The amount of light that semiconductors can emit depends on their internal luminescence quantum yield (QY), int, and the number of photons that leave the semiconductor. A material’s performance as a photovoltaic material is linked to how well it works as an external emitter. This is because ext is connected to how far the real open circuit voltage in a solar cell is from its ideal value.
To fully understand how a semiconductor emits light, you need to know a lot about how charge carriers recombinate. In the past ten years, a lot of theory and experimental work has been done to try to figure out how charge recycling works in lead halide perovskites. These studies have shown that this material has some special qualities.
In this chapter, we will look at the different ways that charge carriers recombine in lead-halide perovskites (LHP) to see how well they emit light. Figuring out how these things work will help us decide if LHP can be used as an active material for laser devices, especially for electrically pumped lasers that work at room temperature (RT), which is the holy grail of solution-processed materials for optoelectronics.
Light-induced processes that happen slowly, like photo-activation and photo-darkening, can also change the way LHP emits light. These processes can last from seconds to hours. Due to the material’s “soft nature,” these processes are closely connected to changes in its structure, such as ion movement or material breakdown.
Charge-Carrier Recombination in Lead-Halide
Perovskites
The recombination of charge carriers in semiconductors affects how much light they give off. This can happen through visual or electrical stimulation. Lead-halide perovskites (LHP) use electrons and holes at the bottom of the conduction band for recombination. The semiconductors in these materials are direct-gap, which means that charge carrier cooling should happen faster than recombination. Recombination can happen through radiative means, states that are trapped because of flaws in the structure, or interactions with other carriers.
Differential equations are used to look into how charge carriers recombine, but assumptions about bulk perovskites make these equations easier to understand. The ABC model, which uses three words to describe the chances of single molecules, double molecules, and triple molecules happening, shows the main recycling processes in halide perovskites and some of the unique photophysics of these materials.
In general, electron-hole exchange is a process with two particles: an electron and a hole. This particle dependence can be changed, though, in some situations. There is a one-particle dependence for defect-induced trapped charge carrier helped recombination, and radiative bimolecular recombination, in which an electron recombines with a hole and extra energy is released as a photon. In trimolecular Auger events, an electron and a hole recombine without giving off radiation. This transfers extra energy to a nearby charge carrier, which makes it excited.
The research will mostly look at bulk-like systems that are dominated by free carriers and changes in enclosed systems that are dominated by exciton carriers.
Monomolecular Recombination
In solar devices, the monomolecular rate constant A is a very important part of the recombination process. For example, trap-assisted recombination looks at how localised flaw states interact with either holes or electrons. This type of recombination only depends on the groups of electrons or holes. These processes are especially important when the energy level is low, which is what most solar devices experience when they are working.
When there are electron traps and a fast electron trapping rate ktrap, the recombination rate is given by R = ktrapneNT(1 – f) = Ane. In this case, it takes a lot less time for electrons to move into trap states than for holes to move back into trap states. In this case, the rate of recombination is only affected by the number of holes in the material. The number of charge carriers per particle changes, making the system monomolecular. It was found that this kind of charge carrier trapping mostly happens when free carriers are moved to electronic trap states with the help of phonons.
The way trap states affect recombination dynamics depends on how energetic they are. The way charge carriers recombine will not be changed by trap states that are deep inside the conduction or valence band. If the energy difference between a trap state and the conduction band minimum (CBM) or valence band maximum (VBM) is less than the thermal energy kBT, it is easy for ions to get into it. These states act as shallow traps that don’t cause nonradiative recombination but do cause doping. Deep traps are states of trapping that have an energy difference bigger than kBT. Recombination from those spots can only happen in a nonradiative way through vibrational decay paths where electrons and electron holes meet again in the middle of the trap. Shockley, Read, and Hall were the first to suggest this nonradiative recombination through multiple phonon emission in 1952. It is now widely known as Shockley–Read–Hall (SRH) recombination.
The LHP structure is made up of three parts: A is usually methylammonium (MA), formamidinium (FA), or caesium; B is lead; and X is iodine, bromine, chlorine, or a mix of these. These materials are made through solution processing, and their crystal structure is softer than that of regular inorganic semiconductors. This makes the flaw density naturally high, but perovskites can act as good transmitters because they have a lot of shallow traps and not many deep traps in their bandgap.
