Electrons and ions move during electrical passage, and conductivity is a measure of how well it works. Modern technologies like metal-based electrocatalysis, semiconductor-based microchips, ceramic oxides-based fuel cells, metal oxides-based lithium-ion batteries, electroencephalography-based, and brain-computer connections depend on being able to fine-tune a material’s conductivity. Figuring out a material’s conductivity is important for many reasons. This chapter is about ionic conductivity in metal-halide perovskite (MHP) semiconductors. It will talk about the theory of ionic transport, the internal and external factors that affect ionic transport, and how ionic buildup hurts the performance of MHPs function devices.
Theoretical Basis of Ionic Transport
Ionic transport in solid-state thin films is usually sped up by flaws that cause hopping reactions, which can happen in the bulk or at the edge. 𝼎i = Zi^2e2NACvDv^kBTVm shows the process. 𝼎i is the ionic conductivity, Zi is the ionic charge, NA is Avogadro’s constant, Cv is the vacancy concentration, Dv is the vacancy diffusion coefficient, and Vm is the perovskite molar volume.
Because there isn’t much heat energy at low temperatures, the void concentration Cv stays the same. At high temperatures, on the other hand, the number of vacancies rises rapidly with temperature, depending on how much energy it takes for Schottky flaws to form. The temperature also changes the diffusion coefficient Dv. Dv0 stays the same, while Ea is the starting energy for void diffusion.
The situation gets more complex at high temperatures because the number of defects changes, as shown in Equation (11.3). This is the case for a chemical formula called ABX3. The number of empty spaces in perovskite at a certain temperature can be written as CX = [VX] = (Ks)(1∗5)exp (−ΔHS)kBT.
There is a strong link between the quality of the polycrystalline perovskite film and the hopping distance, ionic radius, and local crystal structure, which affect the Ea value. Ions move more quickly through crystals that have more and bigger interstitialsites, ions that are smaller and less charged, and shorter lengths between jumps.
Characterizations of Ionic Transport
Optical, electrical, and electrochemical techniques can be used to study ion movement in solid-state thin films. To move ions, you need the right electric field, which is generally made up of two electrodes that can apply an electric field to the sample while it is still in place. The wires can be put on the sample to make a structure that goes up and down or side to side. It is best to study ionic transport using the lateral structure because it has a higher ratio of ionic transport than the vertical structure. This makes it possible to do in-situ optical characterisations during the electric poling process and makes it easy to use outside stimuli like light and gas absorption.
Galvanostatic DC polarisation measurement is a simple but useful way to find out the ratio of ionic conductivity to electronic conductivity for electrically characterising ionic transport. It is possible for this test to make both ions and electrons move back and forth without hurting the subject in any way. The voltage instantly hits a fixed point, V0, and then slowly rises until it reaches the saturation point, VS. Stoichiometric polarisation usually acts in a short-lived way like this. This is because the electrodes stop the moving ions. In the constant state, the ions’ electrochemical potential difference goes away, and only electrons flow (i = iele, iion = 0) with Vs = iRele. This is what we call ionic conductivity.
A normal electrical way to find out how ions and electrons move over time is impedance spectroscopy research, which is similar to galvanostatic polarisation. When a step voltage is applied to R1C1, the electric current decreases in a way that is shaped like an exponential function of the characteristic time. There is a complicated resistance between AC power and current.
Light photography, photoluminescence (PL), time-resolved photoluminescence (TRPL), and photothermal induced resonance (PTIR) microscopes are all useful for figuring out how things work optically. AFM tip working in contact mode as a local reader of IR spectra and maps with a precision of up to tens of nanometres are used in PTIR. The IR laser is pulsed and its wavelength can be changed. It lets you map out where certain chemical species are found and has made it possible to characterise a wide range of samples, such as plasmonic nanomaterials, metal-organic frameworks, polymers, and most recently, MHPs.
A solid-state electrochemical cell is used to find the mobile ion species by watching the chemical reaction happen at different surfaces for electrochemical characterisations.
