Theory
This part is about the science of solar cells and is meant for both students and people who aren’t experts. It gives easy-to-understand starts to Sections 5.2 and 5.3 without giving detailed explanations like in books by Würfel or Nelson.
Power-Conversion Efficiency of a Solar Cell
The goal of research into solar cells is to make them more efficient by making one that keeps its best features at both the module and square kilometre levels. To do this, processes that are recorded in microseconds must be able to be repeated over and over again in the solar cell module for decades, giving the power-conversion efficiency (PCE) that was measured at the start.
The efficiency of the solar cell is a very important thing to know about it. There are different ways to figure out the PCE, which is the percentage of the solar power that can be turned into electricity. These include trial-and-error methods, methodical optimisations, and strategies that are based on knowing how things work and how long they take. The electrical power density is equal to the product of the current density (J = I A, where A is the amount of light from the sun) and the voltage (V).
When some of the sun’s radiation is filtered out (mostly absorbed), the AM1.5G spectrum is left behind. This is solar radiation, which comes to Earth’s surface as broad-spectrum temperature radiation. When you add up all of these wavelengths, you get Isolar, which is 100 mW/cm2 (1 kW/m2).
Before we look at the electricity that the solar cell provides, we look at the current density J. The inner photoelectric effect is what makes our solar cell work. In this effect, a solar photon moves an electron from occupied border orbitals to unfilled orbitals, or from the valence band (VB) to the conduction band (CB). It is thought that the electron and the hole, which is the only positive charge left in the valence band (VB), can move around and make a photocurrent. So, each photon that is received can only make one pair of electrons and holes, unless multiparticle processes happen and use the energy of a photon to make more than one pair of electrons and holes.
Not every ray from the sun can be received and turned into an electric current in a real solar cell. The amount of photons that are received and changed is known as the incoming photon-to-current efficiency (IPCE) or external quantum efficiency (EQE), and it changes with 𝼆. You can write the current density as J = e ∫ √ 0 EQE(𝼆) solar(𝼆)d𝼆.
It’s also known as “efficiency,” but EQE is not the same thing as PCE. EQE and J lose energy because light hits them and bounces back, absorbs, or passes through them. Also, the internal quantum efficiency (IQE), which shows how many of the received photons add up to J, might not be unity because of problems with collecting charge carriers.
It’s harder to figure out the leftover voltage because you need to use both thermodynamics and semiconductor physics. The next part will give a simple description of what happens when these methods are used.
The Ideal Solar Cell: Shockley–Queisser Limit
The semiconductor material(s) used in a solar cell are the main reason why it makes energy when light hits it. The excited electron stays that way for a while before it calms down and combines again with the hole. This makes the electron-hole pair store energy. Since the electron is now at a higher energy level than it was before, most of this energy is potential energy. The border orbitals in a semiconductor are made up of a range of valence states and conduction states, which are known as bands. There is also a region between the bands that can’t carry electricity, which is called the bandgap energy (Eg).
It can only take in photons with more energy than Eg. This makes electron-hole pairs that quickly heat up to the band edge. This means that the potential energy is close to Eg, no matter what the energy of the photon that hit it is. During the thermalisation process, extra energy is turned into heat, which limits the highest photogenerated voltage (PCE).
This “bandgap energy” can’t be fully turned into electrical energy because of how thermodynamics works in solar cells. The electricity has no entropy, but the electrons and holes in their bands do have some entropy. The part that doesn’t have any entropy is called electrochemical energy, and it can be shown by the electrochemical potential or a quasi-Fermi level (QFL).
How far apart the QFL and band edge are from each other depends on how many charge carriers there are (n for electrons and p for holes). There can be a higher voltage when there are more electrons and holes in their respective bands. Due to the fact that entropy conservation means that the energy flow scales with temperature T, T has a direct effect on the voltage.
To sum up, the voltage that is made by light in solar cells is mostly because of the semiconductor material(s) that are used and the potential energy that is kept in the pairs of electrons and holes.
If you follow the standard testing settings (STC), the PCE of a solar cell is found by taking the highest current density (Jmax) and the maximum voltage scaled with energy (Eg). You can find the maximum current density (JSC = Jmax) and maximum voltage scales with Eg, but you can’t get to them under STC. Figure 5.3b shows the highest open-circuit voltage (VOC) that can be reached as a function of bandgap.
It is not possible to get the biggest current and voltage at the same time because the given power is zero in a short circuit (0 V, JSC) and an open circuit (VOC, 0 mA). The MPP is picked as the highest power point, and the fill factor FF = VMPP JMPP JSC is used to find the PCE of the solar cell. The PCE vs. bandgap is then found by plotting the Shockley–Queisser (SQ) limit.
