Halide perovskites have shown potential optical qualities, making them ideal solar collectors in perovskite solar cells (PSCs). In just over a decade of study, PSCs have reached record power conversion rates (PCE) of over 25%, which is getting close to the Shockley–Queisser (SQ) theoretical limit. A single junction solar cell can have a PCE of up to about 31%, which is just a few percent less than the SQ limit. Recent progress in making PCEs better has slowed down. This is because efforts to improve the absorber makeup, shape, and engineering of the hole and electron transport layers have been thoroughly studied and are now at full capacity.
In the past few years, there has been more interest in looking into other advanced solar ideas that could be used to get even more energy from the sun. Photons with less energy than the absorber bandgap are the main cause of losses. These photons could be used in ideas like tandem and intermediate band solar cells. The second biggest source of loss is high-energy photons from the sun that cool down. The hot carrier solar cell (HCSC) and multiple exciton generation solar cell (MEGSC) are new ideas that could be used to make solar cells more useful.
Potential of Perovskites for Next-Generation Photovoltaics
Xing et al. were the first to show how halide perovskites could be used in next-generation solar ideas. They found that the CH3NH3PbI3 (MAPbI3) halide perovskite had a slow hot hole cooling process. They used transient absorption (TA) spectroscopy with energy-selective excitations to find that the hot carrier cools down slowly, taking about 0.4 ps. When the higher energy pump was used instead of the lower energy pump, the band edge photobleaching (PB) rise time dynamics and decrease in the higher energy PB slowed down.
The writers figured out how the energy bands of MAPbI3 were aligned and attributed the 0.4 ps lifetime to the hot holes cooling down. The hot electron cooling time was found to be the same in later work, at about 0.4 ps. A lot of research has shown that slow-hot carrier cooling works the same way in other halide perovskite mixtures and even in nanoparticles.
Halide perovskites take longer for their hot carriers to cool down than most organic semiconductors, which only need about 100 fs to cool down. This slow hot carrier cooling time is needed for both High-Cell Solar Cells (HCSCs) and Multi-Electron Gestriated Cells (MEGSCs), which are new photovoltaic ideas that are meant to go beyond the SQ limit. This slow cooling time is needed for HCSCs to get rid of the hot charge and for MEGSCs to make the multi-exciton production process work well.
Hot Carrier Cooling Mechanisms
Charge carriers in a medium that are made by light and have more energy than their bandgap energy are called “hot carriers.” They cool down quickly as they lose extra energy in different ways until they hit the edge of the band. The cooling process is complicated, with many competing steps happening at the same time. There are different stages that can come from these processes that happen at different times. Figure 10.3 shows the main steps and goes into great depth about each one.
Carrier Thermalization (10–100 fs)
To make a quasi-thermalized carrier distribution, non-thermally excited carriers go through carrier thermalisation in the first few femtoseconds after photoexcitation. This process is mostly made up of carrier-carrier scattering events, which quickly spread extra energy among the population of carriers that are not in equilibrium. During this first stage of carrier cooling, the energies of the carriers stay the same. The rates at which carriers heat up in halide perovskites rely on both activation energy and carrier density, with rates going up as both go up. In halide perovskites, this process usually ends in 100 fs. Carrier-carrier spreading is the main way that this process works.
Lattice thermalization (100 fs to >1 ns)
Polar semiconductors like halide perovskites cool down in two stages. The second stage is dominated by phonons. Longitudinal optical (LO) phonons are released at this stage. They lose energy to the grid. The process keeps going until the temperature of the carriers reaches the temperature of the lattice and the carriers fully heat up to the temperature of the lattice. This is the main way that extra energy in hot carriers is lost, and it’s also where most of the processes that cause the hot carriers to cool down slowly in halide perovskites happen.
Polaron formation (100–1000 fs)
There are LO phonons that circle polar semiconductors, which move as a big quasiparticle in the lattice. These phonons are made up of polarons, which are electrons or holes. It is thought that these polarons cause slow cooling in halide perovskites because they have different transport features than bare carriers. The Fröhlich coupling constant (𝛀) shows how strongly electrons and phonons are coupled, and the time it takes for polarons to form is similar to the time it takes for LO phonons to live.
Slow Hot Carrier Cooling in Halide Perovskites
Hot Phonon Bottleneck
When it comes to semiconductors, phonons are very important for how the hot carriers settle. After heating, hot carriers lose their extra energy through the Fröhlich interaction. They do this by releasing zone-centered LO phonons, which then break down into acoustic phonons. The chain process will keep going until the carrier temperature and the lattice temperature are the same. The Klemens, Ridley, and Vallée-Bogani decay channels are the three main types of phonon decay that can be used for polar cubic semiconductors.