Mobile Ions in Perovskite Film Under Electric Field
MHPs’ crystal structure makes it easy for ions to move around inside the crystal, especially at the surface and grain boundaries. Using first-principles calculations to look at the Ea of different ions through Schottky flaws shows that there is a basic connection in MAPbI3 materials: Ea(I) Ea(MA) Ea(Pb). With an activation energy of 0.58 eV, I moves along the I–I edge of the [PbI6]4− octahedron. Four I− ions with a higher activation energy of 0.84 eV move around the unit cell face as MA+ moves through it. With a movement energy barrier of 2.31 eV, Pb2+ ions move in the direction of the unit cell. It is thought that VI is the main flaw in perovskite, which is why VI conductivity is higher than ionic conductivity in MHPs.
Different theory works could lead to different outcomes, depending on the movement path and process. To give you an example, the Ea values for I−, Pb2+, and MA+ ions are found to be 0.08, 0.80, and 0.46 eV, respectively. It was shown in another study that a deprotonation process can allow a proton to exist in MHPs. This proton has a lower activation energy of 0.07 eV thanks to a quantum twisting mechanism. A lot of theory research is built on the bulk, not the surface or grain border, which would help studies more.
In order to find direct proof of ionic transport, Yang et al. created a solid-state electrochemical cell called Pb|MAPbI3|AgI|Ag. This cell had one electronic electrode (they called it “+”) and one ionic electrode (they called it “-“). Using a scanning electron microscope (SEM) image, energy dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD) to characterise the material, PbI2 was found at the boundary of Pb and MAPBI3. It showed that I− can move easily through the MAPbI3 film and gave strong proof that ionic transport is possible in MAPbI3.
Also, Yuan et al. used PTIR imaging to show how the MA+ ions were spread out in space on a horizontal MAPbI3 device before and after electric poling. The results showed that the MA+ ions were moved around in the perovskite film. Cryogenic galvanostatic characterisation between 17 and 297 K showed that protons can move.
The Factors Affecting Ionic Transport
in Perovskites
Researchers have found that the relaxation time of ionic transport in perovskite films can be very different, even when the electric poling state stays the same. The quality of the crystal and its surroundings may control this behaviour. Understanding these things and getting a clear picture of how MHPs work can make the device more stable.
Moisture
In 2015, Leijtens et al. looked into how water molecules affected the movement of ions in the MAPbI3 film. They found that the bare perovskite film breaks down quickly in an electric field of about 0.06V¼m−1 when the humidity is 30%. But if you put a layer of PMMA on top of the film, it slowly goes yellow over many hours. Most MHPs have a build-in field of about 1V¼m−1, which is two orders of magnitude stronger than what Leijtens found. Water molecules adsorb on the perovskite crystal surface and form hydrogen bonds with organic cations (MA+ or FA+). This makes it easier for ions to move through the material. This outside disturbance weakens the connection between MA+/FA+ and the octahedron around it, which makes it easier for MA+/FA+ to move. So, for better stability, you need a neutral setting and tight containment.
Light Illumination
Perovskite devices can keep working properly after being stored in darkness for a few months in an inert gas setting, but they break down quickly when exposed to light. To learn more about how light affects perovskite film, Zhao et al. used an optical lens to look at how the shape of the perovskite changed when the light intensity changed using an Au/MAPbI3/Au device structure. The researchers used electric poling and found that as the light levels rose, more pinholes and dendrites (PbI2) appeared in the perovskite film.
One possible mechanism was found: when there was a strong electric field and light, the heavy I moved towards the cathode and turned into I2. The MA+ also disappeared as CH3NH2 gas as it moved from the cathode to the anode, and the MAPbI3 component slowly changed into PbI2. In other words, light can help ions move around.
The next question is how light improves the movement of ions in the MAPbI3 film. A theory says that light can raise the try frequencies of ionic transport, and another says that photo-crystal interaction can lower the energy barrier for ionic transport. To get a better idea of how much energy is needed for ionic transport, Zhao et al. used cryogenic galvanostatic tests to find out how the ionic conductivities changed with temperature when different light levels were applied with a very small current on the Au/MAPbI3/Au material that was cooled with helium.