For the best PCE of about 33%, the bandgap should be between 1.1 and 1.4 eV. For smaller bandgaps, the PCE goes down because the voltage goes down because of higher thermalisation losses. For higher bandgaps, it goes down because the current goes down because of higher transmission losses of the wide-gap semiconductor. With a bandgap of about 1.5 eV, the SQ limit for FAPbI3 is 32%.
A lot of information is given about the science of perovskite solar cells, such as their efficiency, open-circuit voltage, and recombination. It comes from the NREL efficiency chart, and the perovskite point (FAPbI3) comes from Jiang et al. The red circle shows where the current NREL chart record of 25.5% is likely to be found.
Radiative Limit, Reciprocity, and Detailed Balance
It’s important to know that the SQ limit is a type of the radiation limit of a solar cell in order to understand light readings. Let’s say we turn on the light but leave the solar cell’s circuit open. This means that the photogenerated electron-hole pairs can’t be taken out. Instead, the concentration of them grows until the rate of recombination meets the rate of charge carrier generation. Why is this? The recombination rate changes based on how many electrons and holes are available. For the device’s voltage to hit VOC, the solid angle and spectral distribution of the photon flux must get bigger.
Radiative recombination is the opposite of absorption and can’t be avoided because of this. When there is a sudden start to absorption (SQ case), radiative recombination leads to a maximum VOC that is about 0.27 V lower than Ege, where Ege = 1.5 eV. In real life, the start of absorption is not sudden; it is spread out. This is because absorption is weaker near the bandgap because there are fewer possible states. A typical absorber layer thickness will not be enough to fully soak up light that comes in with an energy close to the bandgap energy. On the other hand, photons with a little less energy than the bandgap can also be absorbed because of something called subgap states. The number of these states tends to decrease exponentially away from the band edge. This makes what is known as a “Urbach tail” in the absorption spectrum.
If the absorption doesn’t start all at once, the things we’ve talked about so far still apply. The real absorption spectrum is all that needs to be used to (re)calculate the radiation limit. The principle of precise balance can be used to guess the light spectrum in this case. This principle says that when everything is balanced, the amount of photons that are received and released is the same at all wavelengths. Equilibrium means that there is no light and no electricity is applied. This means that the photon flow that is received comes from the thermal background radiation, which is around 300 K.
For this reason, a wider absorption start moves the emission spectra to lower energies and raises the total emission strength. This is because the thermal background radiation increases exponentially as energy decreases. When we compare this to the SQ case, we can say that we made it so that recombination mostly happens at lower energies than the main absorption (like in materials with Stokes shift). So, for a given bandgap and JSC, this means that VOC (and PCE) is smaller than in the (ideal) SQ case. So, the more general radiation limit is always less than the SQ limit, and it’s not good to have absorbers with a lot of different tail states. The gap between the radiative and SQ limits is very small for MAPbI3, which has an Urbach energy of 14 meV, which is about the same as c-Si’s 11 meV.
Non-radiative Recombination and Role of Contacts
There are three main types of recombination that happen in real solar cells: Auger recombination, Shockley–Read–Hall (SRH) recombination, and Surface recombination. Most of the recombination in these cells is not reactive. Auger recombination is a natural part of semiconductors. It is especially important in indirect semiconductors because recombination at the bandgap needs a big amount of momentum transfer that the released photon can’t do. It usually doesn’t matter for PSCs when the sun is shining, but it can slow them down when the sun is intense or change the results of tests when a laser is used.
Many mistakes can happen in the bandgap, which is also known as the trap, and these mistakes can cause recombination to happen. This is called Shockley–Read–Hall (SRH) recombination. RSRH = np − n2 i𝜏p(n + n1) + 𝜏n (p + p1) (5.9) shows the rate. For a p-doped semiconductor where the lifetimes of the electrons and holes are the same, Eq. (5.10) can be shortened to RSRH = np 𝼏pn + 𝼏n p.
There is a speed S for surface recombination that is usually written as Rsurf = S(n − n0) (5.11). In a solar cell, the absorber is close to the electrical contacts so that photogenerated charge carriers can be easily extracted. So, S is affected by the features of the contact layer. To get the best PCE, you should avoid this losing process and choose your partners carefully. This can be made easier by a semiconductor that has large energy adjustments for minorities or by a back surface field that has a lot of electricity on it. Passivation methods can be helpful if the source of S is mostly surface flaws in the perovskite semiconductor itself.
All of the recombination processes we’ve talked about can lower JSC and FF when they are competing with charge extraction (CE), which means that charge moves to the electrodes at the same rate and for the same amount of time. The VOC is set by these recycling processes because all photogenerated charges join when the circuit is open. We can write the total recombination rate as R = ∑ Ri when several recombination processes are going on at the same time. A radiation yield can also be written as 𝛾 = Rrad ∑ Ri (5.12).
Because their spectra and outputs control VOC, luminescence qualities are important for solar cell materials and devices. We will learn more about luminescence readings in Sections 5.2.3–5.2.5. They should help us figure out how potential our absorber material is in a solar cell.