Because halide perovskites have very symmetrical crystal structures, the Ridley channel isn’t good at getting rid of extra energy. Instead, the Klemens channel cools the carriers in these materials. Because halide perovskites have a low LO phonon energy (about 10 meV for lead iodide perovskites and 20 meV for lead bromide perovskites), the Vallée-Bogani channel is not as good at what it does. It was found that this process works best for GaAs, which has a higher LO phonon energy of about 36 meV.
It was found that halide perovskites have a hot phonon bottleneck effect, which explains why the hot carriers cool down so slowly. Because there is a big space between the LO and LA phonon branches, the Klemens decay channel was slowed down. This created a big phonon bandgap that made the LO phonon relax more slowly. Also, halide perovskites have a low LO phonon energy, which causes a lot of LO phonons to build up at the lowest LO phonon branch. This can stop more LO phonons from escaping and make it more likely that phonons will be absorbed again.
In conclusion, when small LO phonon energy and big phonon bandgap are present together, the effective LO phonon lifetime gets longer. This causes the hot phonon bottleneck effect to show up in halide perovskites.
Auger Heating of Hot Carriers
Auger heating causes a second stage of hot carrier cooling to show up in the cooling curves of halide perovskites when there are a lot of them. At high levels of about 1019 cm−3, this process becomes important, which makes it more likely that multiparticle impacts will show up. These multiparticle effects show up as a fast decay component with higher carrier densities. They last for tens of picoseconds, which is about the same length of time as the nonradiative Auger recombination (AR) lifetime of halide perovskites. This Auger heating process moves energy to a third carrier without using radiation, warming it up above the band edge. This process adds tens of picoseconds to the lives of hot carriers, which lets them stay above the temperature of the lattice for longer. The hot carriers would cool down in a few picoseconds without these effects.
Large Polaron Formation
Long-lived, energetic hot carriers can still be seen at carrier densities as low as ∼1016 cm−3. This is below the Mott density of 1018 cm−3. This is because hot carriers are screened by a lot of polarons. When an electron is positioned at a lattice site, it changes the shape of the lattice around it. This changes the way oppositely charged ions are attracted and repelled, creating a polarised cloud of ions that moves with the charge carrier. To put it another way, this is like a charge carrier dressed in phonons. You can think of it as a kind of quasi-particle called a polaron.
Putting a polarised cloud of ions (phonons) on top of charge carriers blocks the charge carriers and slows down the rate at which phonons spread. Because of this blocking effect, the cooling of hot carriers slows down a lot after polaron creation. In MAPbI3, the extra energies of the carriers start to fall off quickly in the first 0.5 ps. After that, the rate of cooling slows down a lot as polarons form, and the carriers can stay about 100 meV above the bandgap energy for nanoseconds.
One big difference between this process and the ones we’ve already talked about is that it only works well when there are few carriers (about 1016 to 1018 cm−3). In this range, as carrier density rises, the number of hot carriers drops, which is the exact opposite of what you would expect from the hot phonon bottleneck process. For even higher carrier densities than the Mott density, the carriers exist as ionised plasmas, and the hot phonon bottleneck and Auger heating effects control most of the cooling of the hot carriers.
Spectroscopic Signature of Hot Carriers
Ultrafast spectroscopy is a popular way to study how hot carriers cool down in halide perovskites because it can resolve events in real time, letting scientists fully grasp the main steps of hot carrier cooling down after carrier thermalisation. Ultrafast TA and time-resolved photoluminescence (TRPL) are the two ultrafast methods that are used the most.
Transient Absorption
Because it is so sensitive to photoexcited species, TA spectroscopy can be used to study many different aspects of how carriers move through materials. It can also be used to watch how hot carriers cool down in halide perovskites. The main photophysical processes that lead to carrier cooling happen in the first 1–2 ps, and that’s what we’ll talk about here. When there are a modest number of carriers, the main photophysical processes that lead to cooling happen in about 1 ps. At energies below the bandgap value, a generated absorption band breaks apart, and the main PB peak moves to the red. The larger view of the contour plot in Figure 10.7a makes this redshift stand out. It is caused by the Burstein–Moss and band gap renormalisation (BGR) processes acting against each other.
On the high-energy side of the PB peak, the TA spectrum clearly broadens. The hot carrier group calls this part of the TA spectrum the “high energy tail.” This spreading out happens at the same time as the main PB peak growing, and it shows how fast the hot carriers are cooling down. TA spectroscopy can be used to describe the cooling of hot carriers in two main ways. A simple way to start is to look at how ground state bleach (GSB) changes in the TA spectrum of halide perovskites. After an above-bandgap high-energy pump activation, the carriers cool down and fill up the band edge again in a time frame similar to the time it takes for hot carriers to cool down. You can use the GSB dynamics rise time to find out how long it takes for the hot carriers to cool down. If you increase the pump energy and/or fluences, the GSB rise time will get longer.