There are two different parts to the activation energy region: Ea1 (T >250 K) and Ea2 (180 K
To study the changing process of ionic transport, the temperature-dependent relaxing time (kinetic constant) could be taken out. Below 80 K, the ln(Kion) of MAPbI3 behaves in a way that is not affected by temperature. This is likely because the ions are deeply quantum tunnelling instead of classically hopping. H+ is the most likely ion for this to happen with because H has a very low mass.
Experiments and theories strongly suggest that the horizontal lines in Figure 11.8b below 80 K are caused by H+ moving around in MAPbI3.
Perovskite Composition
It is very important to understand the ions that cause light-enhanced ionic transport in order to make perovskite materials that are more stable for use in devices. The perovskite that Zhou et al. changed for light excitation was MAPbBr3, MAPb(I0.9Br0.1)3, and CsPbI2Br. We could still see plane branching structures in MAPbBr3 and MAPb(I0.9Br0.1)3 films when the light was brighter. This shows that halide anions are not the ones moving the ions faster because of the light. The perovskite film didn’t change much when CsPbI2Br was added to the same structure, though, and there was no light-induced phase segregation. This is similar to what Beal et al. found. This means that the Cs replacement stopped the movement of ions.
We found the starting energy for ionic transport in CsPbI2Br and MAPbI3 by measuring the galvanostatic force. Compared to MAPbI3, the Cs-perovskite barrier for ionic transport stays the same (0.45 eV) even as the light intensity increases. This shows that ionic transport in the all-inorganic perovskite film is not affected by light. The fact that light improves ionic transport in an organic cation-based perovskite film strongly suggests that the organic cation plays a key role in the complex interaction between photoexcitation and ionic transport. Because of this, Cs replacement is a good way to stop cation movement.
Ion migration is not the same as the moving of charged flaws in MHPs. Instead, carriers, traps, and mobile ions interact with each other in a dynamic way, which could be what changes the ionic conductivities. For a perovskite film with a lot of empty spaces, the interstitial ions could move and fill them up at the start of the ionic transport process. During this stage, the “healing effects” will lower the amount of mobile ions, which will then lower the ionic conductivities.
If there are more empty flaw states in the bromide-based perovskite, more charged ions could make up for them and briefly lower the ionic conductivities. During the early stages of migration, ions can fix some defects. However, if they are transported for a long time, they can permanently change the perovskite, leaving a lot of defect states near the electrodes (shown by reduced fluorescence), and this can make the cells unstable.
Grain Boundary
Ionic transfer is more likely in solid-state films where there are more flaw states. Ionic transport can happen through grain boundaries (GBs) because of a lot of lattice instability, grain confusion, extra volume, and wrong bonds at GBs. In modern MHPs, low-temperature solution methods are used to make them, so the target film has a lot of GTs. Even though defect states at GBs might not work as deep-level traps, they could still help the hopping-dominated movement of ions.
By looking at the amount of current hysteresis at GBs and in the grains of polycrystalline MAPbI3 films, Shao et al. found that ions move more quickly at GBs. They discovered that smaller grains could cause stronger I–V hysteresis and make the ionic conductance a bigger part of the total conductivities in galvanostatic characterisation. When looking at numbers, the perovskite film with bigger grains (about 1 μm) had an activation energy of 0.50 eV in darkness and 0.14 eV in light for ionic transport. On the other hand, the value dropped to 0.27 and 0.08 eV for perovskite with smaller grains (300 nm). In a single crystal, the starting energy for ionic transport is about 1.10 eV when it’s dark and 0.47 eV when it’s lit up.
To sum up, making the grains bigger and blocking defects at GBs might make the devices in perovskite materials more stable. Ionic movement in perovskites is affected by grain size, grain confusion, too much volume, and the wrong bonds.
Lattice Strain
When GBs form and the perovskite crystals’ lattice expands due to heat, they cause compressive stress and tension strain that are spread out in both the out-of-plane and in-plane directions. Ostwald ripening can happen after thermal processing. This can partly release stress and lower the densities of GB. But leftover strains can get as high as 50 MPa. Zhao et al. looked into how strain affected the stability of the MAPbI3 film. To do this, they bent the film into convex and concave forms, which increased and decreased lattice strain. A big part of the convex film went yellow after 500 hours of light, which was proven to be PbI2. The concave film, on the other hand, was very stable and didn’t show any signs of PbI2.