Determining Efficiency and Characterizing
Recombination
This part talks about common electro-optical methods used to characterise perovskite solar cells (PSCs) and how they can be used in processes that limit performance. Focussing on real and broad issues rather than specific theory details, it talks about the underlying beliefs and problems.
The Current Density–Voltage (J–V) Curve
Most of the time, a solar model is used to measure the current density-voltage (J–V) curve of a solar cell in order to find its PCE. To do this, you need to correctly measure the power coming in and going out, as well as the brightness of the light and any variations from the normal AM1.5G range. Finding the right JSC should be easy if you know the IPCE of the test device and multiply it by the AM1.5g photon flux spectrum. Then, you can integrate this over 𝼆.
It’s important to record a stable PCE for Perovskite Solar Cells (PSCs) because the J–V graphs can show recurrence. It is thought that JSC changes linearly with light strength. This seems to be true for PSCs but not for all types of solar cells. When testing the IPCE, there needs to be background lighting.
To find the electrical power density, you need to take the observed current I and figure out the current density J. This is done by correctly defining the lit area A. An opening (mask) is used to block light from some parts of the device. This is especially useful when measuring small devices with a lot of relative error in area and edge effects. When voltages are close to VOC, the dark current becomes important, and the aperture doesn’t define that area. This means that a measurement with a mask is usually fine, but not ideal.
To find the PCE, the MPP is used as the output power after the J–V curve has been found, as shown in Equation (5.7). However, this method is based on the idea that the device is pretty much in a steady state at all voltages during the I–V measurement’s voltage range. The J–V graph for PSCs shows hysteresis, which is caused by a strong influence on the voltage scan rate and direction. That’s why it’s best to do I–V studies at slow scan speeds, like 10 mV/s, and keep an eye on factors like VOC, JSC, and the MPP for a while. It is now normal for PSCs to report a stable power flow.
Determination of the Bandgap and the “Voltage Deficit”
The voltage deficit (VOC) is an important number in the study of semiconductors because it shows how well recombination works and how it is described. It is important to get an exact reading of the bandgap energy (Eg) because the absorption doesn’t start suddenly and the light might be spread out. To find the bandgap, you need to know how the material(s) work electrically. If you have a semiconductor, you can define bands because the valence electrons are strongly spread out. You can then use the classical bandgap to find the absorption coefficient close to the bandgap energy (Eg) by looking at the shape of the total density of states.
You could also plot 2(𝛀) because 𝛀 changes a lot more than h𝼈 at the start of absorption and look for a line. The Tauc plot is the name of this graph [22]. Eg is found where this line meets the abscissa. But it’s hard to tell what kind of bandgap it is just by looking at a Tauc plot. To find out what kind of bandgap it is, you should use other data or theory.
It’s easy to see the bandgap in emission because the luminescence (photoluminescence [PL] and electroluminescence [EL]) that happens when electrons and holes recombine at the band edges is pretty narrow, and the energy of the maxima is close to but slightly higher than the bandgap that was found from absorption. It’s easy to find the peak frequency in PL, but it’s not so easy to figure out what it means because optical effects like outcoupling and reabsorption can change the material’s “intrinsic” PL.
The bandgap is harder to find and define when the material is not a simple semiconductor. Excitonic transitions are important for organic semiconductors. There are two types of gaps: visual (which are related to excitons) and electrical (which are related to free charges in the highest filled molecular orbital [HOMO] and lowest unoccupied molecular orbital [LUMO]). The Tauc plot is not a good choice for excitonic transitions. Instead, you should use peak maxima or absorption onsets to show the optical gap of such a material. It’s not enough to just show the peak value in molecular systems like organic semiconductors because absorption and emission can be greatly moved (Stokes shift).
When it comes to perovskites, like Br-based perovskites and lower-dimensional perovskites like 2D perovskites, excitonic changes are important. The absorption traits of these materials are strong, like excitons, and the light emission is strongly moved with respect to the absorption start. When there is an indirect bandgap, the absorption event needs a phonon to keep the momentum stable. If this phonon’s energy is not very small compared to the photon’s energy, the bandgap found in a Tauc plot could be changed to account for this (often unknown) phonon energy. It has been seen that Cs2AgBiBr6 has indirect transition properties, with phonons absorbing and emitted, giving rise to Eg = ETauc a/e ±Ephonon = 1.95 eV.
It is said that visual properties of what is basically the same material are very different, and these differences have a big effect on the maximum efficiency. When things are this complicated, it’s helpful to compare them to what we know about Eg for that material from theory, such as by doing density functional theory (DFT) calculations. DFT, on the other hand, often gives bandgap values that are off by a few hundred meV.
