A lot of research has been done on metal halide perovskite semiconductor materials because they have unique optical qualities that could be used in solar cells, light emission diodes, and X-ray detectors. Perovskite has the chemical formula ABX3. The letters A through X stand for cations that are one-valent, cations that are two-valent, and halide anions. In 2009, Kojima et al. reported the first attempt to use perovskite nanocrystals in solar cells. They used the nanocrystals as light absorbers in a regular sensitised solar cell that used a liquid solution based on iodide and triiodide. Perovskite solar cells (PSCs) have made a lot of success in the last ten years in terms of how well they convert light to electricity. For single-junction solar cells, the current best efficiency is 25.5%.
Many interesting things about metal halide PSCs have been noticed since study on them began. One of these is how the device changes over time in the low-frequency range. Understanding this is important for basic optical characterisation and performance rating, since lighting and solar devices need to work for a long time.
Early on in the research, many of the results were not accurate because samples were not always the same and the reaction changed slowly during measures. As gadget quality has gotten better and the number of researchers has grown, more and more things can now be linked to natural traits. However, there is still not a lot of agreement on how to understand the reactions that have been seen.
Overview
The amazing semiconductor qualities of metal halide perovskite come from the fact that it can be made from cheap materials using wet chemical methods at low temperatures. The material is soft, though, because of its structure and the way it was made. It is likely to react with internal parts of outside agents, which creates ionic gaps. Ionic motion happens in the characteristic material class MAPbX3 when ions hop between nearby sites. This causes long-range movement and other effects. Many times, a lot of ionic motion becomes the most important thing about mixed metal halide perovskite.
When an external voltage or an internal photovoltage is applied, the electrical charge is moved around to find a new balance. This is done through electronic and ionic carriers. In metal halide perovskite, the movement of ionic charge changes the internal band bending conditions. This leads to polarisation at the surfaces and makes it harder to figure out what the observed electrical current means. Unlike most other photovoltaic semiconductors, mixed hybrid perovskites (MHP) combine easy ionic diffusion, photogeneration of carriers, and luminescence properties to make interesting things that can be seen, like halide phase segregation linked to changes in composition caused by light.
Several main types of materials and devices can be used to look into these effects. A standard solar cell is made up of a thin layer of active metal halide perovskite that has selective connections. The characteristic value of this layer is 100–500 nm. For transfer and mechanism studies, symmetric contacts are used in a different arrangement.
It is important to know what direct current (DC) does when a bias voltage is put on it. In a symmetric structure, the dc is usually an electronic current of a single type of carrier moving through the sample. This makes the sample more electronic conductive and speeds up the movement of the halide.
The kinetic response of a semiconductor device is more complicated than that of a simple RC circuit because of the different transport phenomena, interfaces, and other factors that affect the similar circuit. These factors determine the main physical responses to small disturbance signals. The most important thing for understanding how metal halide perovskite materials behave physically is to find the right corresponding circuit and a good way to read it.
Carrier Transport
General Determination of Transport Coefficients, Diffusion
Coefficient, and Mobility
Several methods have been used to find out how easily electrons can move in metal halide perovskites and how fast ions can move through flaws in lead halide perovskite materials, especially when the temperature is room temperature. Using techniques like galvanostatic measurement, impedance spectroscopy, the classical transmission line method, and blocking luminescence in electrodes that are contacted on the sides have given exact numbers for the diffusion coefficient of halide defects, which is about DVI = 1 108 cm2/s for MAPbI3 or MAPbBr3. It has also been studied how cations move for external Li+. The movement coefficients are different depending on the makeup and how they were made.
Mixed Ionic/Electronic Conduction and Time Constants
Carrier conductivity is an important number in semiconductor devices because it controls power losses and tells us which species control how carriers move when something outside the device moves. Total conductivity in mixed ionic/electronic materials is made up of both electronic and ionic conductivity. Which current (ionic or electrical) will be strongest in any given scenario is based on the ratio of conductivities.
At room temperature, the diffusion coefficient (D) and carrier mobility (𝖁) are two important kinetic factors in perovskite semiconductors (PSCs) based on MAPbI3 or MAPbBr3. Some of the tests that are used to find mobility values are Galvanostatic voltage measurement, IS, PL suppression, external Li+, PLQ, SCLC, and Halide vacancy transport (VI+).
