PSCs, which are polycrystalline thin-film organic-artificial lead halide perovskite solar cells, have reached a record power conversion efficiency (PCE) of 25.5%, which is higher than other inorganic solar cells like Cu(In,Ga)Se2 and CdTe. This high PCE is mostly because lead halide perovskite emitters have better photovoltaic qualities, like having a very long carrier lifetime and a low shockley-reed-hall non-radiative recombination rate. Lead halide perovskites often have more flaws than their single-crystal peers. This makes them have unique flaw qualities that you won’t find in most solar cell absorber materials.
A theoretical study of the defect properties of metal halide perovskites and halide perovskite derivatives shows that lead halide perovskites have special benign defect properties, such as point defects with low formation energies that make shallow levels and point defects with high formation energies that make deep levels. These features come from the antibonding link between the Pb lone-pair s and I p orbitals, the correct energy position of the Pb lone-pair s orbitals, the high ionicity, and the high electronic dimensionality. When you replace Pb with Sn and Ge, the number of acceptor defects goes up by a lot. This is why non-Pb halide derivatives don’t have the unique safe defect qualities that lead halide perovskites do.
Defect Properties of ABX3 Halide Perovskites
Pb-Based Halide Perovskites
Point flaws, surfaces, and GBs in polycrystalline absorber thin films are very important for how well the device works. To make free carriers, high-performance solar cells need shallow-level point defects. They avoid deep-level defects to stop non-radiative recombination. A lot of research has been done on flaw features in metal halide perovskites using density functional theory (DFT) studies.
Point Defects
In lead iodide perovskites, native point flaws are very important for the movement of carriers and the solar qualities of thin-film absorbers. Shallow acceptors (donors) are what cause p-type doping, and defects with energy levels deep in the bandgap act as Shockley–Reed–Hall non-radiative recombination centres. These are what cause the minority carrier lifetime to be short and the open-circuit voltage (VOC) of the solar cells to be low. The atomic orbital theory can help us understand the general trend of point defect levels in lead iodide perovskites.
The energy bands are made when atoms that are bound together mix their orbitals. The defect levels, which include both point and structure defects, are made when bonds are broken or added, causing hanging bonds and wrong bonds. The general electric structure of the host material can help you figure out where the flaw levels come from at the atomic level.
The empty Pb p orbitals are the main source of the conduction bands and valence bands in lead iodide perovskites. Because of how the ions are arranged in lead iodide perovskites, there isn’t a strong covalent antibonding link between Pb p and I p. This means that the conduction band minimum (CBM) shouldn’t be much higher than the atomic Pb p states. Lead iodide perovskites have a valence band maximum (VBM) that is mostly made up of I p states and some Pb s states as well.
For an I vacancy, the defect state is made up of the Pb bonds that are hanging around the I vacancy, creating a dry donor state (Dd). There is a Pb vacancy, and the defect state is made up of I hanging bonds around it. These bonds form between the VBM and the I p atomic orbital level.
In antisite defects, the wrong links between cations or anion pair up to make defect states. There are also interstitial defects that can be caused by either hanging bonds or wrong bonds, based on the shape of the defect. Deep gap states could be made by wrong bonds, like the wrong Pb p–Pb p and I p–I p bonds in lead iodide perovskites.
DFT simulations have been used to study native point flaws in lead halide perovskites in great detail. For MAPbI3, Yin et al. first looked at all the possible intrinsic point flaws by using the generalised gradient approximation (GGA) functional to do the calculations. This function matches the bandgap found in the experiments. They discovered that defects with low formation energies, like I interstitial (Ii), MA-on-Pb antisite (MAPb), MA vacancy (VMA), VPb, MAi, PbMA, VI, and MAI, have very shallow transition energy levels.
