“Hysterical” current-voltage behavior of perovskite solar cells
Power transfer rates have gone up by a huge amount thanks to the development of perovskite solar cells (PSCs). The diode equation can be used to figure out the current density-voltage (J-V) plots that show how well a solar cell converts light into electricity. The most important number that can be found by measuring a solar cell’s JV is its maximum output power density (Pmpp), which is found at the maximum power point (MPP). The open circuit voltage (VOC), short-circuit current density (JSC), and fill factor (FF) are often used to show pmpp. It is the solar cell’s power conversion efficiency (PCE) that is measured in relation to the power that hits it. The incident power is usually a standardised reference spectrum that is normalised to a power density of 1000 W/m2.
Hysteria around hysteresis
As perovskite solar cells (PSCs) have developed, there have been arguments about whether J-V measurements are the best way to judge how well the device works, since they are often greatly affected by scan conditions and show feedback between measurements taken in different scan directions. This could make the power exchange rate too high or too low. When J-V data for solar cells is reported, not much else is said about the experiments besides the type of light source and potentiostat or source-meter unit that were used. Several studies have stressed how important it is to describe the qualities of the light sources used and how the active area is described when talking about the performance of solar cells.
Depending on the direction and speed of the voltage pass, PSCs may work very differently. Since hysteresis is talked about in almost half of all papers on PSCs, it is very important to be clear about the exact scan conditions. In 2013, hysteresis in PSCs was first talked about, and it was also talked about at science events like the autumn MRS meeting that year.
It’s not just PSCs that have J-V hysteresis. Cadmium telluride (CdTe) devices also show hysteresis in capacitance-voltage readings that gets worse as the device breaks down because of CuI1 ions moving around. When the scan rate is very fast, high-performance silicon devices with a lot of internal capacitance show J-V loops. When charge carrier movement in the liquid solution becomes a rate-determining step at high scan rates, dye-sensitized solar cells (DSCs) show unique capacitive effects.
Different ways of checking the accuracy of device performance data have been created. These usually include tracking the maximum power point, comparing short-circuit current densities with the integrated external quantum efficiency, and/or looking at PSCs at scan rates in both fast and slow time domains. Some scientific magazines need experimental power transfer efficiency data to be checked, and it’s now normal for new record efficiency claims to be checked by a third party.
Scan-rate dependence
The debate over hysteresis in perovskite solar cells (PSCs) has made it clear that measurement scan-rate, s, and voltage-sweep direction need to be spelt out. The scan rate by itself is not enough to describe the scan conditions if the J-V scans are not done in a straight line. Instead, J-V readings are usually done in a way called “staircase voltammetry,” where the potentials are added one after the other. To do this, you need to set the voltage step size (ΔV) and the delay time (td) or voltage setting time (td) before taking samples of the current for a set amount of time (ts).
The Φt span that goes by before the next voltage step would be the sum of td, ts, and maybe even twait, which is the time spent waiting. This difference in how measurements are done in different labs is shown in Fig. 4.2, where the scan rate is 50 mV/15 s 5 3.33 mV/s. The bigger current transient reaction for the voltage step from 0.65 V to 0.6 V shows that when the voltage changes, the current goes over and then drops off at an exponential rate.
In order to take J-V readings in a steady state, there must be enough time between each voltage step for the rapid reaction to settle down. Finding the right delay time, td, is as easy as figuring out the device’s transient reaction and setting the delay time to be about three times the longest transient time constant, τlong: td. 3 τlong.
The study of transients in the J-V response helps to explain the difference in J-V between forward and backward scans and figure out the minimum td needed to make J-V measurements in steady-state circumstances. You can learn more about how a dynamic device responds by looking at the magnitude and characteristic transient time constants.
The current density that changes over time, J(t), can be shown as the sum of the transient components, Jtrans (t), and the device’s steady-state current, JSS. Chen et al. [20] used a graph and study of current changes during a step-wise change in the applied potential to show how the size and length of a voltage step affect the outcome and lead to hysteresis. The transient current response can be used to figure out the smallest td that is needed to measure J-V on a device that is almost in a steady state.
Quantification of hysteresis: hysteresis indices
Hysteresis indices (HI) are a way to measure the J-V difference in perovskite solar cells (PSCs). Different meanings are used to figure out these values, like the difference between the forward and backward currents at a certain voltage, combined J-V curves, or device performance descriptions. For very short and long delay times, the difference between J-V sweeps may not seem to show any hysteresis, but the exact device performance may be very different.