The second way to figure out how the hot carriers move from the TA spectra of halide perovskites is to make cooling curves, which show how the carrier temperature (Tc) changes over time after being excited. The early-time TA spectra of halide perovskites show that the high-energy side of the main PB peak has a clear widening, which means that hot carriers are present. By fitting the TA spectra over a number of time delays, either by using a Maxwell–Boltzmann (MB) distribution function to get a rough idea or a full-spectrum fit, the carrier temperatures can be found and used to make the cooling curves.
But it’s important to show A correctly and not think of it as a steady number of states. The Elliott equation is good enough to describe A fairly accurately within the small range needed for fitting. The whole TA spectrum can be reproduced clearly with this method, and there are no problems with the choice of fitting region like there are with the MB distribution fitting method. The fitting can also be used to correctly find the numbers Tc and EF.
Fluorescence-Based Techniques
To study how hot carriers cool down in halide perovskites, fluorescence-based methods such as TRPL or rapid photoluminescence (PL) can be used. When the pump intensity is modest to high, the PL peak of halide perovskites clearly shifts to the blue side and gets wider towards the high energy side. There is a widening because of radiation coming from hot carriers with energies higher than the material’s bandgap energy. Depending on how fast the hot carrier cools, this widening decreases over time.
Similar changes can be seen in the recovered carrier temperatures from the PL spectra, which proves that the high-energy emission comes from hot carriers. When halide perovskites are excited with continuous waves (CW) at high enough levels, hot PL radiation can also be seen. It is also possible to see the main PL peak getting wider and more blue when the excitation fluence is changed from 0.5 to 40 W cm−2. This finding proves that the hot carriers can stay alive even when the light is on all the time.
The generalised Planck equation can be used to describe the emission profile of halide perovskites, just like it can be used for other group III–V semiconductors. It is important to use the right model for A(E), and the Eliott equation is often enough to describe it within the fitting window. The MB distribution form in Equation (10.3) is also sometimes used as a rough guide to fit the high energy region of the PL peak for energies higher than the quasi-fermi level.
But this might make the exact numbers of Teh that were found less accurate. The full form (Eq. (10.3)) should be used when these numbers need to be exact. If you fit the PL spectra at different times after the excitation, you can make cooling curves that show how the hot carriers cool down. It is possible to get the power-dependent steady-state photoluminescence (SSPL) spectra, which are the time-averaged TRPL spectra, and fit them with Eq. (10.3) to see how Teh changes with pump strength. It is possible to measure the impact of hot carriers in the steady state by looking at how the SSPL bands change with pump fluence and the direction of Teh.
We can measure the steady-state power loss due to thermalisation to the grid (Pth) by adding the thermalisation coefficient Q. For situations where the hot carrier needs to cool down slowly, a low Q number is better.
Hot Carrier Extraction
By taking out halide perovskites before they cool to the band edge, hot carrier extraction is a way to use their extra energy. The perovskite layer can be paired with the right extraction material to make this happen. But this process is up against the hot carrier cooling process, so for the extraction to work well, the rate of extraction should be faster than the rate of cooling. Studies have shown that bathophenanthroline (BPhen) and bathocuproine (BCP) can be easily extracted from halide perovskites using hot carriers.
To make sure that hot carrier extraction works, the kinetics of TA are studied both with and without the carrier extraction layer. When hot carriers are successfully extracted, the TA spectra get smaller, especially on the high energy side, and band edge dynamics build up faster. This means that the hot carriers cool down faster with the extraction layer.
Another way to study hot carrier extraction is with pump-push-probe (PPP) spectroscopy. With this method, a third “push” pulse is added after the carriers have cooled all the way to the band edge. This re-excites some of the cold carriers above the band edge. Lim et al. showed how to use PPP to move hot carriers from MAPbI3 into BPhen. They saw a slowing down of the TA band edge behaviour and the formation of a Schottky barrier at the contact between the two materials.
Utilizing Hot Carriers in Halide Perovskites
Hot Carrier Solar Cell
For decades, researchers have been trying to make a hot carrier solar cell (HCSC) that works. They have started with traditional group III–V semiconductors and are now working on halide perovskites. The SQ limit of about 33.7% limits the potential highest PCE that a single-junction solar cell can have. One of the main ways that the PCE is limited is by the cooling loss of carriers that take in sun photons with above-bandgap energy. When you collect these extra energies, they raise the highest PCE to about 66%. This extra energy is lost to the grid as phonons.