Some of the timescales that describe kinetic events in PSCs MAPbI3 and MAPbBr3 at room temperature are electronic transport across d=100 nm, diffusion of halide vacancies over a distance, the response of ions that have gathered on the perovskite surface, and diffusion of cations over a distance. A lot of the current comes from electronic current, unless the density of moving ions gets a lot higher than electronic density.
We can figure out the average travel time for a perturbation gradient to settle in an MHP layer by looking at how carriers move through it: d = d2 D.
Measurement of Ionic Conductivity by Galvanostatic Transient Method
The galvanostatic method is used to separate the total conductivity of an Au/perovskite (MAPbI3 or CsPbI2Br)/Au structure from the electrical conductivity of that structure. When a weak current is applied to a symmetric sample, the voltage and current rise slowly over time until they hit a peak. In the beginning, the resistance is linked to the total conductivity. In the end, the resistance is only linked to the electrical conductivity.
Due to the perovskite’s tendency to react and break down, as well as important surface processes, the galvanostatic measurement is prone to mistake. Some writers get the ionic conductivity from the end, steady current, which is obviously not right. One important factor is the size of the ionic transmission when light is present. It was seen that CsPbI2Br has a fixed activation barrier for hopping that doesn’t depend on how bright the light is. This is different from MAPbI3, which is strongly affected by light. Because of this, writers think that photogeneration causes a big rise in ionic conductivity.
As shown in Figure 6.5, it is thought that the ionic and electronic conductivities have almost the same value when the light is on. One reason for this finding is that the presence of a photogenerated minority carrier makes the halide more mobile. For instance, hole trapping makes iodide move faster, but this can only happen when n-type samples are lit up. Using a hole capture device can stop the iodide from moving around. This explains why the mixed halide separates into different stages, which can be undone by putting the sample back in the dark.
Measurement of Ionic Diffusion by Impedance Spectroscopy
One way to find diffusion in a thin layer with a clear spectral shape is to use the IS method. The transmission line model says that there is a change from a 45° feature at high frequency to a vertical feature when capacitive charging happens. If you use Equation (6.4) to find the characteristic frequency, you can find the diffusion coefficient.
When ions move through a thin layer, the transmission line impedance is made up of a chemical capacitance and a spread transport resistance. At low frequencies, the impedance spectrum changes a lot because of ending at the boundary, which is shown by the boundary impedance, ZB. When there is a boundary that blocks charge transfer, the impedance goes up vertically. When there is a boundary that lets charge transfer, the impedance makes an arc at low frequency and goes down as the charge transfer rate at the contact goes up.
There is a big electrical part in the MHP that makes it hard to measure ionic conductivity most of the time. In the dark, touched carrier transport (TiO2) samples of low-doped monocrystalline MAPbBr3 are different. For polycrystalline devices, it is possible to see the full diffusion resistance linked to ionic transport. When a biological layer is added, the resistance pattern changes, which is what you would expect from a partly absorbent border.
Using the relationship 𝼏d = D𝼇/d2, we can figure out that the chemical diffusion coefficient for Br− is 1.8 × 10−8 cm2/s. This is based on how the frequency of the ankle is related to the thickness of the perovskite layer.
In conclusion, the IS method gives a clear spectral shape for finding diffusion in a thin layer. At high frequency, the shape changes from a 45° feature to a vertical feature that is linked to capacitive charging.
Ionic Drift Causes Suppression of Luminescence
The fast movement of ions in lead halide perovskites has a big effect on how electronic devices like solar cells work. To clearly connect electrical data with the electronic/ionic reaction, techniques that can resolve space are needed. It is possible to see changes in chemical makeup, photoluminescence response, and electrical response all at the same time by measuring interdigitated contacts with channel lengths of hundreds of μm.
In these kinds of systems, a voltage bias similar to that at the highest power point in a working PSC in the dark causes ions to move, which can be chemically tracked with X-ray photoelectron spectroscopy (XPS) research. Across the perovskite channel, the chemical make-up changes, creating an iodine-rich positive contact and places with iodine flaws. On the other hand, looking at the photoluminescence (PL) by stimulating it at 35 mW/cm2 while applying bias shows that a dark front forms and moves forward over time. At the same time, as the dark front moves forward, the material becomes resistant, which can be seen by the drop in current and the impedance reaction being measured at the same time.