The HI reaches its highest point at a delay time of 54 ms, which means that the J-V difference is biggest at a scan rate of about 1.5 V/s. When scan rates are slower, hysteresis and performance go down. When scan rates are fast and hysteresis is almost nonexistent, performance goes up. It is called “anomalous” hysteresis when the J-V hysteresis goes up as the scan rate goes down. This happens because the sensitive device can only respond so quickly.
The main thing to remember is that J-V measures done at a single scan rate are not enough, and “negligible hysteresis” (a low HI) is not enough to make sure that the right measurement conditions are used. Instead, looking into the J-V reaction and HI as a function of the delay time can help us understand how a device changes over time, and it should be characterised in great detail to find out how hysteresis happens. When giving J-V measurement data for PSCs, critics and magazines often want you to talk about inertia and give J-V data at different scan rates.
Pre-conditioning & poling
The starting voltage of the J-V scan and the conditions the devices are under before measurement can have a big effect on the shape of the J-V curves and the hysteresis they show. When the device is dark, its J-V curves take on an s-shaped shape. However, light soaking under forward bias can change these curves to look more like diode curves. On the other hand, light soaking under reverse bias can move devices towards an s-shape, which suggests that charge carrier extraction barriers at interface layers change. This means that internal conditions change during storage, lightsoaking, and pre-biasing. This causes recorded performance to change over time, but at a slower rate than the scan-rate dependent phenomenon. The sensitivity of PSC devices can be turned around by poling effects.
Origin of hysteresis
Early reports on phenomenology suggested that hysteresis might be caused by the intrinsic material properties of metal-halide perovskites, such as ferroelectricity, charge carrier trapping and de-trapping, and ion migration. This led to experimental and theoretical research on the fundamental material properties in PSCs.
Capacitive and non-capacitive origin of hysteresis
The J-V difference seen in Perovskite Solar Cells (PSCs) is a feature of capacitive behaviour, and the magnitude changes depending on the scan rate. The difference is thought to be caused by capacitive charging or releasing currents, which depend on the capacitance and the size of the voltage step per time interval. You can add these currents as extra, scan-rate-dependent parts to equation (4.2), and you can use a similar circuit with a double diode and a double capacitor with very large capacitances to model the actual hysteretic J-V curves. It has been found that devices that work at around 0 V in the dark and are monitored at middle voltage scan rates have capacitive currents in the nA/cm2 range. But effects that aren’t capacitive play a part in the J^V hysteresis because capacitive currents from charge carrier storage alone aren’t enough to explain the strong hysteretic effects at slow scan rates. Hysteresis is caused by non-capacitive effects like changes in how well charge carriers are collected and how electrons and holes mix because the built-in potential changes as ions re-equilibrate. It’s not easy to figure out what short-lived events happen in PSCs because of the strong connection between ion rearrangement and electron and hole dynamics.
The dielectric response of metal-halide perovskites
Time- and frequency-resolved methods are very important for figuring out the time scales of short-lived events that cause hysteresis in metal-halide perovskite devices. The main topic of this work is how the dielectric constant changes with frequency in metal-halide perovskite devices. Poglitsch and Weber found that the complex permittivity of methylammonium lead iodide (MAPbI3) changes with frequency and temperature. They think this is because of the dynamic disorder of the methylammonium (MA) cation in the material, which is thought to block free charge carriers and create ferroelectric domains. MAPbI3 perovskites have been shown to have ferroelectric regions when they are poling by piezo-response force imaging. Scientists have used quasi-elastic neutron scattering (QENS) and pump-probe vibrational spectroscopy to find that the MA cation’s molecular movements happen within 3 ps.
The current-voltage study of perovskite solar cell materials has been explained by changes in how the cations soften their dielectric. It’s not likely that ferroelectricity caused by cation reorientation is the main cause of current-voltage hysteresis because the reaction happens so quickly. This talk will mostly be about how ions move and how that changes the electric field distribution and charge carrier traps (PSCs), since these are the most likely reasons for the current-voltage feedback seen over seconds to minutes.