A HCSC is a type of solar device that can collect both hot and cold carriers. It is one of the most hopeful ways to get around the SQ limit. A diagram of the HCSC shows the hole transport layer (HTL) and the electron transport layer (ETL). To get the hot carriers, you need energy selective contacts (ESCs) for the holes and electrons that are placed at energy levels above their respective band ends.
When hot carriers are taken out of the cell, the voltage goes up, which is higher than what a normal solar cell can do because it only takes out cold carriers. This is how you find the HCSC’s outdoor voltage:
eVext = ¥eh (TL Teh) + ¥eh (1 – TL Teh)
To get back to the normal solar cell case when Teh = TL, Eq. (10.6) is simplified. Vext is the limit set by the quasi-Fermi level splitting of the cold carrier distributions in the cell.
The highest possible power conversion efficiencies (PCE) for an HCSC under 1 Sun solar light tend to go up with Teh. This is mostly because the cell’s Vext gets bigger, as shown in Equation (10.6). For smaller values of Eg, the increases are bigger because as the bandgap value goes down, more sun energy is made, which creates hot carriers.
In a real device, energy will be lost to the lattice around it because of the temperature difference (ΔT) between the hot carriers and the lattice. This puts extra limits on Teh. Because of this, the best value of Teh that maximises the PCE might not be as big, it depends on the value of Q. Halide perovskites have Q values less than 1, which are the lowest values for any material system. This makes them good options for being used as HCSC absorbers.
Toward the Realization of Perovskite Hot Carrier Solar Cells
An interesting alternative to regular single junction solar cells is the idea of a High-Cell Single Junction Solar Cell (HCSC). Some proof-of-concept work has been shown, but making a real HCSC gadget that works and makes things better is still a big task. Using perovskite books as an example, this piece talks about the difficulties and things to think about when making them.
Cooling Loss to the Lattice
Keeping hot carriers at high temperatures under steady-state sun lighting is the hardest part of making high-performance solar cells (HCSCs). There have been studies on the slow hot carrier cooling qualities in halide perovskites, but they were done under very bright, usually single-color, high-energy pump lighting. When the sun shines, the high-energy photons have a much lower spectral strength than when they are used in spectroscopy studies. This makes these effects less clear.
Spectroscopy studies show that high carrier temperatures usually drop quickly in the first few picoseconds because of strong LO phonon coupling in these polar halide perovskite semiconductors. In steady-state conditions, the average carrier temperature should be a lot lower, and the highest power conversion efficiency (PCE) is expected to be a lot lower, especially when the Sun is shining.
The idea of the thermalisation coefficient (Q) helps us figure out how much thermalisation loss there is in a steady state. Lower numbers of Q mean less thermalisation loss. The highest PCE values go up as Q gets smaller. As Q gets bigger, the PCE values go down and drop off towards the SQ limit efficiencies that match to a fully thermalised carrier distribution.
As the amount of sunlight drops, lower Q values are needed to get any PCE improvements from hot carriers above the SQ limit values. The stated Q values for halide perovskite thin films are between 0.26 and 0.66 W K−1 cm−2. This means that improvements will be somewhat noticeable above 1000 Suns of lighting, but will only be slightly noticeable below 100 Suns.
It might be easier to get PCE gains from hot carriers when the amount of sunlight is lower if you use them in halide perovskites. Getting the Q numbers even lower through engineering methods like quantum confinement could help get around this problem.
Energy Selective Contacts
It’s hard to find the right HCSCs, even though studies have shown that hot carriers can be efficiently extracted from halide perovskites and changed into the right chemical forms. Energy-selective ESCs, on the other hand, need a narrow energy window and have not been studied much. This is very important because ESCs can lose extra power if the frequency is not narrowed during carrier cooling. It’s harder to find an ESC with a low barrier for hot carrier extraction because of the Schottky barriers at the contacts. Tunnelling barriers in quantum wells and minibands in quantum dots are common ways to make semiconductors.
Loss of Cold Carriers
Getting both hot and cold carriers to work is hard when you want to make a High-Cell Solar Cell (HCSC). There should only be a few cold carriers in an ideal HCSC. Most of the carriers should be hot. In real life, however, thermalisation to the nearby lattice lowers the HC temperature, so this is not likely to happen. So, for HCSC devices to work well, they should be able to easily pull out both hot and cold carriers to get better results than regular solar cells.
HCSCs that have been tested in the lab are still just proof of concept, and their efficiency is even lower than that of regular cells. Low PCE in ESCs is caused by their bad electrical qualities, like low carrier movement and high resistance. These problems also happen with colloidal nanocrystals (NCs) and quantum dots (QDs), which are held together by long-chain shielding molecules.
