Because they have many different physical qualities, perovskites have been studied a lot in the fields of condensed matter physics and material studies. A lot of research has been done on oxide and fluoride perovskites to find out about their photonic and electrical features, as well as their multiferroicity, superconductivity, piezoelectricity, and metalinsulator transitions. Recently, hybrid perovskite solar cells (HPSCs) made from organic and artificial lead halide materials have become a very interesting group of materials in the field of photovoltaics.
Perovskites are crystals that look like CaTiO3 and have the general chemical formula ABX3. A is a small organic dipolar cation like Cs1 and B is usually Pb21 in the lead halide perovskites that have been studied for photovoltaics. X can be a halide (I-, Br-, or Cl-). How the structure, bandgap, and optical qualities work rely on what kinds of cations and halides are used.
One of the NREL charts for approved cell efficiencies recently showed a new high of 23.7% for a perovskite solar cell. This number is higher than the highest efficiency ever reported for a lot of well-known solar materials, like CdTe (22.1%), CIGS (22.9%), and multicrystalline Si (22.3%). But it’s still hard for all of the rival technologies to beat single crystalline Si (26.1%) or Si heterostructured solar cells (26.6%), whose prices have dropped a lot in the last few years.
The described HPSC devices’ efficiencies were tested on small area lab devices (.1 cm2), but it’s still very hard to get stable high efficiencies with big area cells (.1 cm2). MAPbI3 is sensitive to things like water and high temperatures, for instance. A report came out not long ago saying that HPSC could stay stable for up to 1000 hours when exposed to a light source equal to one sun (1000 W m22 at AM1.5 G).
Most likely, multi-cation cascades can also be used to get a better effectiveness. Perovskites may need to use joint methods, though, in order to really compete with single crystal silicon. When compared to epitaxially grown III-V semiconductor tandem systems, metal halide perovskites tandem devices are very flexible and could be made with very low-cost ways that pay for themselves quickly in energy.
To make paired HPSCs or fully artificial PSCs that work very well, it is important to measure their crystalline structure and symmetries. This knowledge is very important for managing the structure and basic optoelectronic qualities of a strong device structure that works well for a long time. X-ray diffraction and Raman spectroscopy are useful for finding out about the qualities of a material, like its crystal structure, symmetries, displacements, flaws, micro-crystallinity, orientations, vibrations, phonon lifetimes, and how these things change when the material changes. These methods give us important details that we need to find structure-to-property links between materials and function.
XRD and Raman spectroscopy
This method of X-ray and Raman characterisation has been used to find a lot of different microstructural, morphological, and chemical traits, ranging from subatomic molecular chemistry to device-scale alignment. Instrumentation, X-ray and light source strength, and detection technologies have all gotten better over the years, which has made these methods more common. Now it’s possible to get high-quality data and quantitative information that can be used to get accurate accounts of the molecular structure and architecture of materials that are of interest. This huge amount of data, along with electrical characterisation and modelling, is often used in a wide range of situations, from basic research to making design rules that help people make smart choices about materials and whole devices.
Max von Laue found that X-rays could be diffracted from crystals and found the constructive reflection maximum condition. This was a huge step forward in the development and use of X-ray diffraction. W.H. Bragg and W.L. Bragg made a geometric analogue that met the Laue condition and allowed the Bragg equation to be written for constructive diffraction. Since the wavelength stays the same and the angle θ is changed to the angle where the intensity is highest, B, the Laue requirement for the intensity I(R)-max is now naturally met by the constructive interference for a fixed wavelength.
The highest level of strength at angle θ can help you figure out the lengths in solid materials, which shows their internal structure and symmetry. But the shape of the top tells us how many crystalline surfaces are needed to make or cancel out the non-constructive interference signal. Peak form research can be used to find out about crystallite size, pressure, and local disorder. If the sample is textured or single-crystalline, it is possible to measure the crystal symmetry or crystallite orientations by extending the diffraction analysis to directions other than the Bragg angle. This can be done by rotating the sample, using a wide-angle detector, or moving the detector to angular ranges that are perpendicular to the Bragg angle.
In the broadest sense, a pole figure can be used to fully describe the spread of diffractions from a sample that is complex and has different crystallite orientations. In RP phases, the crystalline unit cell can be seen as a stretching of the dimensions in the perovskite structure, with layers of perovskite symmetries (ABX3) in between. The general formula for RP phase composition is An11BnX3n11. For more complex A-site cation compositions in RP phases, they can also be written as An-1A0-2BnX3n11. Here, A and A0 (A-prime) are two different cations, and B is usually a Pb, Bi, or Sn metal cation that is part of the hybrid metal halides.