Ionic defect formation & migration
Researchers have looked into metal-halides and metal-halide perovskites as ionic carriers for turning sunlight into electricity. Hysteresis is mostly caused by ionic defects, which aren’t directly caused by an ionic current. Instead, they are changed by changes in the interfacial charge carrier extraction efficiencies, the electric field distribution within the device, the trapping and de-trapping of electronic charge carriers into ionic defects, and the non-radiative recombination rates. When MAPbI3 is illuminated, the low-frequency response of its dielectric constant shows a huge rise to about 1000. This rise is even more noticeable as electronic charge carriers are created. The size of this low-frequency component and the effect of light depend a lot on the design of the device. This is because the interface between the charge selective contact and the perovskite will change how many ions build up by affecting the ion transmissivity, and the surface termination may have a big impact on the defect density at this interface.
In the journals, there are ongoing arguments about which ionic species would be most responsible for the fleeting photocurrent reaction. The movement of halide ions (vacancies) and MA cations has been tested by measuring them on MAPbI3 pellets. The diffusion coefficient was found to be between 1028 and 1027 cm2/s. Perovskite semiconductors are thought to have defect levels between 1017 and 1020 cm23, which means that halide vacancies and interstitials are always present. It’s most likely that halide vacancies will move, with an EA of 0.2 to 0.8 eV and a D of 10212 cm2/s. It is thought that cation diffusion happens at a higher activation energy and has a slower reaction. However, cations have been shown to have mobilities of about 1029 cm2/Vs, which means they can move quickly through a 300 nm perovskite absorber layer.
Modeling hysteresis
The main reason for hysteresis in metal-halide perovskites is that ionic charge carriers move around within the perovskite layer through drift and diffusion. This can be seen when an outside field is applied. This redistribution changes how charge carriers are extracted. Negative ions tend to gather at the electron selective contact, which makes it harder to extract charge carriers and results in a lower extracted charge carrier density. On the other hand, positive ions build up at the electron selective contact, which helps charge carriers leave the material and makes the net removed charge carrier density higher.
Different methods, like similar circuit models and numerical device modelling, have been used to describe hysteresis. The first ones are mostly used to describe the frequency-dependent impedance response and the whole J-V curve. The second ones give more information because the J-V curve can show how the built-in potential changes and how band-bending happens when ions build up at interfaces that make it hard for charge carriers to get out at certain contacts.
Drift-diffusion simulation is a popular way to model semiconductor devices. In this method, electrons and holes are thought to be movable, while ionised dopant atoms create a localised space charge. Recently, these models have been expanded to include mobile ionic species with much lower diffusion constants and mobilities in order to simulate hysteresis. But these kinds of models are hard to use because they need a lot of input factors, many of which are unknown.
Several computer studies have reached a point where they can be partially compared to actual data. This can be used as a starting point for more precise modelling as electronic factors like dielectric constant, mobilities, and ion densities are better understood. To sum up, the simulation studies have advanced to a point where they can be partially compared to experimental data. These results can be used as a starting point for more precise modelling as electronic parameters like dielectric constant, mobilities, and ion densities are characterised in more detail.
A window into device operation
Perovskite Solar Cells (PSCs) have feedback that changes depending on how they are measured and can be affected by different sources. This part shows how the size of hysteresis and the rapid reaction of a device can be different depending on its age, perovskite makeup, and design.
Device architecture & selective contact layers
The amount of hysteresis seen in perovskite solar cells (PSCs) is greatly affected by how the devices are built, especially the electron and hole selective contacts that are used. This is thought to be ion buildup or flaws at the perovskite and charge selective layers, which greatly affect how charge carriers are extracted and recombined at the interface. Most of the time, n-i-p devices have more noticeable device design than p-i-n devices. The n-i-p device with titanium dioxide and spiroMeOTAD selective contacts (TiO2/MAPbI3/spiroMeOTAD) has the most different J-V curves. The HI0.8Voc reaches its highest point after 200 ms, which shows that the device’s reaction rate is limited. When phenyl-C61-butyric-methyl-ester (PCBM) is used instead of TiO2 or a TiO2/PCBM double layer is used, hysteresis is greatly decreased.
Inverted p-i-n devices, first described by Docampo et al. [78], are made up of nickel oxide (NiOx) and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS) as hole-selective contacts. They don’t have nearly as much hysteresis as other p-i-n devices. However, hysteresis may become noticeable at lower temperatures, and the lack of hysteresis does not mean that mobile ionic species are not present.