You could also use intense solarillumination, which raises the number of hot carriers in the carrier pond. This would make the effects of the phonon bottleneck stand out more and let carriers heat up a lot. It might be possible to keep a bath of cold carriers that is always being refilled, which could help the HC people stay alive. Solar cells would have higher Voc and PCE if only the hot carriers were taken out at a higher energy level.
These problems might be solved in the future with more research into designing the right gadget layout and finding possible ESCs.
Multiple Exciton Generation
MEG, which stands for multiple exciton generation, is a process that turns one high-energy photon into many electron-hole pairs. It is also known as carrier multiplication (CM) or impact ionisation (II) in bulk materials. This process is like singlet fission (SF) in organic molecules and is seen as a possible way to get around the Shockley–Queisser (SQ) limit in a single junction solar cell.
Under normal conditions, when a single photon is absorbed, it only creates one exciton, which is a pair of electrons and holes. The extra photon energy above the bandgap can’t be taken out as electrical energy. Instead, it will finally be lost as heat through crystal movements. In discrete electronic states caused by quantum confinement, hot carriers with energies at least twice as high as Eg could pass the extra energy to another carrier and excite it across the bandgap.
With the MEG/CM/II process, it is possible to raise the PCE of a single-junction solar cell from 33.7% to 44.4%, which is higher than the SQ limit. The impact ionisation process was first found in bulk semiconductors in 1953. It has since been studied in great detail in bulk materials like Si, Ge, PbTe, PbS, and PbSe. Different halide perovskite materials have been found to contain MEG that works well, which opens the door for the next wave of solar cells.
MEG Metrics
It is important to measure the MEG quantum yield (QY), the MEG efficiency (𝼂), and the MEG threshold (Eth) when looking at the MEG process in materials. The ideal MEG QY/QE is a step-like rise at energies that correspond to each integer multiple of Eg, denoted as h𝜈/Eg. MEG QY is the number of excitons produced per received photon. Real-life events, on the other hand, don’t usually show this ideal step-like behaviour. Instead, the QE slowly rises as the photon energy increases.
The graphs were made using the model suggested by Beard et al., which looks at how the MEG rate (kMEG) and the hot carrier cooling rate (kcool) compete with each other. A photon with a lot of energy can turn a single exciton into an excited single exciton state n∖1. This state can either cool down to a relaxed single exciton state n1 or, if energy conservation allows, create an excited biexciton state n∖2. This state can also cool down to a relaxed biexciton state n2 or even make a trion state n∖3. This process of cascades keeps going until the last excitons have less than twice the bandgap energy in energy.
To figure out the QY, you need to find a relationship between the rates kMEG and kcool. This can be written as:
kMEG = kcoolP(h₼ – hth)s. The MEG threshold energy is given by Eth = h𝼈th. P is a constant that describes the competition between MEG and carrier cooling, and s is a number that ranges from 2 to 5. The value of s for halide perovskites is close to 2.
This is how you can describe the MEG efficiency:
There is a bigger P number that makes MEG work better: 𝼂 = P1 + P (10.10). The number of P also tells us whether the start of MEG is smooth or sudden, which is what should happen in a perfect world.
With Equations (10.9) and (10.12), you can find the QY for each value of h₼/Eg. Time-resolved spectroscopy methods, most often TA spectroscopy, can be used to measure important MEG properties of the material.
Multiple Exciton Generation Mechanisms
The Debate Over the MEG Threshold and MEG Mechanism
Multiple Exciton Generation (MEG) is thought to work in two main ways, according to the research: noncoherent impact ionisation and coherent combination of multi-exciton and single exciton states. It was found that the MEG limits are 3Eg and 2Eg. The MEG noncoherent model says that after taking in photons with more energy than the bandgap, the extra energy-carrying hot carriers are spread out based on their effective masses, which are me for electrons and mh for holes. To make more electron-hole pairs, at least one of the carriers should have hₜ >Eg.
You can write the MEG threshold energy (Eth or h₼ CM) as Eth = (2 + me/mh)Eg. When me = mh, the MEG barrier is about 3Eg. If me = mh, however, it can be lowered to 2Eg. Most lead-based semiconductors, like lead selenide (PbSe) NCs, have a MEG threshold of about 2.9Eg. The MEG barrier can drop to about 2.17Eg in cadmium selenide (CdSe), and it can get close to 2Eg in indium arsenide (InAs).
A second way to think about MEG is in terms of the orderly combination of single- and multi-exciton states. It uses a time-dependent density matrix method that lets it look at different coupling strengths between single and multi-exciton states, different dephasing rates for these states, and a short pulse excitation of the NCs all at the same time. The model looks at a number of the processes that cause MEG in NCs, such as how fast calm single excitons and biexcitons return to the ground state.