The research is mostly about the features of lead halide perovskites, especially MAPbI3, which has good flexibility in conducting electricity and can handle small defects better than other materials. MAPbI3 mostly has small flaws, and unlike most p-type thin-film solar cell absorbers, it can change how it conducts electricity based on chemical potentials. The better good flaw features of Pb halide perovskites are due to the strong Pb lone-pair s orbital and I p orbital antibonding coupling, as well as the high ionicity of MAPbI3.
Lead halide perovskites also have a strong covalent nature that can cause deep flaw states to form that don’t usually happen in ionic materials. For instance, when a flaw gets negatively charged, the structure changes in a big way. The two Pb atoms that were apart because of the gap move towards each other and form a dimer after taking on the extra electron. This dimer formation was only seen in a molecular dynamics experiment that took place at about room temperature. It doesn’t happen when the flaw structure is normally relaxed at 0 K.
It makes a deep defect level in the bandgap when a Pb dimer forms, which lowers the energy in the −1 charge state and moves the ε(0/−) transition level from the CBM to 0.38 eV below the CBM (or 1.25 eV above the VBM). It was seen that a Pb dimer formed for both Pbi and PbMA flaws, which led to the same deep states in the bandgap.
The research discovered that among point defects, only the iodine interstitial (SOC) and its complexes cause deep amounts of electron- and hole-trapping inside the bandgap, which act as places where recombination doesn’t happen through radiation.
Ideal Grain Boundaries
Polycrystalline semiconductor absorbers (GBs) can have a big effect on photovoltaic qualities. Intrinsic GBs can create deep levels in bandgaps, which is thought to be bad for the performance of solar cells. Ideal GBs in MAPbI3, on the other hand, are naturally good. The structure model of ο5(310) GB for CH3NH3PbI3 has standard GB traits like wrong bonds and bonds that hang down. A density of states (DOS) study of CH3NH3PbI3 shows that GBs don’t make any states in the bandgap. Some GBs, like ο3(111) GB, don’t have many flaw states that show up deep in the bandgap. The good qualities of GBs might be due to shallow point defects, since the atoms at GBs have the same chemical conditions as individual interstitials and gaps. This makes hanging bonds and wrong bonds like I—I bonds and Pb—Pb bonds. This kind of good GB behaviour isn’t seen in Si, GaAs, or CdTe.
To sum up, GBs in polycrystalline semiconductor absorbers can have a big effect on their photovoltaic properties. However, ideal GBs in MAPbI3 are naturally harmless. The good qualities of GBs can be described by shallow point defects. This is because the chemical environments of the atoms at GBs are similar to those of individual interstitials and gaps, which creates wrong bonds and bonds that hang off.
Ideal Surfaces
It has been used to study the structure and electronic features of the surfaces of Pb halide perovskites, in particular MAPbI3. The research showed that the tetragonal phase has two main phases on all four of its surface faces. The more likely (110) and (001) surfaces have both endings at the same time. The electrical structures of the stable empty and PbI2-rich flat terminations on these surfaces are mostly the same as those in bulk MAPbI3, with no bandgap states. Because they don’t have any states in the bandgap, these better surface qualities may also help explain why Pb halide perovskites have a long carrier lifetime. These better surface features may also help explain why Pb halide perovskites have a long carrier lifetime for solar uses.
Surfaces and Boundaries in Real Thin Films
It is true that ideal graphene oxide (GB) and perovskites’ surfaces are electrically neutral, but real perovskite films may have point flaws like I and Pb interstitials. I atoms move through GBs in perovskite films, which is thought to be partly to blame for the hysteretic effect seen when measuring the current and voltage of solar cells. The DFT calculations show that in κ5(210) GB, an interstitial I has an energy level that is about 0.26 eV lower than the one in the bulk regions. This means that some I interstitials are likely to separate into GBs and change the features of the GBs.