Because the movement of electrons in hybrid perovskites is many orders of magnitude greater than the movement of ions, it is possible to come up with a mathematical model based on the idea that most of the current flowing through the film is electronic. The electric field changes the local distribution of ions in the sample’s mass, and moving flaws cause solid-state processes that boost non-radiative recombination, creating a dark area. By looking at the measured current across the current, we can figure out that DVI = 5 × 10−8 −6 × 10−9 cm2/s for perovskite compositions of CH3NH3PbI3−xClx and much lower for compositions with large organic cations, which is good for the operation of the device in an LED configuration.
Interpretation of Capacitances in Semiconductor
Devices
The IS method checks the complex resistance, which is how the voltage and current change over time. To find the complex dielectric constant, you need to know the complex capacitance, which is given by C(𝼏) = 1 i𝼏Z(𝼏). The sample area A and thickness are also needed. The IS method can be used to look into the charge distribution of ionic/electronic systems because knowing the capacitance is important for understanding comparable circuits and making a physical model from observations made in the lab. Both the capacitance and the dielectric constant change with frequency. The function C′ (f) can be shown as increases in the capacitance as the frequency drops. Different types of capacitance can cause the capacitance steps and plateaus to mean different things. These include bulk polarisability, dielectric relaxation phenomena, chemical capacitance in semiconductor systems, contact capacitances at current collectors, and the presence of mobile ions that cause double-layer capacitance. The Mott–Schottky capacitance plot method is used to describe the features of semiconductor barriers. It is based on the Schottky barrier at the metal/semiconductor interface. There is also a sensitive reaction for bulk flaw levels. d AZ(𝼏) is used to figure out the complex conductivity of a sample with an electrode area of A and a thickness of d.
Dielectric Relaxation
The real part of the dielectric constant shows how much charge builds up due to polarisation, and the dielectric loss, shown by 𝼀, shows how much energy is lost over and above the dc dissipation. The real part of the permittivity changes with frequency, and the dielectric loss is closely linked to it. The real part of the permittivity usually goes up when there is a rise in the dielectric loss, which is caused by a certain dielectric relaxation process. Δ𝼀 = 𝼀s − 𝼀∞ shows the change in complex permittivity from its high frequency value. Here, 𝼀s is the real part of the dielectric constant’s static value and 𝼀∞ is its high frequency part.
Chemical Capacitance
The chemical capacitance in semiconductors is linked to the shift of the electron Fermi level (EFn) and the change in the number of electron carriers (n). It has a direct relationship with film thickness (C₼ = c𝼇d), but the dielectric capacitance has a relationship with d that goes the other way (Eq. 6.11).
Electrode Polarization
In systems with ions, electrode polarisation happens because low-frequency transmission is blocked because ions can’t get through the metal collection contact. This makes the measured ionic conductivity go down, leaving only the observed electrical conductivity. Ions build up at the contact interface, creating a capacitance due to the surface space charge. This capacitance is independent of film thickness and can be modelled using the standard Gouy-Chapman diffuse double-layer model. The capacitance can be shown mathematically as Csc = 𝼀𝼀0𝼆D, where N is the number of ionic charges per unit area. Because of this event, the apparent permittivity values in the 𝼀(𝼏) plot are very high.
Depletion Capacitance at the Schottky Barrier
A Schottky barrier forms at the point where an n-type semiconductor meets an electron-extracting layer with a low work function. The contact barrier height is set by the work function offset between the semiconductor layer and the touching material. The flat-band voltage is then set by this offset. Based on these ideas, the carrying bands of the bulk absorbing layer appear to be bent because of charged flaws that are stuck in place (space charge). At the point where the semiconductor and metal meet, these depletion zones cause capacitive reactions. The capacitance value is controlled by the width of these zones. If there is a uniform distribution of dopants with density N in the space-charge region, then w = √Vfb – V. This means that C−2sc = 2 q𝜀𝜀0N (Vfb – V). The Mott–Schottky plot shows Csc −2 vs. V, which shows that there is a depletion zone. The picture lets you figure out the doping density and flat-band voltage.