It was suggested by Schaller and Klimov that MEG in CdSe and PbSe NCs could be explained by a third mechanism based on direct multiplication generation via a virtual exciton state. This mechanism would explain the very short MEG (50–200 fs) that neither the non-coherent nor the coherent models can explain.
Underlying Mechanism of the Efficient MEG in Perovskite
It’s still not clear how multiple exciton generation (MEG) works in halide perovskite materials. MEG limits for halide perovskites can often get close to about 2Eg. This is because perovskite materials have a slow hot carrier cooling rate (1/𝼏cool). This slow cooling rate is better for MEG because 𝼏cool-int, the time it takes to cool down from the original photoexcited state to the MEG threshold state, is longer than the MEG rate.
If you know the PB rise time, you can figure out the total cooling time 𝼏cool. It’s also possible to figure it out by subtracting the cool h𝼈 from the cool h𝼈. It takes about 90±5 fs for the 7.5 nm FAPbI3 NCs to cool down, which is less than 90 fs. In FAPbI3 bulk materials, cool goes up as h𝼈/Eg goes up, which is an interesting effect. On the other hand, cool goes down in 7.5 nm FAPbI3 NCs, just above the MEG threshold.
A different idea for the 2Eg MEG barrier in perovskite materials is that electrons and holes might not be sharing their extra energy evenly. The MEG threshold might be close to 2Eg if the second conduction or valence band energy is close to that value. This would mean that quantum confinement is not needed. This idea works for Pb chalcogenide materials, but more research needs to be done on perovskites.
Controversy and Pitfalls Over Photocharging and Artifactual
MEG Signal
Photocharging artefacts are the major reason for the big difference between MEG QY and MEG rates in some early studies. The hot exciton moves to the band edge with rate 𝓾 cool in the first case without MEG. The QD then relaxes into state n1, which has a single cold exciton. When MEG is present, the high-energy photon can make multiple excitons at a rate of MEG, and the QD changes into state n2. The multi-exciton QD can then relax into the single exciton state n1 through the multi-excitons’ AR at a rate of AR. But problems can happen when the QD is photocharged, which creates a charged state that lasts a long time and is represented by nT. This state will last longer than the time between laser waves, which is what this artefact is based on.
When this photocharged QD takes in a photon from the next laser pulse, it makes a hot trion that cools with a rate of cool, and the QD that contains the trion moves into the state n2T. The trions in the QD can then return to the state nT through a nonradiative AR process with a rate of trion that works like multi-exciton recombination (described by AR). Because MEG and AR both work with trions, this photocharging artefact can make it easy to mistake MEG for AR. Photographic flaws like these can make the MEG QY seem higher or the MEG cutoff seem lower than it really is.
For NCs or QDs that are colloidal, the photocharging effects can be lessened by moving the samples enough or making them flow continuously within the activation space. This stops the formation of trions. Solid samples, like bulk films, can be put on a sample stage that can be moved steadily away from the laser beams to lessen the effects of photocharging.
How the ratio of early to late-time signal amplitudes (A/B) was used to describe the MEG effect is what’s wrong. The strength of the signal is related to the average number of photogenerated excitons in a QD with Poisson distribution. When the sample is excited above the MEG threshold, a fast decay component shows up in the PL decay trace. This causes important MEG measures, such as the MEG QY, to be overestimated. The analysis of MEG from both PL and TA spectroscopy will be affected by photocharging artefacts, since the ratio of the amplitudes A and B is also used in TA spectroscopy, which is the more common way to look at MEG. So, photocharging effects must be carefully thought through and lessened in order for MEG measures to be correctly calculated.
Efficient Multiple Exciton Generation in Halide
Perovskites
MEG studies have been done on different perovskite materials since 2018; these include FAPbI3, CsPbI3, FAPb1−xSnxI3, and FA0.6MA0.4Pb0.4Sn0.6I3. Their low MEG threshold, high efficiency, high QY, and right Eg all point to the possibility of using them in high-efficiency MEG solar cell devices.
Low Multiple Exciton Generation Threshold
As low as 2Eg has been found in either NCs or bulk films in most work on MEG in halide perovskites. Other perovskite materials, like CsPbI3 NCs and (FASnI3)0.6(MAPbI3)0.4 bulk films, have a MEG threshold of about 2Eg. The MEG threshold for FAPbI3 NCs is about 2.25Eg. The brightest light is in the visible range above 350 nm. This means that a low MEG threshold is good for making MEG PSCs that work very well. If the bandgap of the material is small enough, MEG may form in ideal parts of the sun spectrum where the light is very bright (>350 nm). We don’t want MEG limits that are too high for bands below 350 nm.