Figuring out Eg isn’t always easy, and voltage differences reported in different sources might not be the same. Taking the transition point of the EQE would be a good idea for materials with a sharp absorption start, like 3D lead-halide perovskite. The non-radiative voltage loss of a device is easy to measure with this bandgap. This is the most important quality factor when comparing devices with similar perovskite materials and different designs. It looks like the Urbach energy is about the same for a lot of lead-based perovskites. The radiation limit VOC,rad (Eq. 5.8) is what is meant instead of Eg (“voltage deficit”). This limit can be found very accurately.
Electroluminescence
You can measure the non-radiative VOC loss (ΔVOC,non-rad) by checking the photon yield (PL) of a device when it is exposed to sunlight and the circuit is open. Monochromatic excitation is often used to keep emission and excitation from overlapping in the same spectral range. To find the external EL yield (EL), you can also drive a current through electron injection and hole injection. 𝛾EL = released photon flux Iinj−e is used to find the external EL yield. ΥVOC,non-rad is found by taking the number where Jinj = JSC. This method works well for solar cells based on MAPbI3. EL shows all the different kinds of non-radiative recombination (SRH, surface) that happen in the device. When compared to EL, PL returns can give you more information.
Photoluminescence
It is possible to measure the amount of light yield without touching the sample using photoluminescence (PL) yields. You can use this method on pictures and gadgets where you need to tell the difference between internal and external returns. When you know PL and the bandgap (or VOC,rad), you can figure out the system’s internal voltage, which is the device’s open-circuit voltage. This “voltage” can be found even in films that don’t have connections. It shows the average QFL breaking in the picture.
When you directly compare the PL of a device and a film, you can see the losses caused by the contacts. The PL yield of a film is mostly limited by non-radiative bulk or surface recombination. In a device, nonselective contacts can cause interface recombination, which can lower PL even more. For two recent cases, this is shown in Figure 5.9. In Figure 5.9a, the implied VOC is almost the same no matter what the stack is made of. On the other hand, in Figure 5.9b, the implied VOC of the triple-cation solar cell is lower than that of a perovskite film. This is because the surfaces and a material that isn’t completely passivated cause recombination. You can turn the J–V curve into a power–voltage curve by comparing it to the fake J–V curve, which is made from VOC vs. light strength. This shows how the losses affect the MPP.
You can figure out the internal voltage by looking at PL, but the quasi-Fermi level splitting might not be constant in a film or device; it might have slopes that move towards the surface. This happens when there is a lot of surface recombination and the electron-hole conductivity is very low. This means that the charge carrier flux to the electrodes needs a lot of pushing force through gradients in the QFLs. If you compare PL and VOC (or EL) for a device, you can already learn about surface recycling as a limited process.
Usually, PL depends on how bright the light is, which should be mentioned when giving numbers for the PL yield PL. Higher PL is good for increased VOC because it means less non-radiative recombination. PL quenching studies are often used to test charge transport layers (CTLs) or surface changes, though, and a better quenching rate is thought to be a good thing. It is said that this shows that the charge extraction is working well. The tests are done on stacked stacks that don’t have any electrical connections. In a steady state, all the photogenerated charge carriers would rejoin, and the PL cooling records this recombination. As a result, more non-radiative recombination means greater quenching, and the VOC is likely to be smaller than for a reference sample with less quenching. If getting charges out of the reference device or even breaking up excitons is slow, then greater cooling means that charges are being taken out better, which increases the photocurrent and FF of the solar cell.
Transient Photoluminescence
In order to measure how fast photoluminescence (PL) fades in a solar cell, transient photovoltage (TPL) is used. It can be done on single films, layered stacks, or whole devices, and is recorded as a function of time after a short laser light flash. In TRPL, the behaviours of processes that change the emission probability are captured. This probability is mostly thought to directly map charge carrier concentrations. Time constants, which are thought to show how long charge carriers last, are found by fitting a multi-exponential decline to an observed pulse. However, it’s not easy to figure out what a multi-exponential fit means when it comes to a number of time constants.
When it comes to TRPL on a single film, we can say that faster decay means faster recombination. We would have a pretty even charge distribution in the absorber and one main (non-radiative) recombination path that could be described with a minority lifetime bulk in the simplest case. After that, TRPL should look like a single exponential decay, with the decay constant being the bulk lifetime (PL ∝ nphoto ∝ exp (− t𝜏bulk)). If surface recombination is happening, 𝼏bulk can be changed to a useful lifetime 𝼏eff using the following equation:
1.
𝜏eff = 1 𝼏bulk + 1 and 𝼏surface = 1 𝼏bulk + 2S.
But TRPL data on perovskites usually behaves in a more complicated way, so it’s best to use multi-exponential or extended exponential functions that give you a number of factors. Since there isn’t a physical model for this kind of behaviour, it’s not clear how to understand the different time factors, which makes the fit less useful.