Capacitance Associated to Defect Levels
Capacitive methods, like thermal admittance spectroscopy (TAS), are often used to find trap and doping flaw levels in active semiconductors. TAS is the most common method. It changes the number of electrons occupying flaw levels by sending and receiving alternating electrical signals. Because of Fermi level modulation, there is extra capacitance seen either in the depletion zone or in the semiconductor layer. If you look at the capacitance spectrum derivative and use the equation g(E𝼏)=−Vbi𝼏 qdkBT dC(𝼏) d𝼏, you can find the electronic density of states (DOS).
Surface Polarization and Capacitances of MHP
General Properties of the Capacitance of MHP
Mixed hybrid perovskite (MHP) has mobile ions, which means that strong charge builds up at the electrodes. Numerical models show that the ionic and electronic levels that build up at the contacts have special charge correction qualities. The strong buildup of ions and electrons at the perovskite/TiO2 contact was directly shown by Kelvin probe force microscopy (KPFM).
At low frequencies, a very big capacitance is seen in MHP, which is mostly caused by ionic processes. In Figure 6.10, you can see typical C-f graphs for MAPbI3 cells and different contacts. When it comes to capacitance in the dark, a peak at high frequencies and a big rise at low frequencies are common features. The low-frequency capacitance is very sensitive to the type of links used.
In order to describe the main capacitances, it is necessary to look at how they change with thickness. This is shown in Figure 6.11 using flat PSCs made of FTO/TiO2 (compact)/MAPbI3/spiro-OMeTAD/Au. The thickness of the MAPbI3 layer was changed from 400 nm to 200 nm. The capacitance changes with the thickness of the perovskite layer at different temperatures. The capacitance is taken from (a) the low-frequency plateau that is caused by the electrode polarisation and (b) the middle frequency plateau that is caused by dipolar polarisation.
When the frequency is around 1 kHz, the capacitance spectra show a peak whose value changes with the opposite of the thickness of the perovskite layer, as shown in Equation (6.11). This kind of capacitive input comes from the polarisation of the dielectric.
Finally, the fact that mobile ions are present in MHP says that strong charge builds up at the sensors. What kind of connections are used and how thick the perovskite layer is affect the surface polarisation and capacitances of MHP.
Metal-hydride perovskite (MHP) solar cells are being looked at because they are meant to be used in solar energy applications. The research shows that the low-frequency capacitance (<10 Hz) gets very high, which means that the MAPbI3 film width doesn’t really matter. This low-frequency dark capacitance is not related to mass dielectric relaxation; instead, it has to do with how electrodes are polarised. The capacitance–frequency plot shows a peak at high frequency, which is linked to the polarisation of the dielectric, and an overabundance of capacitance at low frequency, which is caused by electrode charge buildup.
The high-frequency peak seen in Figure 6.12b (C = 100 nF/cm2) is likely caused by the orthorhombic perovskite phase having the highest permittivity at low temperatures, along with the dielectric input from the aspiro-OMeTAD and TiO2 contact layers. When the temperature is changed, the different relaxation traits move along the frequency line, which is what you would expect from a phenomenon that is triggered by heat. Lead halide perovskite MAPbX3 crystals change phases at a temperature of about 160 K, going from having an orthorhombic shape to a tetragonal shape. When the capacitance spectra of fully perovskite-based solar cells are measured, this phase change causes the dielectric constant to rise by a big amount.
It turns out that the capacitance values show other things when the MHP device is lit up. Based on the amount of light, as seen in Figures 6.10 and 6.13, the capacitance goes up by a large amount. This kind of extra capacitance has been explained by the formation of a zone where most of the electronic carriers gather near the contacts. This model says that Cs will change depending on the voltage that comes after the next statement. However, new experimental results have shown that the voltage dependence that is exponential and has a slope of 1/2kBT does not always happen. In multicomponent perovskite absorbers, other dependences are seen that point to much more complicated ways for charges to build up and mix.
It is easy to see what happens physically when ions build up at the outside edges of a device that is measured in the dark and has TiO2 as the layer that moves electrons and Au as the layer that selects holes on the MHP. In the low frequency range, a flat peak in capacitance is seen that is about 1 µF/cm2. This is normal for a double-layer capacitance. The capacitance slowly rises to 10 μF/cm2 in devices with layers that can absorb ions. This can happen either by diffusion into the layer or by a chemical process (spiro-OMeTAD).