A perovskite material with a small bandgap and a low MEG threshold, like a Pb/Sn mixed perovskite with a bandgap of 1000 nm and a MEG threshold of 2Eg, might work well for MEG PSCs. In the 300–1400 nm range, the AM1.5G solar spectrum doesn’t have a lot of radiation, so any improvement from MEG probably won’t make a big difference in how well the solar cell works.
High Multiple Exciton Generation Efficiency
When it comes to MEG efficiency (), halide perovskite QDs do better than inorganic QDs. The highest value is 100% when QY gets close to 200%. This is almost as good as it gets for MEG performance, which can hit 75% or even 98%. It is better for MEG to have a high rise because it brings the material closer to the ideal step-like increase. A higher MEG efficiency means a higher MEG QY at low light levels, which is good for the performance of MEG PSCs.
Large Multiple Exciton Generation Quantum Yield
Halide perovskite materials have a high MEG QY of about 1.6 at 2 or 3Eg, which means they could be useful for MEGSCs. Halide perovskites are good materials for MEGSCs because they have a high MEG QY, a low MEG cutoff, and a high MEG efficiency. Time-resolved spectroscopy is usually used to figure out the MEG QY, which can be written as Rpop = A/B = 𝛿▨N0▩QY 1 − exp(−▨N0▩). Without MEG, it is possible to guess how the single exciton population will decay, and ▨N0▩ is the average number of photogenerated excitons for each NC or QD. To get the MEG QY, use Equation (10.16), which fits the relationship of Rpop against ▨N0▩.
Spectroscopic Signatures of Multiple Exciton Generation
Transient Absorption Spectroscopy
TA spectroscopy is the most common way to study MEG because it lets researchers directly watch the exciton population with enough time precision. It is easy to spot MEG because it has a fast multi-exciton decay component with higher amplitude in the band edge photogenerated excitons (PB dynamics) when the pump strength is very low. Each QD takes in one photon when MEG is not present, creating a single exciton with a very low N0 value. It takes a few to tens of nanoseconds for these single excitons to go through a relatively slow single exponential decay. On the other hand, MEG can happen at high pump energies, and a single photon can create multiple excitons in a single QD. These many excitons will join back together much more quickly through the AR process. This will cause a fast decay component to show up, which will give the PB dynamics a multiexciton lifetime.
The extra fast decline part that can be seen when the pump strength is low and the energy of the pump is high is thought to be the MEG fingerprint. This part is missing from the PB dynamics when the energy of the pump is lower than the MEG cutoff. When MEG is used, the starting signal amplitude (A) will be higher than when MEG is not used. This means that Rpop >1 even when N0 is low. For data collected below the MEG threshold, on the other hand, Rpop tends to 1 at low ▨N0▩, which means that MEG effects are not present.
Also, the same analysis as in Figure 10.23 can be done at different pump energies to get the MEG QY values. This makes it possible to plot how the MEG QY changes with h𝼈/Eg. From this, the MEG efficiency 𝼂 and the MEG threshold energy can be found by fitting the region linearly to MEG. To see this more clearly, look at Figure 10.24. Panel (a) shows the plots of the MEG QY versus energy for different-sized FAPbI3 NCs. Panel (b) shows the same study done on PbS NCs.
As a MEG signature, the change in the absolute value of the starting amplitude ∎ΔAmax∢, which is related to the number of excitons, can also be used. A higher |ΔAmax| value for the same photon flux means that more excitons are being made. You can also get a rough idea of the MEG QY by fitting the slope of ∿ΔAmax∣ as a function of fluence.
When the pump fluence is low, ∺ΔAmax∣ rises in a straight line with the pump fluence, and the gradient can be found using a linear fit. If the QY is equal to 1 in the case without MEG, then the MEG QY can be found by dividing the gradient of the case with MEG by the gradient of the case without MEG.
Photocurrent-Based Techniques
To study MEG in PbSe QD screens, the transient photocurrent (TPC) technique is used. A fast oscilloscope is used to watch how the photocurrent changes in a photoconductive switch after a rapid laser excites it. The time development of the photocurrent can be shown by the equation j(h𝜈, t) = q(h𝜈)eEne(t)𝼇e(t) + nh(t)𝼇h(t). Multiple excitons present at the start of time show up as a fast, short decline component.
It is possible to write the average number of electron-hole pairs in each QD as (2p2 + p1)∖(p1 + p2) (10.19). If MEG is not present, Nx stays 1 as fluence gets close to 0, which is in line with TA measurements. You can write the dynamics of a single exciton as j(t) ∂ ux = (1 – f) + f e−t∖𝼏x (10.20).