The findings show that the surfaces that form between the perovskite and charge selective contacts play a key role in determining how much hysteresis there is. The way the perovskite absorber and n- or p-selective contact layer interact physically and chemically at the interface affects how the layers stick together and the flaws that are created at the interface. The simulation results show that the entrances to the charge-transport layers are very important for seeing hysteresis.
This doesn’t seem to fit with the ion movement theory at first look. There are, however, different shielding and carrier capture effects because of energy barriers at the surfaces, changes in the conductivity of the charge transport layers, and changes in the distribution of ionic species that act as binding sites. Ions that are moved around might change how well charge carriers receive charges in different ways. Another important factor is how permeable a selected contact layer is to certain types of ions. J-V hysteresis is very small in devices made of organic PCBM and inorganic CuI or CuSCN contacts. This is likely because ions don’t build up at these contacts.
Light and temperature dependence
The low-frequency real part of the permittivity in perovskite solar cells (PSCs) goes up as the light level rises, no matter what kind of device the PSC is. This effect has been seen no matter what kind of gadget it is or what specific contact layers are used. Levine et al. looked into how hysteresis, which is measured by the hysteresis index (HIint), changes with light and temperature for n-i-p (a–c) and p-i-n (D–f) type devices at various scan rates. The plots showed that hysteresis goes up as the scan rate goes up, up as the temperature goes down, and down as the light strength goes up. For n-i-p devices, the effect of scan rate and temperature is more complicated, and the temperature correlation is stronger than for p-i-n devices. This shows that the EA of the underlying process that causes hysteresis is very different for each type of device. It also shows that the interfaces between charge selective contacts and perovskites play a key role in how hysteresis changes with light and temperature.
Researchers Pazoki et al. looked into how photon energy affects hysteresis and found that blue light excitation causes much stronger J-V hysteresis than red light excitation. They think this is because thermalisation helps ions move or vacancies form. Inverted hysteresis of mixed perovskite absorber devices was found to be very different when blue and red light were used, which was because more charge carriers were created in the recombination area close to the titanium dioxide electron selective contact. Conditions of illumination need to be spelt out in order to learn more about the possible different sources of short-lived events in metal-halide perovskites.
Perovskite layer morphology and composition
Device hysteresis can be changed by changing the shape and make-up of the perovskite absorber layer. It has been found that small-grained films with low coverage have higher hysteresis than large, monolithic-grained thin films with high coverage. In metal-halide perovskites, grain boundaries don’t seem to be as bad as they are in other semiconductors, but they can still make charge carriers mix up and stop the movement of charge carriers and ions. Intensity modulated photocurrent spectroscopy (IMPS) studies show that bigger monolithic grains have a faster device reaction, which supports the idea that grain boundaries in the direction of charge carrier transfer are bad and cause more noticeable hysteresis. On the other hand, even though they have small grains, vacuum-deposited perovskite solar cells can have very little hysteresis.
Small changes in the stoichiometry of the perovskite absorber layer could lead to self-doping effects that change the way the perovskite layer’s internal field is distributed. Extra lead iodide (PbI2), which can be created by heat breakdown or added as an extra during production, has been shown to improve the performance of devices. In their study [95], Jacobsson et al. looked into how precursor stoichiometry affected the performance and hysteresis of standard n-i-p devices. They discovered that samples that were stoichiometric or slightly low in PbI2 had lower device performance and an integral hysteresis HIint. This was because the photocurrent was lower in these samples. This was because too many organic cations stopped charge carriers from moving across surfaces.
Compositional engineering has been shown to be a useful method for improving devices in recent years. In their study [24], Jacobsson et al. compared 49 different mixtures of cation/anion alloys of methylammonium/formamidinium (MAyFA1-y)-lead(Pb)-bromide/iodide (BrxI1-x)3. Because performance is steadily going up, hysteresis is low in this case. As the photo-induced phase splitting process starts because of halide ion movement, hysteresis also gets worse.
It is important to tell the difference between compositional variation effects on hysteresis and structural effects in samples because mixed cation/anion predecessors form in different ways. This phenomenon, called “inverted hysteresis,” is thought to be caused by energetic extraction barriers at the surfaces to selected contacts. These barriers could be lowered when ions build up, allowing for a better collection of charge carriers during the forward scan. A block like this could be caused by an imbalance in energy, changes in makeup, or bad band bending from ionic charges building up. Long-term light-soaking in reverse bias conditions was shown to cause inverted hysteresis in devices.