Complexity of Mott–Schottky Analysis
Using capacitive methods to find doping densities is hard because of mobile ions, background doping density, and a big low-frequency capacitance caused by wire polarisation. As an example of a problem with using Mott-Schottky (MS) analysis, look at Figure 6.15, which shows how devices usually work when CH3NH3PbI3−xClx is used as an absorbent. At low forward voltages, it’s easy to tell the difference between the depletion-layer capacitance Cdl and the surface capacitance Cs. At higher biases, the surface capacitance Cs takes over.
The flaw density that was estimated came out to be N = ≈1017 cm−3. This is pretty much the highest level that the MS method can be used in perovskite semiconductors. More capacitive systems hide the fact that much lower flaw counts are being extracted. Figure 6.15b doesn’t allow the MS analysis because it’s not possible to tell the difference between Cdl and the Cs that hides lower contributions. At common MS measure frequencies (1–10 kHz), Cs makes up most of the capacitive reaction.
It is possible to see a change between these two extreme situations (clear viewing of Cdl or blocking effect caused by Cs) when looking at formamidinium-based PSCs with MS. Because there are both fixed and mobile impurities in perovskite semiconductors, applying prebias before measuring capacitance may change how the ions are distributed and how much electrons are doped in the active layer. The MS shape that goes with it changes, showing a move between various sensitive modes.
Measurement of Trap Density
You can use Eq. (6.18) to describe the amount of defects in perovskite materials without thinking too much about it, since not all cases of extra capacitance are easily explained by traps. The spectra in Figure 6.16a show two steps in capacitance, which can be linked to the behaviour of flaw bands that are turned on at different frequency ranges. But in PSCs with oxide-selective contacts, the big low-frequency capacitance controls the electrical reaction and hides other capacitive inputs that come from flaws in the bandgap going through electronic changes. The blocking effect is less noticeable when fullerene derivatives are used as electron-extracting layers to lower Cs. This lets defect bands within the bandgap be seen. The solar cell with fullerene electron-extracting layers shows a clear peak at 104 Hz, which may be connected to responses from bulk defects.
Impedance Spectroscopy and the Equivalent Circuit
Model
Interpretation of Equivalent Circuits
When handling IS data, complex resistance and capacitance-frequency plots are often used to look at resistive and capacitive factors individually. When processes are far apart in terms of frequency, the complicated impedance plot shows different lines. To make a full physical model, you need to make a corresponding circuit that has resistances that come from dominant loss processes and elements that are spread out in a way that takes into account both serial and parallel carrier phenomena.
The complex resistance plot has two lines for high-performance devices with good extraction layers that are recorded under light. The device’s series resistance (Rseries) is the resistance of the lines and charge collectors. This can be read straight from the plot by measuring the distance between the beginning of the coordinates and where the high-frequency arc meets the y-axis. Some information about the capacitance contributions of the HF and LF resistances was given in Section 6.5.
It was suggested that both resistances came from the same physical source because they depend on voltage and light in similar ways. However, HF and LF resistances act in different ways for multicomponent perovskite absorber layers, which shows that the recycling processes are much more complicated. You can find the time constants for the equivalent circuit by multiplying ₻2 by R3Cg and ▽1 by R1C1. In Figure 6.18, you can see that 𝼏2 follows the trend shown by the HF resistance (R3) for MHP devices made with different active layer thicknesses. Since Cg is not connected to the resistance part R3, the time constant that goes with it can’t be thought of as a typical time for any physical process. Alternatively, 𝼏1 shows numbers that are not affected by light in both short-circuit and open-circuit situations.
The recombination resistance (Rrec) is a differentiable value that is given by Rrec = (𝼖j 𝼖V)−1. It changes depending on the recombination current and voltage. The HF and LF resistances seen in simple perovskite materials come from the same place, so the Rrec can be thought of as the sum of R3 and R1. The recombination resistance is also linked to recombination events happening at the surfaces, known as surface recombination. These events have average times of 0.1 to 1 second (s = Rrec,sC1), which were found for a number of different perovskite formulas.
The loss of photovoltage is connected to the decrease in the number of holes on the surface, which leads to a 0.3 V drop compared to the ideal radiation limit. It is possible for the dynamic behaviour of the perovskite layer to change a lot while the gadget is being tested. The IS analysis shows that the Rseries goes up with polarisation because the effect of iodine movement on the external surfaces changes the extraction layers. It is important to remember that looking at how Voc changes with light intensity in devices that have never been polarised by light bias or an external voltage shows that the recombination kinetics are typical of recombination in the bulk of the perovskite semiconductor, where ideality factors are close to 1. On the other hand, polarising the device with light or an applied bias lowers its ability to extract. This changes the recombination process from being localised in the bulk to surface recombination with the external contacts (ideality factor ≈ 2).