It was found that strain-accelerated breakdown was linked to ionic transport. To keep wetness out, the perovskite was topped with a thin layer of polystyrene. Conductance readings that changed with temperature showed that the activation energies for the convex, flat, and curved MAPbI3 films got bigger over time when the conditions were dark and 25 mW cm−2. The activation energy was lowest in the curved film, which means that ions moved through it the most slowly.
Chen et al. found that a MAPbI3 single crystal changed its compression strain by 1% when it was exposed to an electric field of 3.7Vμm−1. The electrical response is caused by electrostriction, not the piezoelectric effect. The electrostrictive response is thought to be caused by the movement of ions and defects. In a normal perovskite solar cell with a built-in field of about 0.3–0.65 Vμm−1, they thought that about 0.01%–0.03% compression pressure could be made.
The Impact of Ionic Transport on Perovskite Films
and Devices
Ions can move through perovskite film at 0.3V¼m−1 or less, which makes photovoltaic effects switchable in horizontal devices that need low activation energy. To fix the inherent instability in highly stable MHPs, it is important to understand how device decay and ionic transport work.
Phase Segregation
In 2015, Hoke et al. saw that light could separate the phases of mixed-halide MAPb(IxBr1−x)3 perovskite plates in a way that could be undone. The perovskite film that had more than 20% bromide in it changed its PL redshift from 1.9 to 1.68 eV in less than a minute when it was exposed to less light than a sun (15 mW cm−2) at room temperature. Using XRD and absorption to study MAPb(IxBr1−x)3 revealed that it split into I-rich and Br-rich domains. The PL spectra returned to their original positions after being stored in darkness for five minutes, showing that perovskite has different stable states when it is dark and when it is lit.
The PL spectra in CsPb(BrxI1−x)3 changed in the same way by Beal et al. for 0.4 x <1. When the I-rich part of perovskite has a smaller bandgap, it could act as a charge-trapping flaw and lower the open circuit voltage (Voc) in MHPs. The second period for the PL shift is close to the ionic transport, so it is thought that the phase segregation is linked to the ionic transport. However, more proof is needed to prove this.
Later, Zhao et al. used galvanostatic measurement, in-situ PL scan, and real-time optical microscope recording to keep an eye on how the ions moved through the MAPbI3 film. After the current was turned on, they saw that the PL strength dropped in a few seconds at both the anode and the cathode. This showed that the number of defects increased across the perovskite film. Near the anode, there was a clear blue shift around 10 nm. This may have been caused by the band-filling effect caused by the iodine gaps with n-doping.
After electric poling, DFT calculations showed that I trimers can form in the I-poor area and Pb dimers can form in the I-rich area. This creates deep-level flaws about 0.3 eV below the conduction band minimum. So, ionic transport-induced trap states can act as nonradiative recombination centres in the perovskite film, shorten the lifetime of the charge carriers, and lead to the breakdown of the solar cell.
Doping Effects
In solar systems, the interface is very important for moving charge carriers, and ions that have moved can change this process by gradually building up on the interface. In a balanced solar device, an enormous photovoltaic effect can be created when electricity is applied and light is shining on it. When ions gather in the perovskite close to the electrodes, they can cause p-type and n-type doping, respectively. It is thought that n-type doping can be caused by positively charged iodine vacancies or MA+ interstitials and p-type doping can be caused by negatively charged MA+ vacancies or I- interstitials. This was proven by KPFM testing on an Au/Perovskite device where a piece of the Au electrode had been peeled off. Potential images showed that positively charged ions move towards the cathode, making a p–i–n structure. If the bias is turned around, the structure can change to n–i–p. The surface topography didn’t change much in the poling areas, so it can’t be said that the surface topography affected the surface potential characterisation. Because MHPs have a planar heterojunction structure, interfaces may be more sensitive to ions that build up. For long-term stable MHPs, it is very important to passivate interfaces.
SCLC and TFT Devices
A common way to find out about the carrier motion and trap densities of semiconductors is to use space charge-limited current (SCLC) characterisation. The dark JV curve of a single carrier device with symmetric ohmic contacts on either side of a semiconductor is used to do this. Measurements of SCLC can find several regimes, such as low voltage, high slope because of trap filling, and the SCLC regime at high voltage.