One big problem with TRPL is that it isn’t usually done as a small-signal perturbation method. Instead, a bright laser pulse is used on a sample that isn’t lit up. To make sure that a fit with Eq. (5.16) is correct, should stay the same (for example, it shouldn’t change a lot when the number of recombination centres changes). Also, tests should be done with different levels of excitation (which changes the starting charge density right after the light pulse n(0)) to see if all the data can be fit with the same and 𝼏 (Figure 5.11a).
When multiple stacks are looked at, things get even more complicated. In most cases, there is a double layer with a CTL next to the perovskite absorber. Most of the time, a TRPL test on this kind of stack should show fast PL cooling, which means that charge transfer is good. The reasonable thought is that the charge will not add to the PL of the absorber after it has been moved. But it can’t give charge carrier-selective information, which would need more specific knowledge about the link than just how it works electronically.
To sum up, TRPL is a useful and strong method. But, the level of excitation should be made clear, and extra information like steady-state PL and TCSPC should be used to learn more about how charge transfer to the CTL, interface recombination, and bulk recombination work together in the perovskite.
Electrochemical Impedance Spectroscopy
EIS is a strong way to study electrical and electrochemical devices. It focusses on figuring out processes that happen over a range of timescales by looking at how the device responds to changes in frequency. The reason for this is that EIS can be done with different amounts of power and light. The answer we get is a complex resistance (the impedance) Z or admittance 1Z that tells us about the system’s reactive (capacitive or inductive) and resistive behaviour at each frequency. If the resistor is present, the current responds instantly to the voltage signal (this is called a “in-phase” component), but if the reactive parts are present, the current responds later (this is called a “out-of-phase” component).
The hard part is figuring out what these numbers mean. The main question is: What do the numbers R and C mean in a real sense? For dye-sensitized solar cells (DSSCs), models have been made that let us get information about how charges move, recombine, and shift in and at TiO2 as well as how they interact with and move through the electrolyte. You can tell them apart by the frequency and voltage ranges that show signs of certain processes. For PSCs, however, there is not yet a fully formed model that can be used to understand EIS data.
If you want to use EIS to explain device data, here are some things you should think about: To check for repeatability, stability, and self-consistency, the voltage could be swept up and down, for example. This is especially important when higher voltages show “odd” behaviour. Charge movement in PSCs is thought to happen on time scales smaller than µs. This means that EIS, whose highest frequencies are around MHz (1 µs), can’t resolve it. On the ns time scale, charge input into CTLs can be found.
EIS data and J–V data should always be compared and the extra value should be carefully looked at. Especially when looking at EIS data from two devices that are at different voltages and only one arc can be seen, this is very true. Since that’s the case, this arc usually depends a lot on voltage. You can get information from the geometric capacitance and the differential resistance of the J–V curve.
PSCs often show characteristics at low frequencies (less than 100 Hz) that have to do with how well the material conducts ions. If you think of capacitance as an RC element, it changes a lot depending on the light and can reach huge numbers. People have wrongly thought that these traits are a huge dielectric constant or a buildup of very high electrical charge levels. What these traits really mean is that the perovskite is a mixed conductor of ions and electrons.
Finally, EIS can’t be thought of as a normal way to describe something in order to understand how PSCs work. Instead, work needs to be done to improve similar circuit models and create computer models that better match the physical traits of the perovskite mixed ionic–electronic conductor.
Transient Photovoltage Decay and IMVS
The TPV decay test finds out how much the voltage drops after a small-signal perturbation light pulse. This tells us about how recombination works by figuring out how long charge carriers stay in the system. This signal is usually fit by a single exponential function, and it can happen again and again at different light levels. It is often used with a charge-extraction measurement to make a graph of TPV vs. mean charge density. Intensity-modulated photovoltage spectroscopy (IMVS) is a similar frequency-domain technique that should give you time values that are the same as TPV.
Drawing a graph of vs. extracted charge or light strength can show the recombination order for charge carriers that are produced by light. For thin-film solar cells (PSCs), it’s hard to figure out what the time constants from TPV/IMVS readings mean because voltages are recorded as a change in potential between two external contacts. This means that other processes, like the electrodes’ charging and releasing times, are involved. The high capacitance of the perovskite film between the electrodes makes this a very big problem.
To find TPV, one can figure out the RC time by using geometric capacitance and resistance. The RC time can then be found as a differential resistance at VOC for a certain light strength. It is assumed that 𝼏 = RCgeo plotted vs. injection current will go down as current goes up. R is the diode’s recombination resistance. But it’s hard to tell how much of the charge that isn’t caught is actually removed and where it comes from.
In conclusion, the typical TPV experiment is not usually a good way to figure out how recombination works in PSCs. If you take measurements at higher light levels or look at TPV in a more complete way, you might still learn something about charge carrier lives.
The Ideality Factor
The diode ideality factor (nID) is an important quality factor in perovskite solar cells because it tells us about the main recombination processes by using the recombination order. But figuring it out can be hard, and what it means is more complicated than most people think. This is the reason why some perovskite writing has a hard time making sense of things.