Overall, the impedance response has information from both of the inputs because the perovskite layer has a complicated dynamic response and the conductivity is a mix of electronic and ionic. The main reaction could be electric or ionic, depending on the measurement conditions (dark vs. light or applied voltage bias), and certain studies need to be planned to separate them. The low-frequency capacitance is linked to the wire when it is dark. You can find out about the intrinsic features of perovskite material and contacts by picking the device setup and test settings with care. To give you an example, you can get the most ionic current by choosing monocrystals with low doping density and measuring them in the dark with a low voltage bias. It’s important to be careful when looking at full solar devices because the effect of moving ions and the interaction with the outside contacts can make it harder to figure out how the electricity works.
Negative Capacitance Phenomena
Strange things like inductive loops and negative capacitances show up in the complex impedance plane of metal-hydride perovskite (MHP) devices. In some situations, the impedance response gets complicated when an arc of middle frequency and some inductive elements appear. Many systems, like Nb2O5, have a charge extraction contact that doesn’t work well. This is seen because it has a high charge buildup resistance. When this happens, the corresponding circuit needs to be changed to account for these new features. An inductor, an intermediate frequency resistance (R2), and a capacitance (C2) can also be added.
In many cases, it’s not clear where intermediate loops and arcs come from because they point to devices that aren’t working well and different comparable circuits may fit the data. When you simulate these circuits, they make impedance spectra that are typical of the PSC. These spectra are made up of two arcs and a buildup of low-frequency capacitance Cs. Negative capacitance effects depend on the surface conditions, and in composite contacts, very large inductive effects were seen. It was recently found that the drop in resistance that happens when the frequency is lowered is linked to electrical processes that happen at the chosen frequency.
Researchers have also looked into the link between ionic and electronic buildup at the surface and how that might affect the rates of electron transfer and recombination, which can help explain why some materials have very high capacitance and inductive behaviour. Later in Eq. (6.25) for a model that makes the inductive dynamics, we talk about how the internal voltage can relax on its own. The J–V curves fit well with the surface polarisation model, and the similar circuit analysis model in Figure 6.20 also fits well. This means that the ionic relaxation time r is about 20 seconds for all the different types of PSCs that were tested at room temperature.
Application of IS Model to Understanding of Memory Effects
By using the reversible chemical reaction of moving ions with outside contacts, memristors can be used to make electronic devices that can store information. A 2D perovskite device, like resistive random access memory (ReRAM), has two clear states: the ON state, which is efficient, and the OFF state, which is very resistant. The external voltage speeds up the change between these states by causing ion transport, which controls the movement of ions forward and backward to the reactive contact. This method works very well for cycling and repeating in a device set up with PCBM/Ag as the reactive contact and PEDOT:PSS as the non-reactive contact.
A dc voltage of 0.2 V is slowly applied to a device that is originally in the OFF state (I = 10−7 A), raising the recorded current by about 4 orders of magnitude over the course of 60 minutes. The big low-frequency resistance goes away when the device is turned on. This is because of an electrochemical process with ions at the contact that gets rid of the electronic barrier.
In the OFF state, the LF signal shows a capacitance related to ionic accumulation in the range CDL ∼10 μF/cm2. But when the conductive state starts, the capacitance rises dramatically to 10 mF/cm2 at 10 mHz, which is more than three times higher than normal double-layer and Helmholtz-layer capacitances. This shows that iodide ions are reacting chemically with the outside Ag surfaces, creating AgI.
Intensity-Modulated Photocurrent Spectroscopy
Another way to look into the features of Multi-Hertz (MHP) solar cell devices is to use optoelectronic methods. The photovoltaic external quantum efficiency (EQEPV) is the relationship between the amount of electricity that is collected (JE) and the amount of photons that hit a surface area () at a certain wavelength (𝼆). EQEPV(𝼆) = je(𝼆) j𝼙(𝼆) tells you the EQEPV of a solar cell. The photocurrent of the solar cell can be found by combining the EQEPV with the incoming spectral flux over the range of bands of light. Researchers use a method called Intensity-Modulated Photocurrent Spectroscopy (IMPS) to measure how the recovered current density changes when the modulated photon flux changes slightly over a wide frequency range, usually between 10−2 and 106 Hz. Then, Q(𝜏) = j̀(𝼏) is used to find the IMPS transfer function Q (6.23). The IMPS transfer function’s low-frequency limit matches the EQEPV from the differential spectral response method when the chopper frequency is zero. This is important to keep in mind.
