inductors by introducing a capacitive coupling in the slow relaxation variable. The extended model is able to explain naturally previous observations concerning the transition from capacitor to inductor in impedance spectroscopy of MAPbBr solar cells and memristors in the dark. The model also generates new types of oscillating systems by the generation of a truly negative capacitance distinct from the usual inductive effect.

Radiative Recombination Processes in Halide Perovskites Observed by Light Emission Voltage Modulated Spectroscopy.

The kinetics of light emission in halide perovskite light-emitting diodes (LEDs) and solar cells is composed of a radiative recombination of voltage-injected carriers mediated by additional steps such as carrier trapping, redistribution of injected carriers, and photon recycling that affect the observed luminescence decays. These processes are investigated in high-performance halide perovskite LEDs, with external quantum efficiency (EQE) and luminance values higher than 20% and 80 000 Cd m-2 , by measuring the frequency-resolved emitted light with respect to modulated voltage through a new methodology termed light emission voltage modulated spectroscopy (LEVS). The spectra are shown to provide detailed information on at least three different characteristic times. Essentially, new information is obtained with respect to the electrical method of impedance spectroscopy (IS), and overall, LEVS shows promise to capture internal kinetics that are difficult to be discerned by other techniques.

Assessing the Drawbacks and Benefits of Ion Migration in Lead Halide Perovskites.

Since the inception of the unprecedented rise of halide perovskites for photovoltaic research, ion migration has shadowed this material class with undesirable hysteresis and degradation effects, limiting its practical implementations. Unfortunately, the localized doping and electrochemical reactions triggered by ion migration cause many more undesirable effects that are often unreported or misinterpreted because they deviate from classical semiconductor behavior. In this Perspective, we provide a concise overview of such effects in halide perovskites, such as operational instability in photovoltaics, polarization-induced abnormal external quantum efficiency in light-emitting diodes, and energy channel shift and anomalous sensitivities in hard radiation detection. Finally, we highlight a unique use case of exploiting ion migration as a boon to design emerging memory technologies such as memristors for information storage and computing.

Interpretation of the Recombination Lifetime in Halide Perovskite Devices by Correlated Techniques.

The recombination lifetime is a central quantity of optoelectronic devices, as it controls properties such as the open-circuit voltage and light emission rates. Recently, the lifetime properties of halide perovskite devices have been measured over a wide range of the photovoltage, using techniques associated with a steady state by small perturbation methods. It has been remarked that observation of the lifetime is affected by different additional properties of the device, such as multiple trapping effects and capacitive charging. We discuss the meaning of delay factors in the observations of recombination lifetime in halide perovskites. We formulate a general equivalent circuit model that is a basis for the interpretation of all the small perturbation techniques. We discuss the connection of the recombination model to the previous reports of impedance spectroscopy of halide perovskites. Finally, we comment on the correlation properties of the different light-modulated techniques.

Interpretation of Mott-Schottky plots of photoanodes for water splitting.

A large body of literature reports that both bismuth vanadate and haematite photoanodes are semiconductors with an extremely high doping density between 1018 and 1021 cm-3. Such values are obtained from Mott-Schottky plots by assuming that the measured capacitance is dominated by the capacitance of the depletion layer formed by the doping density within the photoanode. In this work, we show that such an assumption is erroneous in many cases because the injection of electrons from the collecting contact creates a ubiquitous capacitance step that is very difficult to distinguish from that of the depletion layer. Based on this reasoning, we derive an analytical resolution limit that is independent of the assumed active area and surface roughness of the photoanode, below which doping densities cannot be measured in a capacitance measurement. We find that the reported doping densities in the literature lie very close to this value and therefore conclude that there is no credible evidence from capacitance measurements that confirms that bismuth vanadate and haematite photoanodes contain high doping densities.

Dynamic Instability and Time Domain Response of a Model Halide Perovskite Memristor for Artificial Neurons.

Memristors are candidate devices for constructing artificial neurons, synapses, and computational networks for brainlike information processing and sensory-motor autonomous systems. However, the dynamics of natural neurons and synapses are challenging and cannot be well reproduced with standard electronic components. Halide perovskite memristors operate by mixed ionic-electronic properties that may lead to replicate the live computation elements. Here we explore the dynamical behavior of a halide perovskite memristor model to evaluate the response to a step perturbation and the self-sustained oscillations that produce analog neuron spiking. As the system contains a capacitor and a voltage-dependent chemical inductor, it can mimic an action potential in response to a square current pulse. Furthermore, we discover a property that cannot occur in the standard two-dimensional model systems: a three-dimensional model shows a dynamical instability that produces a spiking regime without the need for an intrinsic negative resistance. These results open a new pathway to create spiking neurons without the support of electronic circuits.

Enhancing the Electronic Properties and Stability of High-Efficiency Tin-Lead Mixed Halide Perovskite Solar Cells via Doping Engineering.

Overcoming Voc loss to increase the efficiency of perovskite solar cells (PSCs) has been aggressively studied. In this work, we introduce and compare rubidium iodide (RbI) and potassium iodide (KI) alkali metal halides (AMHs) as dopants in a tin-lead (SnPb)-based perovskite system to improve the performance of PSCs by enhancing their Voc. Improvement in terms of surface morphology, crystallinity, charge transfer, and carrier transport in the SnPb perovskites was observed with the addition of AMH dopants. Significant power conversion efficiency improvement has been achieved with the incorporation of either dopant, and the highest efficiency was 21.04% in SnPb mixed halide PSCs when the RbI dopant was employed. In conclusion, we can outline the enhancement strategy that yields a remarkable efficiency of >20% with a smaller Voc loss and improved storage, light, and thermal stability in SnPb PSCs via doping engineering.