The dark J–V curve in the exponential region can be used to find the diode ideality factor (nID). But parasitic resistances could hide this area, which could cause ideality factors to be too high if these resistances are not taken into account. To keep this from happening, you can find a differential ideality factor that changes with voltage. The number goes up as the voltage goes down and up because the shunt resistance and series resistance limit the voltage and current, respectively.
To be even more sure of the nID that was found, tests that depend on temperature should be made. In the organic and perovskite fields, it is generally thought that a nID of 1 means a “bimolecular” recombination process and a nID of 2 means defect-assisted recombination (SRH). But things are much more complex than that. The meaning that was given only works in certain situations, and a clearer distinction is needed.
When nID = 1, radiative recombination takes over, which directly means that VOC is getting close to the radiative limit. It is correct to think that nID = 2 means SRH recombination. This is true for the unique case of recombination in the device’s depletion region (i.e., the bulk perovskite; normally, it is thought that the perovskite is intrinsic), which means that n≈p. When recombination happens near the contacts or there is a lot of doping in the perovskite, nID goes down and can get close to 1.
nID =1 forVOC ≪ VOC,rad shows the situation that was just explained. One special case is surface/interface recombination, which can lead to nID = 1. This can happen for example with a badly selective electrode, like PEDOT:PSS in PSCs.
change from 2 to 1 in the nID value with VOC:
If VOC gets close to VOC,rad, this means that SRH has changed to radiation recombination. If VOC gets close to VOC,rad, this means that SRH has changed to surface recombination. It’s possible for nID to be less than 1 when VOC reaches its maximum value in highly nonselective contacts. nID >2 could mean that trapped charges are recombining through a spread of tail states after any resistance effects have been ruled out.
Aside from electrical measurements (J–V curve, VOC), nID can also be found using electro-optical measurements (EL), where nID = s+1 and s is the slope of the double logarithmic plot of EL vs. current. You can also plot the number of photons released vs. voltage and get a nID for the radiative recycling process, which is 1 for PSC.
Space Charge-Limited Currents
A common way to measure flaw levels in perovskite single-carrier devices (PSC) is to look at the J–V curve and find different transport limits. This is called space charge-limited currents (SCLC). The theory is well-developed for figuring out trap densities and ranges and mobilities, but the stated data for PSC isn’t always clear because there isn’t enough information about how well the method works. Some things to think about are whether the contacts are Ohmic, whether the J–V curve point is symmetric at 0/0 for a symmetric device structure, and whether the voltage ranges are big enough to fit different power-law equations. When it comes to layers, SCLC and TCLC have clear relationships with layer thickness. In the Ohmic region, leakage currents often rule, which changes the doping densities and characteristic voltage used to figure out trap densities. For perovskite single-carrier devices, the hysteresis and repeatability of second readings are very important. This is because devices with only metal contacts have bad “poling” effects because mobile ions change the charge injection properties.
Recombination in Perovskite Solar Cells: What
We Know
In this last section, we want to address the different causes of recombination in
PSCs based on the fundamentals introduced in Section 5.1. We intend to give a
5.3 Recombination in Perovskite Solar Cells: What We Know 153
brief overview here, but detailed description can be found in numerous reviews
elsewhere.
Intrinsic Properties of the Perovskite Crystal
As we talked about in Section 5.2.4, the non-radiative recombination rates depend on the fundamental features of the lead-halide perovskite crystal and its defect physics. These are low because the crystal has high PL yields and a low voltage deficit.
Relatively High Absorption and Fast Radiative Recombination
If you raise the rate of radiative recombination or lower the rate of non-radiative recombination, you can get high PL results. As a result of their high radiative recombination coefficients, lead-halide perovskites have high absorption coefficients that are close to their straight bandgap. This feature makes it possible for thin layers with non-radiative lifetimes of 10 μs and short diffusion lengths. Non-radiative recombination is the main process in organic semiconductors (OSCs), which causes large inherent voltage losses. This doesn’t have to happen when output gets close to that of the pure material, which is where absorption takes place. When it comes to PSCs, a low Urbach tail lets the radiation limit be close to the ideal (SQ) limit.
Shallow Defects and Defect Tolerance
The Shockley-Read-Hall (SRH) formula says that the energy of the trap state is a very important factor in how likely it is that defects will help atoms come back together. It works better as a recombination centre when the trap energy is close to the midgap. Because of this, midgap traps should not be present in optical semiconductors.
It has a number of inherent point flaws that cause shallow states, especially for halide gaps, which leave behind “dangling bonds” or “undercoordinated Pb.” The reason for this preference for shallow states is the way the conduction and valence bands of PSCs are made up of Pb(6s, 6p) and I(5p) orbitals rubbing against each other. Antibonding valence states are intended to make materials that can handle flaws, and broken bonds would create energy states within the bands or close to the band edge, which are known as short traps.