Defect engineering, passivation and external ionic species
It has been found that adding things to perovskite solar cells (PSCs) that specifically passivate flaws can lower hysteresis. Fullerenes have been shown to lower the number of defects by two orders of magnitude. This is because they stop trap states from activating and make it harder for ions to move across grain borders. Yoo et al. studied the impact of various phenylalkylammonium iodides on the perovskite layer after it had been deposited. They discovered that these iodides reduced hysteresis and made JSC and VOC slightly better. This was because they stopped trap-mediated interfacial recombination, which is caused by defect passivation.
The alkali halide forms of rubidium (Rb1) and potassium (K1), along with molecular molecules, have been suggested as new ways to fix defects. It gets less likely that these alkali cations will join the “A-site” of the perovskite crystal structure. Duong et al. showed that regular n-i-p devices for the multi-cation FA0.75(MA0.6Cs0.4)0.25PbI2Br perovskite with a 5% rubidium additive had a higher average power conversion efficiency and a slightly reversed hysteresis. They did this at a scan rate of 50 mV/s. The better device performance and lower hysteresis were due to the perovskite absorber layer being more crystallised and the photoluminescence lifetime being longer. Both of these factors showed that ionic defect migration was slowed down.
The results from the Characterisation Techniques for Perovskite Solar Cell Materials (IMPS) showed clear differences in the middle to low frequency range below 100 Hz. It was found by Son et al. that potassium (K1) was the best at lowering hysteresis for mixed cation PSCs. This study by Abdi-Jaledi et al. confirmed that potassium has a good effect. They said that this is because potassium iodide (KI) makes up for the lack of halides and replaces bromide with iodide.
Not much thought has been put into how outside ionic species, like lithium, might affect hysteresis. These species could be added to the electron or hole-selective layer, for example. Kim et al. studied how J-V hysteresis changes when additives are added to the spiroMeOTAD hole conductor. They found that the additives have a big impact on the interfacial polarisation effects at the perovskite/spiroMeOTAD interface. Li and others looked into hydrogen (H1), sodium (Na1), and lithium (Li1) as extrinsic ions in perovskite solar cells. They found that all of these extrinsic ions clearly changed the performance and repeatability of PSCs.
Hysteresis and stability
In perovskite solar cells, hysteresis is mostly caused by the movement and buildup of ionic gaps and interstitials, which change how the electric field is distributed and how well it collects energy. This could make the gadget less stable in the long run. In particular, non-ion-p devices lose some of their performance when exposed to light but gain some of it back when it gets dark. This shows that there have been complex changes that need to be carefully analysed. Leijtens et al. showed that MAPbI3 breaks down into lead iodide when it is biassed. This happens because the MAcation is lost, which happens because of charged flaws. So, to test the steadiness of a gadget, it should be used in real-world situations with light and bias. Over the span of a device, thermal, photo, and bias-induced decay may cause more local flaws or mobile ionic species, which could make short-term effects stronger in metal-halide perovskite solar cells.
Tress et al. looked at how device performance and hysteresis changed over time in open-circuit conditions with an LED light source shining on the device for 6.5 hours straight. They discovered that hysteresis goes down with age for slow scan rates but up for fast scan rates. It has been suggested that light-induced deep-level trap states or the movement of mobile ionic species cause a device’s performance to drop over the course of hours. But not all types of perovskite solar cells behave in this way; it depends on the charge transfer layers that are used. A better way to measure the performance of a perovskite solar cell material over time is to look at its integral lifetime energy yield (LEY 5 Ñt 0 PCE tð Þdt).
Conclusion and outlook
Hysteresis indices (HIs) are used to measure how different the J-V curves are in solar cells. However, if they are only measured for a small scan-rate region, they are not very useful for science. To avoid confusion, measuring data for the maximum power point (MPP) for a long time should be recorded and shown when talking about how well photovoltaic solar cells (PSCs) work. To make sure that gadget performance measures can be compared, most people in the PSC study group must agree on reliable measurement methods. Hysteresis may have its roots in a number of short-lived processes that happen over a range of time scales. These include the movement of ions, the spread of electric fields, the efficiency with which charge carriers are extracted, and the mixing of charged particles. We need to do more study to find out how the structure of the device, the selective contact layers, the makeup and shape of the perovskite absorber, as well as the chemicals and passivants used, affect the long-term stability of PSCs.
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