The flaw densities for LHP have been found to be high, ranging from 1014 −1017 cm−3 in polycrystalline films to 109 −1012 cm−3 in single crystals. These values are a little higher than those found in pure silicon and other popular semiconductors. Its defect tolerance, on the other hand, means that the material’s electrical qualities are not affected by its high defect density. There is still some disagreement about the exact process that causes the high defect tolerance, but it has been linked to interactions between free charge carriers and trap states, which rely on 𝼏trap and can be explained in two ways.
Bimolecular Recombination
When the number of excited charge carriers in perovskite materials is in the middle, bimolecular processes control charge carrier recombination. If you put an electron at the bottom of the conduction band and a hole at the top of the valence band next to each other, they will recombine directly. This is how perovskite materials recombine. The bimolecular recombination index and ne (nh), which is the electron (hole) density, can be used to describe the recombination rate. A straight bandgap semiconductor like LHP does most of its recombination through photon emission. However, heat recombination through lattice movements can also cause charge carrier recombination from one band to another, which means that the recombination coefficient B needs to be increased.
The recombination lifetimes in LHPs are much longer than what would be expected from a straight direct bandgap semiconductor with the same electronic gap. The recombination process can be slowed down if the charges involved are held or spread out spatially, or if the motion or spin of the particles involved are stopped from moving. Several ideas have been put forward to explain the longer lives that have been seen, and these ideas are still being discussed. Some stories say that long lives are caused by small traps that are filled and then escaped. In shallow trap states, charge carriers can stay alive for milliseconds, which means that trap states can store excited charge carriers. Being in contact with a lattice phonon is the only way for the trapped charge carrier to be raised to its original energy level and reunite radiatively. The mesh needs to contribute heat to this process, which is also known as thermally triggered delayed fluorescence.
The bimolecular exchange coefficient B may be changed by other means. One theory says that the longer lifetimes are caused by polarons, which are local lattice changes caused by attraction and repulsion. Another theory says that the longer lives are mostly due to photon recycling. As photon emission could happen uniformly throughout the material, it is likely that the released photons will be reabsorbed by an absorptive material. This makes the actual radiation emission rate higher. In the future, it will still be hard for the perovskite group to separate its efforts in different types of materials.
Trimolecular Recombination
When the number of carriers is high enough, the third term in (1) controls carrier recombination in semiconductors. An excited charge carrier’s extra energy is passed to another charge carrier at the band edge, which is pushed to a higher energy state. This term refers to many-body Auger nonradiative recombination processes. This reaction takes place when the third “hot” particle relaxes near the band edge and interacts with lattice phonons to keep its momentum. This nonradiative recombination route is important when there are a lot more carriers than in LHPs when they are working as photovoltaics. The Auger process probably won’t be very important in solar devices, but it could be very important in light-emitting uses that need a lot of charge carriers. This is true for lasing uses, where ASE charge carrier limits in the 10–17–18 cm−3 range have been found. Auger coefficients that were found through experiments are thought to be built into the band structure of this material.
Recombination Constants in Excitonic Systems
Recombination dynamics are mostly seen in systems where free carriers are the majority. However, confined systems like quantum dots or 2D perovskites have become famous because they have great optical qualities. In these systems, spatial confinement raises the binding energies of excitonions, which could cause excitonic recombination dynamics. The movement of charge carriers depends on how many excitons (nex) are in the system. This movement can be broken down into two types of processes: one-particle and two-particle.
Radiative recombination is the main way that one-particle processes describe how an exciton recombines. Two-particle events are more likely to happen when the number of exciton is higher. In excitonic systems, two excitons work together instead of two charge carriers in bimolecular processes. Exciton species can also associate with excitons around them and join back together again through a process called exciton–exciton annihilation (EEA), which doesn’t use radiation.
EEA happens a lot faster than exciton recombination and is easy to remove from inputs from single molecules in time-resolved charge carrier recombination kinetics. It is normal for excitonic and free carrier species to live together in many poorly confined systems and materials with low exciton binding energy. The way these two recombination pictures interact can have a big effect on how radiative and nonradiative recombination processes are separated. To find out specific charge carrier recombination kinetics, it is very important to be very careful when using time-resolved photoluminescence (PL) or absorption data.