It is best to keep the flaw number NT (Eq. 5.10) as low as possible so that SRH recombination doesn’t happen too often. It can’t get close to 0 because thermodynamics says that there will be a natural equilibrium defect density. This density depends on the formation energy being low, which means that Schottky defects have a high NT. A lot of the time, deep flaws like iodine interstitials have high formation energies, which could be higher than the perovskite’s own formation energy from its parts.
For defects to become dynamic, they can’t be thought of as fixed. This means that they are harder to combine than static flaws. Self-healing can happen because of entropy and a low activation energy for the spread of flaws.
High Dielectric Constant
At first, people had different ideas about MAPbI3’s static dielectric constant (𝼀r) because tests were affected by mobile ionic charges. But a number of about 30 has been set, which is partly due to the makeup itself. This number is greater than that of other artificial and organic semiconductors. A higher dielectric constant makes it easier for the material to block the Coulomb potential of charge. This makes it less likely that a charged flaw site will pick up a charge with the opposite sign. Changing 𝼀r, on the other hand, can’t make recombination rates go down by a lot. Ionic charge that is mobile can screen trapped electric charge even more. It’s not completely clear what role this charge plays in promoting or reducing recombination.
Low-Frequency Lattice Phonons
We need to know the capture cross section 𝼏 in Equation (5.10) and Figure 5.14a in order to understand how the recombination process works in perovskite solar cells. When electrons are captured, energy is moved to phonons, which causes many phonons to be released. If certain conditions are met, approximations can be used to find ₻ and 𝼏SRH.
There must be more phonons for a shift to the trap level when the phonon energy is smaller. This means that a higher acceptable trap density is reached. As you move away from midgap, this difference becomes more noticeable, which means that 𝼏 depends a lot on the trap energy. The SRH data are added on top of this affect, making it more sensitive to the catch energy.
It would be good to make semiconductors with low phonon energies, which could be done with heavy elements. The rough model is general, but it’s not very good because it doesn’t include flaw (atom)-specific features. Having a phonon energy of 16.5 meV doesn’t make a big difference in 𝼏SRH. Perovskites have a high SRH because they are nanocrystalline and have many areas that can offer a wide range of flaw states.
It’s possible to improve the rough model by adding more local phonon modes and anharmonicity, which could be important for perovskites. A new study that started from scratch found that low non-radiative recombination is caused by low-frequency phonons and a weak overlap of electron and hole states. The writers see this as a breakdown of SRH because defect recombination depends less on the energy of the trap state. Future theory studies will try to figure out how electrons and phonons interact in perovskites.
Further Explanations for Reduced Recombination
Some ideas about why recombination rates are low in perovskite solar cells are ferroelectric polarisation, ferroelastic regions, the Rashba effect, and big polarons. It is important to make sure that these answers fit with the theory described in Section 5.1. They should cause less non-radiative recombination, more brightness, and voltage-operated current (VOC). Be careful with arguments that are based on the fact that charges that are spread out in space are less likely to mix up again. They might explain why charge separation and collection work so well, but they don’t directly cause higher charge carrier amounts at VOC. High radiation rate constants are wanted to control recombination as a whole, as long as charge extraction works well. When talking about changed recombination rates, the order of magnitude is also important. It is important to make sure that the expected features, which only apply to monovalent cations, are correct by looking at changes in the actual data, like the voltage deficit.
Impurities
Impurities are a major cause of flaws and dopants in semiconductors, which makes it hard to figure out what Ge or Si’s natural qualities are. To make and clean electronic-grade silicon plates without these impurities, it takes a lot of work. On the other hand, perovskite compounds, especially organic salts, are not as pure. More impurities and liquid leftovers are added during solution processing, but the high luminescence outputs show that these impurities can be tolerated well. A lot of research has been done on the good effects of additives like potassium or rubidium, but not as much on the bad effects of minor impurities. Some metals, like Bi, have been found to act as recombination centres. For example, Bi replaces Pb in the perovskite lattice, which lowers PL yields and TRPL decay times. It also lowers VOC when added at a ppm concentration. In MAPbI3, iron has a similar effect, but it is not as bad as it is in silicon. Recombination centres have also been found in metal traces that come from contacts, like Au.
Grain Boundaries
As we know from standard semiconductors like Si and GaAs, grain boundaries are often thought to act as recombination centres. But compared to bulk flaws, we don’t know as much about how recombination works on surfaces and at grain boundaries in perovskites. Theoretically, recombination is stronger at grain edges, but it depends on the unknown atomic surroundings.
From a scientific point of view, the role of grain boundaries is debated. Device data or PL measurements are often used to find support for or against increased recombination at grain borders. This lack of clarity can be explained by the fact that different formulas and ways of production could lead to different determinations of grain surfaces, and that many relationships may not be causal.