A small, sharp peak appears above the valence band in the total density of states (TDOS) of the ¿5(210) GB with an I interstitial. This shows that the interstitial I at the GB creates a deep level. It takes 3.47 Å of bonding between the interstitial I and the next-door neighbouring I atom, which is less than the smallest I—I bond length in the ο5(210) GB when interstitial I atoms are not present. In real perovskite thin films, grain boundaries and surfaces or contacts may have non-radiative recombination centres. A lot of people have used surface and grain border passivation to make devices work better in solar cell uses.
Sn-Based Halide Perovskites
Because of the difference in energy between Sn 5s and Pb 6s, Sn-based halide perovskites have different flaw features than Pb-based perovskites. This makes the VBM of Sn-based perovskite have more energy. If you look closely, you can see that Sn- and A-cation vacancies have low energy levels because the Sn 5s and I 5p orbitals are strongly hybridised. There are a lot of hole carriers and electrical transmission when there are a lot of VCs and VSn.
On the side of the donor flaw, most of them have donor levels that resonate inside conduction bands. These levels include Csi, CsI, VI, and others. Only the SnI antisite is different because it breaks the Sn 5p orbitals, making a shallow (0/+) level close to the CBM and a deep (+1/+3) level in the middle of the bandgap. When Sn is present in large amounts, this deep-level defect can be concentrated. This is different from the organometal halide MAPbI3, where all main defects only form shallow levels when Pb is present in large amounts or not present at all.
This is p-type CsSnI3. The SnI flaw is an electron trap and a place where photogenerated electron-hole pairs recombine. When CsSnI3 is used as an absorbent, a high quantity of SnI hurts the performance of the solar cell. A Sn-poor state should be used to lower the amount of SnI in samples of synthesised CsSnI3. But if there isn’t enough Sn, there will be too many holes and too much electrical transmission. This will cause low shunt resistance, which is also bad for the performance of the solar cell.
An Sn chemical potential that is neither too high nor too low should be used to make CsSnI3 as a light-absorbing material.
Ge-Based Halide Perovskites
Ge iodide perovskite has more energy than Sn iodide perovskite because it is smaller and doesn’t bond with other particles. This makes the bandgap bigger and the acceptor levels deeper than in Sn iodide perovskite. The most important natural flaws in CsGeI3 are vacancies. These are made up of Ge and Cs vacancies (VGe and VCs), which accept electrons, and iodine vacancies (VI), which donate electrons.
Finally, VGe and VCs have the lowest formation energy when Ge is low and I is high. Both are shallow acceptors that make it easy for CsGeI3 to make free holes. There isn’t a local donor imperfection that can effectively make up for these flaws. When the Ge-rich, Cs-rich, and I-poor limits are reached, the amounts of VGe and VCs decrease, while VI increases. The VI and VGe creation energy lines cross at 0.43 eV above the VBM. This makes the p-type semiconductor-semiconducting CsGeI3, which can be used as a p-type solar collector.
VI is a key part of making up for shallow native acceptors (VGe and VCs) and stopping metallic conductivity, which is needed for CsGeI3 to work as a solar absorber. VI, on the other hand, can seriously lower electron motion and lifetime because it is a deep electron trap. The fact that CsGeI3 solar cells have a low open-circuit voltage (VOC) makes sense given that they have a deep source VI.
Defect Properties of Halide Perovskites Beyond
ABX3
A2BX6 Halide Perovskite Derivatives
A2BX6 is a combination that is made by taking away half of the B cations from ABX3. This makes vacancy-ordered double perovskites. The most common member of this group is Cs2SnI6, which has a different electronic structure than CsSnI3. The bandgap is straight at the Γ point, but dipoles are not allowed. The electrons are no longer in the dispersive antibonding states of Sn 5s and I 5p orbitals, which creates the CBM. The VBM comes from the antibonding states of I 5p orbitals, which are localised and cause big changes in the masses of the electrons and holes.