Their use with halide perovskites, on the other hand, is not possible because these materials are ionic. Mobile ions cause the well-known J–V hysteresis curves to rise in SCLC measurements, which means that Vtfl can’t be used to get accurate trap density values. It’s harder to use the backward scan to get a better idea of the trap density when a thin layer of PbI2 forms with a small injection barrier.
When the temperature is room temperature, there is clear hysteresis in both forward and backward JV scans in perovskite-based thin-film transistors. Ions move under the electric field and gather at the contact between the perovskite and the insulator. This partly blocks the electric field from the grid. This has a big effect on the modulation of the grid and lowers the motion of the field effect, which makes it hard to get a solid TFT that works at room temperature.
Based on IS data, mobile ions can have a big effect on figuring out the properties and lives of devices. Low-frequency capacitance goes up a lot when it’s lit up compared to when it’s dark and at room temperature. But over a long period of time, this behaviour is caused by the buildup of ions at the junctions. After being used for a long time, the cell device has a transition point in the capacitance-frequency spectra and a negative imaginary impedance below 1 kHz when there is a small poling electric field.
Degradation in Functional Devices
Because Spiro-OMeTAD is soft and organic, it lets ions that have built up pass through the perovskite/HTL barrier and into the HTL layer. In their study, Zhao et al. looked into how mobile MA+ can break down biological HTL. They looked at the XRD patterns of perovskite films in both new and old devices and saw that there was no extra PbI2, which means that the devices were barely breaking down. When the Spiro-OMeTAD layer was replaced with a new film, the cell efficiency went from 4.9% to 11.2% in the restored cells. This suggests that the breakdown of the HTL layer is partly to blame for the loss of efficiency. Time-of-flight secondary-ion mass spectrometry (ToF-SIMS) showed that the MA+ and Spiro distributions were very similar in broken devices, which suggests that MA+ got into HTL. Both MA+ and I− ions move through the PCBM layer and gather on the Ag internal surface in N2 in inverted devices with p–i–n alignment structures. A lot of MAI is lost at the GBs, which causes MAPbI3 grains to fuse together. This makes big PbI2 spaces that don’t conduct electricity well. First, MA+ and I− ions are released from the GBs of the perovskite layer. Then, the MA+ and I− ions move to rebuild the GBs, creating more flaws in both the thin films and the MAPbI3/PCBM interface. An inorganic hole transport material could be used to make the device more resistant to MA+/I− penetration because the covalent bonds in the inorganic crystal are very strong.
Summary and Outlook
At this point, standard micro-hole (MHP) solar cells are not stable enough to meet industrial standards. The first step towards selling MHPs is to solve this problem of instability. Ionic transport can create flaw states in the main perovskite crystal, cause interfacial band doping, and damage the organic hole transport layer, all of which affect the stability of the solar cell device. It has been found that light, organic cations, grain borders, and tension strain can all affect migration and the stability of MHPs. This is because perovskite materials are photoactive, solution-processed, polycrystalline, and contain organic cations. To stop ions from moving towards very stable MHPs, different methods can be used, such as decreasing the number of defects, making grains bigger, adding more caesium, and using a layer that blocks ions for carrier transport materials.
There are still a lot of unanswered questions, like how to separate cation and anion movement at the atomic and molecular levels, how to stop light-enhanced ionic transport, and how to make MHPs less effective without losing their efficiency. Ionic transport is thought to be well controlled in perovskite film based on different needs now that the deep process for it has been uncovered.
Creating artificial MHPs, where ionic transport has been shown to be light independent, is one way to help the solar business grow. Inorganic MHPs, on the other hand, don’t work nearly as well as organic species like MA+ and FA+. You could also make silicon/perovskite heterojunction tandem solar cells with a bandgap of 1.75 eV for the perovskite part. This might make the device 30% more efficient. At the moment, the most important thing is to raise the open-circuit voltage of wide-bandgap MHPs, which drop voltage by more than 0.6V, which is well below the Shockley-Queisser limit. MHPs could become important in the solar business in the future if stable tandem silicon/MHPs could be made with a Voc of 1.3V and Jsc of 18 mA cm−2.
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