To get a better sense of how grain boundaries and the nanoscale affect things, high-resolution methods are used to separate recombination within grains from grain borders. Finding out where they come from on a tiny level and how to control them on purpose are still very important study topics. This will help us figure out the most interesting thing about perovskites, which are their seemingly harmless grain borders and low surface recombination speeds when the conditions are right.
Interfaces: Between Alignment and Passivation
In the solar cell gadget, contacts are very important for getting the majority and stopping the minority. For this reason, picking a good contact layer (CTL) is very important, since many ETLs can lead to high PCE and VOC. The fact that the rise in PCE and VOC in PSCs past has not required any changes to the materials in the contact layer or any special treatment is very interesting. The first solid-state PSC (TiO2) contact materials worked about the same in a number of devices with low voltage deficits, even though they had very different crystallinities.
It is possible to make perovskite solar cells work better by recombinating them with spiro-MeOTAD. Changing the contact qualities in studies, on the other hand, might lead to better PCE, with standard devices showing PCEs on all scales. This shows that the process of reducing VOC is often a mix of several effects. Reducing interface recombination is a must if you want to make highly fluorescent films from lead-halide perovskite mixtures that have been optimised for solar intensity.
In the end, recombination limits the FFF, but in real devices, transport limits (series resistance effects), especially those caused by the selective layers, limit it even more. When you compare the fake J–V graph you get from VOC with measures of light strength, you can separate resistive effects. Modelling of the gadget can help figure out the minimum movement requirements and the need for doping of CTLs.
Because the selection of an interface isn’t directly linked to a material trait, scientists are looking for a way to create CTLs that: What part of the CTL is important? To that extent, energy levels are important because they affect selectivity. This means that the edges of the conduction band for ETL and the valence band for HTL shouldn’t get in the way of efficiently extracting majorities, but they should block minorities with an energy offset. A band that isn’t lined up right for majorities doesn’t always mean that electrochemical energy is lost, but a lot of charge carriers in the CTL close to the interface makes interface recombination more likely.
To lower recombination at the surface/interface, an intermediate is deposited or the surface is treated. These methods are grouped together as “passivation” techniques, and they may go all the way to the grain boundaries. These changes could chemically protect surface atoms that aren’t properly linked, like what has been suggested for Lewis bases and organic salts. However, the helpful effect might not always be chemical. For example, a thin interlayer could also work as a selective (tunnelling) layer, stopping interface recombination with the CTL. In general, changing the surface or contact can affect many of the factors that play a role in recombination.
Mobile Ions
In perovskite solar cells, slow, brief events change the current-voltage curve and VOC, which impacts non-radiative recombination. This can happen because of the electrostatic effect, which adds to the built-in potential and changes the device selection directly if there is a lot of surface recombination. Mobile ions can move around and fix problems or move recombination centres to less dangerous areas. But more research needs to be done on the details of moving species or the process of movement itself. In the future, researchers will focus on doing experiments to gather proof and control the movement of ions.
Summary and Outlook
This chapter talks about the basic science of solar cells and how they can be used in perovskite devices. It is talked about how the possible maximum efficiency changes with the absorber’s bandgap, and the radiation efficiency limit is added to take into account the shape of the absorption spectrum. The open-circuit voltage is controlled by the luminosity of the material and the solar cell as a whole. Higher amounts of radiation recombination mean higher PCE and open-circuit voltage.
Characterisation methods for measuring recombination parameters are shown, but they are hard to understand because the solar cell stack is not uniform, bulk and interface effects interact, the cell works at both high and low injection limits, and there are high capacitances and slow transients. Simulating numerical devices is needed to add to analytical models like simple rate equations so that all types of mobile charges can be taken into account as they move, diffuse, and get stuck.
Even with these problems, efficiencies of more than 25% have been reached, and the devices have high (10%) PL and EL rates. Nanocrystalline perovskite films have unique features, such as a high absorption coefficient at a straight bandgap, charge carrier mobilities, and strong defect tolerance and slow defect-assisted recombination because the defects are mostly small and the nature of the lattice phonons.
FAPbI3 is used as an absorber in solar cells that are more than 25% efficient. It has a bandgap of 1.52 eV and an estimated open-circuit voltage of 1.26 V. With a realistic efficiency ceiling of about 28%, there is still room for more progress. To get the highest level of efficiency, all non-radiative recombination sources must be kept to a minimum. This includes surfaces and connections to the CTLs, which must be completely selective. It is important to keep track of photons and keep parasite absorption to a minimum by using highly reflective back mirrors and CTLs that are very clear.
It can be hard to find interlayers that don’t add series resistance and reduce the fill factor for interface passivation methods. Unknown types of defects and their concentrations, accidental doping, and mobile ions are still problems that need to be solved before we can fully control how well and how often a device works.
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