Different defects in Cs2SnI6 are caused by its different electronic structure and bond nature. Four inherent flaws—VI, Sni, CsI, and VCs—have enthalpy of formation (ΔH) values that are low enough to change the electrical properties. VI has the lowest ΔH (-0.74 eV when I is abundant and -0.28 eV when I is scarce), so it acts as a deep donor with 𝼀(0/+1)=0.74 eV above VBM (i.e. 0.52 eV below the CBM). The n-type situation in Cs2SnI6 is mostly caused by this.
When I is low, Sni has a less deep transition 𝼀(0/+1) at 0.11 eV below the CBM and a small ΔH (≒1.18 eV). This makes Sni and VI the main donors for n-type conduction. CsI has a low H and stays in a neutral charge state at high EF (i.e. n-type conditions). Because of this, it doesn’t help with n-type conduction.
The only shallow donor in Cs2SnI6 is SnI, which has a 𝼀(0/+2) value above the CBM. However, SnI’s high ΔH value means it doesn’t add much to the n-type conductivity, even when I is low. When I is present in large amounts, VCs has a low ΔH (≒1.37 eV) and can act as a deep acceptor. However, at EF only above 0.51 eV from the VBM, the hole density created is too low to make up for the electrons that VI gives off.
The other innate flaws have H values that are too high. For example, VSn has a ¦H value that is too high at all chemical potentials and can be as high as 3.63 eV when Sn is not present. Any intrinsic flaw can’t work as a good p-type source from I-rich to I-poor conditions, so it would be hard to get intrinsic p-type conduction in pure Cs2SnI6. Instead, Cs2SnI6 naturally has n-type conduction because VI and Sni donors are easy to form.
A3B2X9 Layered Halide Perovskites
The possible perovskite molecule A3B3X9 is changed into the A3B2X9 stacked perovskite by taking away every third B layer. The bandgap of Cs3Sb2I9 is almost the same as a direct bandgap because the difference between direct and indirect bandgap is very small (less than 20 meV). The VBM is made up of both I 5p and Sb lone-pair 5s states, while the CBM is mostly made up of Sb 5p states. The effective electron and hole masses that were found are bigger than those for lead iodide perovskites.
The GGA functional was used to study the flaw features of Cs3Sb2I9 and found that the bandgap should be 1.55 eV higher than it actually is. When it comes to flaws, Csi are shallow acceptors and donors, while all the others make deep levels in the bandgap. The CH3NH3PbI3 perovskite has defects that are very different from these ones.
The difference is clear if you look at the qualitative model for guessing how many flaws there are in crystals. The Sb 5p orbitals are more focused than the Pb 6p orbitals. This means that the antibonding between Sb 5p and I 5p is stronger than the antibonding between Pb 6p and I 5p. This means that for Cs3Sb2I9, there is a bigger energy difference between the p orbital of the anion and the CBM than for CH3NH3PbI3.
The main flaws in Cs3Sb2I9 are VCs, Ii, ISb, Csi, and VI. Ii, ISb, and VI make deep levels, while only Csi and VCs make shallow levels. All dominant flaws, on the other hand, only cause low amounts of CH3NH3PbI3.
To use Cs3Sb2I9 as a solar material or for other electrical uses, flaws will need to be carefully controlled and/or passed over.
A2B(I)B(III)X6 Halide Double Perovskites
The halide double perovskite A2B(I)B(III)X6 has been suggested for use in optoelectronics, and solar cells are being tested with Cs2AgBiBr6, which has a bandgap of 1.95 eV. The GGA function says the bandgap should be 1.32 eV, which is a lot less than the number found in the experiment, which was 1.95 eV. The bandgap is slightly smaller when SOC is added, coming in at 1.16 eV. The estimated bandgap for the mixed HSE functional is 2.21 eV. When SOC is added, the bandgap goes down to 1.97 eV, which is very close to the actual number.