Common Recombination Dynamics Measurement Techniques
and Experimental Evidence
To study light radiation in semiconductors, it is necessary to get a precise estimate of the recombination factors. Time-resolved methods work best because they track how a material trait changes over time in relation to the number of different carrier species (free and trapped). When you measure photoluminescence (PL) over time, you can get information about how fast electron-hole recycling processes happen. However, this method is still not the best way to directly study recombination dynamics because it is affected by things like pure nonradiative low charge carrier density recombination, which can change how it is interpreted.
With a time-resolved pump and probe setup, transient absorption spectroscopy (TAS) gives a more accurate reading. This lets us measure how the absorption changes after a rapid charge carrier population event. This can be linked directly to the charge carrier density created at the edges of the valence and conduction bands. We can fit the charge carrier density decrease to the ABC model and get rate constants for each charge carrier recombination process with this direct measurement.
Researchers have also used different methods with a pump and probe set-up to look into charge carrier recombination in semiconductors, especially in Lithium-Hide Perovskites (LHP). The setup for optical pump terahertz probe readings is the same as TAS. An optical pulse is used to create a population of excited carriers, and a probe beam with a THz pulse is included. Changes in the THz range can be linked to the perovskite’s photoinduced conductivity, which in turn can be linked to the carrier density. If you look at the mobility’s spectral shape, you can get detailed details about free charge carriers, excitons, or polarons.
Photoinduced Effects on Charge Carrier
Recombination
It’s not always the same for a semiconductor’s internal light quantum yield (int); it depends a lot on the regime that controls carrier recombination. The ratio of the radioactive to total recombination rates can be written as: int(n) = krad/ktot = Bn2 + An + Bn2 + Cn3.
It’s been interesting to see how the int changes over time when laser treatment with a continuous wave (CW) excitation happens over time scales (seconds to minutes) that are orders of magnitude longer than those involved in charge carriers recombining or getting stuck at defect states. The release of the material has both gone up and down because of these changes.
The main cause of changes is likely to be changes in the flaw density, since B is a feature of the material itself and shouldn’t change if the material’s band structure doesn’t change. Some stories have shown that crystals that have been blasted before show changes in the spectrum of light they give off, which suggests that the crystals’ structure has changed.
Several observations have shown that changes in emission caused by light and trap density are linked. The PL decay dynamics of an LHP film are studied in conditions where trap-assisted recombination is the main process. When the film is exposed to a CW laser source, which increases the PL intensity, the PL decay dynamics slow down. This means that the A rate coefficient goes down and nonradiative recombination works less well. These changes in A were statistically linked to the number of flaws in the material.
To learn more about the kinds of flaws that cause these photoinduced processes, chemical composition and PL confocal imaging methods have been used together for local probe studies. PL changes have been linked to a shift in the halide part of the perovskite matrix. This fits with previous research that linked halide-related flaws to the creation of deep traps in the bandgap of LHP.
The environment around lead-halide perovskites (LHPs) affects the processes that are started by light. In an inactive atmosphere, these materials don’t give off much light, and when they are exposed to light, their photoluminescence (PL) drops in a way that can be undone. This is probably linked to the formation of Frenkel pairs by light, which makes ionic conduction better. When something is exposed to both light and reacting atmospheres (like oxygen or wetness), the PL first gets stronger and then weakens.
As-synthesized perovskites don’t give off much light because they have a lot of solid flaws. The situation gets better when subjected to both outside radiation and air, as shown by the higher PL. It is now known that this behaviour is connected to the “light soaking” problem that often happens in LHP solar systems. PL increase or reduction caused by light are not two different effects; they happen at the same time. The amount of time that one effect occurs depends on how long it is exposed to light.
Molecular oxygen in the environment can also change the shape of LHP defects even when they are not exposed to radiation. When O2 comes in contact with interstitial iodide in its steady Ii− charge state, it changes its oxidation state. This brings its energy level closer to the valence band, making it a shallow trap with less ability to catch things. But molecular oxygen can also hurt the optoelectronic qualities of LHP when it reacts with the flaw that goes with it, which is an iodide void VI. In this case, O2 can move through the perovskite lattice and join with an iodide gap, where it can take in a photogenerated electron and create a superoxide species O2−. This species then reacts with the oxidised perovskite lattice, breaking it down.