Many earlier researches on IMPS of MHP have found that there are one or two arcs in the upper area. In some cases, three arcs have been seen. However, these unique time constants are usually linked to electronic transport traits. This is something that has been done in this field for a long time, ever since dye-sensitized solar cells were studied. Most of the time, the arcs in the upper area are thought to be caused by the movement of ions or electric carriers within the perovskite.
In real experiments on MHP, it is hard to come up with a good explanation for the spectra that are seen, besides using ideas that people already have. The time constants seen in IS are related to how the resistances are connected to the capacitors that go with them, as shown in Figure 6.18. So far, though, it’s not clear whether the resistances are caused by bulk and surface processes or by ionic or electronic nature. So, getting separate IS and IMPS bands and a description that makes sense and shows the key resistors and capacitors in the system is a very important first step. The spectral properties of IS and IMPS are different and don’t always have anything to do with each other. Also, the time factors don’t match up because they are caused by different RC couplings.
Some progress has been made in this study so far. In the early work of Potkett et al. [91], they correctly said that the high-frequency arc was caused by the time constant that was made up of the cell’s series resistance and geometric capacitance. The corresponding circuit in Figure 6.23 [73] makes it clear that the spectral qualities are different and don’t always have anything to do with each other. Also, the time constants don’t match up because they are caused by different RC couplings.
Dynamic Response in Time Transient Methods
Time Transients of Photovoltage and Charge–Discharge Methods
The return of dark polarisation in perovskite semiconductors (PSCs) is due to complicated ionic and electronic relaxing events at the device’s outside surfaces. Open-circuit voltage decays were used to find early proof of slow surface polarisation effects. Because of the buildup of ions at the junction, the photovoltage transition lasts a lot longer than it did under previous short-term lighting. This answer is because there aren’t any mobile electronic providers around. An electrical model for measuring J-V connects hysteresis to the polarisation of the surface, which is shown by a kinetic equation for the voltage across the contact.
The relaxing time measure should show how the ions move on a tiny level after being freed from the contact and redistributing themselves evenly. Weber and his colleagues show more proof that surface polarisation changes slowly. Kelvin Probe Force Microscopy (KPFM) is used to get the time-dependent carrier spread. Only 10 microseconds of light were needed for a localised interfacial charge to form. The interfacial charge can stay for more than 500 ms after the light is turned off, though, which makes the photocurrent transient take a long time to respond. When the surface charge distribution is taken away, the reaction is slow. This shows that the ionic and electronic relaxation processes at the device’s edges are the most important.
Charge–Discharge Methods
Putting a voltage step on a sample and keeping track of the charge it causes in a reference capacitor is one way to measure charging effects, such as dielectric polarisation. This method was used with thick MAPbI3 pellets touching wires made of Au that had been evaporated. The results showed polarisation charges of 1–10 nC/cm2 for voltage steps below 5 V, which proved that there was too much capacitance in the dark.
Significance of Surface Charging in MHP
Several methods are used to study the surface charge and discharge events at the contacts of the perovskite semiconductor (PSC). Like in classical asymmetric trapping-detrapping, the speeds of these processes are different in MHP. Under an electric field or light, ions from the bulk of the perovskite material are quickly provided and moved to the contacts in milliseconds. An electric potential is made when they connect with the surfaces. Ions can be released more easily (PCBM) or more slowly (metal oxides). These time-domain methods add to what has been seen of a large interface capacitance. Ions are seen as a big surface capacitance in the low-frequency domain.
Conclusions
Many approaches have helped us learn more about how MHP devices work, but it is still hard to separate the ionic and electronic conductivities. No one knows yet where the idea of increase under lighting comes from. For low-frequency reaction and long-time dynamics, it is very important to figure out the fundamental features of the perovskite material and connections. IS and IMPS techniques help separate things better.
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