As you can see, the VBM is at the X point and the CBM is at the L point. The VBM is mostly made up of Br 4p and Bi 6 p orbitals that are not connecting with each other, while the CBM is mostly made up of Bi 6 p orbitals and a small amount of Ag 5s and Br 4p orbitals. With the HSE+SOC band edges, the effective masses of holes are 0.24 m0 in the X–Γ direction and 0.96 m0 in the X–W direction. For electrons, they are 0.58 m0 in the L–Γ direction and 0.34 m0 in the L–W direction.
It was found that VAg has the lowest ΔH and serves as a shallow acceptor, with the (0/1−) transition occurring only 0.04 eV above the VBM of the flaws that are built in. This makes VAg a good source for good p-type transmission and doesn’t hurt the performance of photovoltaics. On the other hand, Bi 6s orbitals don’t contribute as much to the VBM, which means that VBi has deep transition levels in the bandgap. VCs is also a shallow acceptor, with the (0/1−) transition level 0.07 eV above the VBM because Cs+ is a very charged ion. There is a brief donor transition at 0.03 eV below the CBM for VBr, but it has a much higher ΔH than VAg and can’t give up enough electrons to make up for the holes that VAg creates.
Out of the four interstitials, Agi and Bri have the lowest ΔH. The (0/1+) transition level for Agi is 0.05 eV below the CBM, and it is 0.26 eV above the VBM for Bri. Bri, on the other hand, is 0.26 eV above the VBM and is a deep acceptor. But their ΔH values are too high for them to have a big effect on the electrical properties. The twelve antisites have ΔH values that are mostly low. This is because AgBi and BiAg are B-site cation-on-cation antisites. AgBi is a deep acceptor and has a low ΔH, especially when Br is present in large amounts. This makes photovoltaics less effective. It has a shallow transition level (0/1+) at 0.02 eV above the CBM and a deep transition level (1+/2+) at 0.42 eV below the CBM.
Studies in theory have shown that lead halide perovskites can’t have an electronic structure that is similar to that of halide double perovskites where both B(I) and B(III) are lone-pair cations. There are special antisites called B(I)-on-B(III) (B(I)B(III)) and B(III)-on-B(I) (B(III)B(I)) that are only found in A2B(I)B(III)X6 double perovskites. These antisites are very important to their electrical features.
As for Cs2TlBiBr6, TlBi and BiTl antisites act as deep donors and acceptors, for sure. The InBi and BiIn antisites in Cs2InBiBr6 behave in a way that is similar to how they behave in Cs2TlBiBr6. Local flaw structures can help us understand the deep nature of B(I)B(III) and B(III)B(I) antisites.
When you look at A2B(I)B(III)X6 double perovskites, the B(I) and B(III) cations are grouped in a NaCl-like pattern. At the B(I)B(III) or B(III)B(I) antisites, this ordered structure is broken, creating what can be thought of as a local “double” perovskite structure. When Tl(III)Bi(III) and In(III)Bi(III) antisites are present, the Tl(I)–Tl(III) and In(I)–In(III) local double perovskites lower the bandgap and act as deep acceptor levels.
The shallow VTl or VIn and deep TlBi or Host (B(I)B(III)) antisite in Cs2TlBr6 and Cs2InBiBr6 look like the A2B(I)B(I)X6 “double” perovskite when Br is present. When InBi are formed, they have low formation enthalpies, which causes degenerate p-type conductivity and high-density trap states in the bandgap. To get the best solar performance, you should carefully use a Br-poor state to stop the formation of harmful deep antisite flaws.
Conclusion
The study looks into the defect qualities of metal halide perovskites and halide perovskite derivatives. It shows that these materials have special traits, like point defects that aren’t very deep, high-energy defects that are deep, and grain boundaries that don’t create deep states. These traits are not present in halide perovskite versions. The unique flaws in lead halide perovskites are caused by the Pb lone-pair s orbitals not interacting with the halogen p orbitals, the Pb lone-pair s orbitals being in the right energy position, the high ionicity, and the high electronic dimensionality.
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