Photo-induced processes have been reported in other mixtures with different cations and in different shapes, like nanocrystals and quasi-2D perovskites. This shows that these processes are universal in this type of material. The complicated story behind these changes caused by light shows how complicated the process is, since many of these changes can happen at the same time. It’s possible that the work to find the perfect system will pay off, as highly effective and stable gadgets will be made.
Lasing in Lead-Halide Perovskites
In Section 12.2, we talk about charge carrier recombination, which happens when a semiconductor gives off an excited electron with a hole attached to it. This causes photons to be recycled, but if a lot of excited carriers are made, the number of electrons in the conduction band may be higher than the number of electrons in the valence band. In this case, a photon that is released without being triggered can cause an excited electron to recombine with a hole. This can cause the release of another photon that has the same range, direction, and optical phase as the first one.
When triggered emission beats absorption, a process called population inversion happens, and the semiconductor shows optical gain. You can add an extra feedback system, like a hollow structure, so that the photons that are released go through the optical gain medium more than once. When there are enough charge carriers above a certain level, optical gain is greater than optical losses (from scattering or reabsorption), and laser output is reached. To make this happen, you need to pick the right material so that nonradiative losses don’t get in the way of the high number of excited charge carriers that is needed for population inversion. You also need to add a feedback system that lowers losses.
Liquid-helix (LHP) materials are now being used in electrically pumped lasing solution-processed devices. Population inversion is achieved by electrically injecting charge carriers, which is important for making these devices work in the real world. In the area of solution-processed materials, this “holy grail” is still hard to find, but a lot of work has been made in the last few years. The progress made in the fields of colloidal quantum dots (cQDs) and organic semiconductor lasers has helped LHP-based lasing.
When solution-processed materials try to make a laser device, they lose a lot of material when they get close to the high carrier density needed for population inversion. But because LHP is similar to other solution-processed materials, a lot of progress has been made in the last few years. New discoveries about low-dimensional structures suggest that this shape could be a fun way to make LHP-based lasers.
The main problem with studies that use CW pumping and Lithium-Ion Perovskites (LHP) for lasing and ASE is that the enhanced emission only lasts a short time. This is called “lasing death,” and it happens at room temperature (RT). Before adding CW light amplification to real-world electronically driven devices, it is important to understand this limitation. The way that CW lasing and ASE work together shows that the reported carrier thresholds for ASE (10−17–10−18 cm−3) are in the area where bimolecular recombination is strongest, which means that losses caused by flaws shouldn’t get in the way. But it turns out that defect-related recombination plays a more complicated role when you look at the laboratory settings in which light amplification happens.
However, because LHP doesn’t transfer heat well, the intense pumping needed to get enhanced emission heats up the sample. This hurts charge recombination by raising the ASE carrier threshold and ultimately leading to the death of the laser. This has to do with the tail states that these materials have because of energetic disorder, which will help empty out the energy bands and raise the carrier barrier Nth. In a semiconductor, Nth should go up with temperature after T3/2 because inserted carriers spread out over a wider energy range in the bands, which stops population inversion. This effect is stronger when band tail states are present, which leads to a dependence shown by
You can find T3 by taking cot2(kbT𝜋 E0) + 1, where E0 is the material’s Urbach energy. CW irradiation at freezing temperatures in a neutral atmosphere also creates flaw states that help charges recombine without radiation. As a result, an order of magnitude increase in k1 has been seen to happen at the same time as the rise in Nth caused by T. This increase also contributes to the lasing death.
Other recombination processes we talked about above are also affected by temperature during heavy pumping, which makes the picture of lasing death even more complicated. Because there will be some T growth, progress will be needed in two areas: flaw control and making LHP more flexible for recombination. A lot of work is being done to look into CW and RT lasing in LHP, but it’s important to remember that low-dimensional structures can get around some of the problems listed above.
Conclusions
LHP materials are interesting because of the unique emission qualities they have, especially in solution-processed materials that have organic molecules. It is well known that they can handle structure disorder, but more study is needed to find out where crystalline flaws come from and what role they play in LHP release. The “soft” nature of these materials makes them unstable and sensitive to changes in their surroundings, which affects their QY. This makes it hard to commercialise and create light-assisted postprocessing methods. Even though more research needs to be done to fully understand how light is emitted, the possibility of using these ideas to make very efficient light-emitting devices is still an important goal.
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