The photocurrent dynamics can be used to figure out the MEG QY. We also looked at how photocurrent behaves when a mercury (Hg) lamp with different band pass filters is on all the time to study MEG in NCs [30]. The writers saw that a photodetector with a 4V bias voltage and light above the MEG barrier at 254 nm had an internal quantum efficiency (IQE) greater than 100%. What we think about MEG behaviour from photocurrent studies might not be the same as what happens in a solar cell device, though, because photodetectors are usually tested with a bias voltage, and the EQE values that are recorded can easily be higher than 100%. It has not yet been shown that perovskite devices can achieve an EQE and IQE greater than 100% when measured from the incident-photon-to-current efficiency (IPCE) or estimated from Jsc.
Utilizing Multiple Exciton Generation in Halide
Perovskites
The goal of studying MEG is to find out how it can be used in solar cell devices. An EQE and IQE greater than 100% under zero bias are proof that devices have more than one excitons. The IPCE is usually used to measure EQE, and EQE/(1−R) is used to figure out IQE. You can also use optical modelling to find the IQE by adding up the recorded extinction coefficient k and refractive index n for each layer. But the quality of optical modelling needs to be thought about in both the n and k modelling steps as well as the general modelling of the device. It has not been noted that EQE or IQE levels above 100% have been seen in PSCs. To help shape future perovskite-based MEGSCs, this talk is mostly about groundbreaking work on PbSe QD-based MEGSCs.
Multiple Exciton Generation Solar Cells
It was reported by Semonin, Nozik, Beard et al. in 2011 that PbSe QD MEGSCs had an EQE and IQE greater than 100%. This shows that MEG can be improved in solar cell devices. We made solar cell devices with a structure of ITO/ZnO/QDs/Au by using 1,2-ethanedithiol (EDT) and hydrazine to change the ligands while the QD film was being deposited. We measured the EQE of devices made from QDs of three different sizes and then determined the IQE based on the reflectivity that was measured in the lab and modelled.
The bandgap gets smaller as the QD size goes up, while the peak EQE and IQE get bigger. It had the best EQE (106±3%) and IQE (130%), both at 3.44 eV, for the 5.6 nm QD. The peak EQE can even hit 114±1% when an antireflection layer is used.
We saw that the start of MEG in all three QDs is the same, which is about 3Eg, by comparing the photon energy to the bandgap and plotting the QY as a function of h𝼈/Eg. The PbSe MEG solar cell devices have a relatively low PCE (∼2–4.5%), but this work shows that a MEGSC is possible and helps with the design of future MEGSCs that might have PCEs higher than the SQ limit.
As for the MEG cutoff, it doesn’t seem to change with QD size. The 3 nm QD has the biggest MEG boost. For perovskite MEGSCs, there needs to be a mix between quantum confinement for better MEG efficiency and a small bandgap for real-world MEG uses.
Potential of Multiple Exciton Generation Solar cells
The highest photon-to-excitation (PCE) that a MEG solar cell (MEGSC) could theoretically reach is 44.4%, given that the MEG QY behaves in a step-like way. In Figure 10.29, the MEG potential for materials with different P values is shown. As P rises, the QE acts more and more like the ideal case, which leads to more and more PCE improvements in a MEGSC. It is possible to get PCE improvements that go beyond the SQ limit. Bigger improvements happen when bandgap energies are smaller.
A good bandgap, a small MEG cutoff, high MEG efficiency, and high MEG QY are the most important things for MEGSC device uses. For MEGSCs, it’s also important that the electron and hole transport layers can move around easily so that carriers don’t get too full, and the idle layer before the absorbing layer needs to be able to let a lot of light through.
Materials with MEG limits below 350 nm probably won’t work well for MEGSC application because the ITO or FTO layers will absorb more energy than the MEG. It is possible to make high-efficiency MEGSCs that break the SQ limit with perovskite materials that have a narrow bandgap (∼1.24 eV), slow HCC, a low MEG threshold, and high MEG efficiencies.
Conclusion and Outlook
Because they cool hot carriers slowly, halide perovskites might be able to break the SQ efficiency limit for next-generation solar cells. Because these materials can have high transport temperatures and very efficient MEG processes, they are perfect for the solar cells of the future. A halide perovskite solar cell gadget could use both the HC and MEG effects to make it more efficient than if it only used one of them. The J-V feature of this gadget would be that MEG enhancement would raise the Jsc and HC enhancement would raise the Voc. When these improvements are put together, they might make the cell’s PCE even bigger than if only one effect was looked at. But competition from one affect also needs to be thought about in order to find a middle ground and the right mix. More research needs to be done to come up with a good device design that can use both effects at the same time and to find good extraction layers with high mobilities. This next-generation solar cell is very efficient and could help people fight climate change and even reverse its affects.
Leave a Reply