Chemical Inductor.

A multitude of chemical, biological, and material systems present an inductive behavior that is not electromagnetic in origin. Here, it is termed a chemical inductor. We show that the structure of the chemical inductor consists of a two-dimensional system that couples a fast conduction mode and a slowing down element. Therefore, it is generally defined in dynamical terms rather than by a specific physicochemical mechanism. The chemical inductor produces many familiar features in electrochemical reactions, including catalytic, electrodeposition, and corrosion reactions in batteries and fuel cells, and in solid-state semiconductor devices such as solar cells, organic light-emitting diodes, and memristors. It generates the widespread phenomenon of negative capacitance, it causes negative spikes in voltage transient measurements, and it creates inverted hysteresis effects in current-voltage curves and cyclic voltammetry. Furthermore, it determines stability, bifurcations, and chaotic properties associated to self-sustained oscillations in biological neurons and electrochemical systems. As these properties emerge in different types of measurement techniques such as impedance spectroscopy and time-transient decays, the chemical inductor becomes a useful framework for the interpretation of the electrical, optoelectronic, and electrochemical responses in a wide variety of systems. In the paper, we describe the general dynamical structure of the chemical inductor and we comment on a broad range of examples from different research areas.

Extracting in Situ Charge Carrier Diffusion Parameters in Perovskite Solar Cells with Light Modulated Techniques.

Frequency resolved methods are widely used to determine device properties of perovskite solar cells. However, obtaining the electronic parameters for diffusion and recombination by impedance spectroscopy has been so far elusive, since the measured spectra do not present the diffusion of electrons. Here we show that intensity modulated photocurrent spectroscopy (IMPS) displays a high frequency spiraling feature determined by the diffusion-recombination constants, under conditions of generation of carriers far from the collecting contact. We present models and experiments in two different configurations: the standard sandwich-contacts solar cell device and the quasi-interdigitated back-contact (QIBC) device for lateral long-range diffusion. The results of the measurements produce the hole diffusion coefficient of D p = 0.029 cm2/s and lifetime of τ p = 16 µs for one cell and D p = 0.76 cm2/s and τ p = 1.6 µs for the other. The analysis in the frequency domain is effective to separate the carrier diffusion (at high frequency) from the ionic contact phenomena at a low frequency. This result opens the way for a systematic determination of transport and recombination features in a variety of operando conditions.

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

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

A Frequency Domain Analysis of the Excitability and Bifurcations of the FitzHugh-Nagumo Neuron Model.

The dynamics of neurons consist of oscillating patterns of a membrane potential that underpin the operation of biological intelligence. The FitzHugh-Nagumo (FHN) model for neuron excitability generates rich dynamical regimes with a simpler mathematical structure than the Hodgkin-Huxley model. Because neurons can be understood in terms of electrical and electrochemical methods, here we apply the analysis of the impedance response to obtain the characteristic spectra and their evolution as a function of applied voltage. We convert the two nonlinear differential equations of FHN into an equivalent circuit model, classify the different impedance spectra, and calculate the corresponding trajectories in the phase plane of the variables. In analogy to the field of electrochemical oscillators, impedance spectroscopy detects the Hopf bifurcations and the spiking regimes. We show that a neuron element needs three essential internal components: capacitor, inductor, and negative differential resistance. The method supports the fabrication of memristor-based artificial neural networks.

From Frequency Domain to Time Transient Methods for Halide Perovskite Solar Cells: The Connections of IMPS, IMVS, TPC, and TPV.

The correlation of different methods of measurement can become an important tool to identify the dominant physical elements that govern the electronic and ionic dynamics in perovskite solar cells. The diverse phenomena underlying the response of halide perovskite materials to different stimuli are reflected in time-domain measurements, where transients appear with time scales spanning orders of magnitude, from nanoseconds to hours. We discuss the connection between different frequency- and time-domain methods to probe the voltage and current response of halide perovskite solar cells to different small perturbations. To solve the frequency-to-time transformation, we start from models of the transfer function of intensity-modulated photocurrent spectroscopy (IMPS) and derive the associated impulse response function, the transient photocurrent (TPC), in response to a short light pulse. Similarly, we determine the transient photovoltage (TPV) starting from the intensity-modulated photovoltage spectroscopy (IMVS) transfer function. We also discuss the open-circuit voltage decays (OCVD). We first show the response of simple equivalent circuit models, and then we treat the full model for generation-diffusion-recombination of electrons that shows a spiraling loop in IMPS. This model gives rise to overshoots in the time domain.

Unique Curve for the Radiative Photovoltage Deficit Caused by the Urbach Tail.

The photovoltage Voc of high-performance solar cells such as GaAs and metal halide perovskites is affected by the exponential Urbach tail in the absorption spectrum, with an energy parameter EU. It has been observed that increasing Urbach energy decreases the maximum photovoltage that can be achieved. On the basis of detailed balance and reciprocity of absorption and emission, we present a calculation that shows that the voltage loss due to the exponential tail in an absorption obeys a universal relation ΔVocrad = (kBT/q) ln(1 - EU/kBT) for EU < kBT, independently of the bandgap.