With X-ray diffraction, you can learn more about the structure and peak shape of things like perovskite solar cells. A phase factor e2i¦k r(i,j) can be used to describe the amount of electrons scattering around a nucleus. This factor can be written as an integral of the charge distribution’s input to an atomic form factor. It is possible to mix different atomic form factors to get a structure factor F 5 P N n51 fatomeikrn. Here, rn is the position of the nth atom in the structure and fatom is the integral in Eq. 2.2. When you put this together with the Laue condition and the notation for Miller indices, you get F hkl ð Þ 5 X N n51 fatome½ ~ i2πð Þ hxn1kyn1lzn (2.3).
This means that all miller index pairs can be seen in simple cubic systems. If all of the hkl are even or odd, the structure factor for the FCC lattice with N = 5/2 and cubic sub-symmetry is 4. Otherwise, it is 0. A typical perovskite structure (ABX3) has a cubic shape with the space group Pm3m, the A-site cation at (0,0,0), the B-site cation at (1,/2, 1/2, 1/2), and the 3 X halogens at (0, 1/2, 1/2), (1/2, 0 1/2), and (1/2, 1/2, 0). The B-site cation may have a small off-center displacement (ΔB) or tilt of the X-B-X axis from two different positions of the halide ion (denoted X and X2 with a shift of X and X2, respectively).
At high temperatures, hybrid perovskites have a structure that is roughly cubic because of the movement of the organic A-site cation. If the B-site central metal moves off-center, it will also create a pseudo-cubic structure. Adding a small amount of length to the unit cell (for example, 0.5% along the c-axis compared to the a-axis) will make it into a tetragonal shape with c/a 5 1.005, and a ΔX of 5 pm will already cause a 0.2 shift in the pseudo-cubic reflection when using Cu K± radiation and Eq. 2.1. A notation called Glazer notation is often used to group symmetries from different tilt pairs. It uses subscripts of 0, 1, and to show tilts around the x, y, and z-axes of the underlying cubic perovskite structure Pm3m.
The study is mostly about how to characterise lead halide perovskites (LHPs) as solar cell materials, which is important for making sure they stay stable over time and during day and night operation. When LHPs come in touch with water, air, light, and temperature, they break down and hybrid lead halogen perovskites are made. These hybrid perovskites are salts that dissolve in water, while perovskites that are not enclosed in a shell dissolve very easily in water.
Depending on the size needed, X-ray diffraction and Raman spectroscopy can both be used to look at the structure of thin films. It is easy for uncapsulated perovskites to dissolve in water, but not so much for hybrid lead halogen perovskites. Perovskites react with almost all metals when they are exposed to heat and light. This causes stress when the temperature changes, which can cause the metals to separate or break down faster. To make solar screens with metal halide perovskite that will last for 25 years, it is still hard to design perovskites that are physically strong.
At the temperatures used in solar cells, methylammonium lead iodide (MAPbI3), a common LHP, could change its shape from tetragonal to cubic. This change in structure phase has a negative effect on the solar qualities. As a result, making temperature-resistant perovskites is very important. One way to get around the phase change with MAPbI3 is to use formamidinium lead iodide (FAPbI3) mixed with it. The organic cation in this mixture changes from methylammonium (MA) to formamidinium (FA). This creates a material that has either a trigonal structure (black colour, α phase) or a hexagonal structure (yellow colour, ε phase), based on the temperature at which it was made.
The study also talks about new XRD tests on LHP, which show how important it is to keep the crystal structure and chemical makeup stable over time. The study also talks about how hard it is to make perovskites that are physically solid and how mixing 3D perovskites with 2D perovskites could work as a chemical fluid stopping layer.
In the end, the work shows how important it is to use X-ray diffraction and Raman spectroscopy to describe lead halide perovskites as materials for solar cells. These two techniques, GIWAXS and GISAXS, when used together, help researchers come up with ways to make perovskites that are physically solid and cover 3D perovskites with 2D perovskites to stop chemical leakage.
The trigonal phase of FAPbI3 can be kept stable without the lattice shrinking or the optical features changing. This is because the I-H hydrogen bonds between the cation and the metal cage get stronger, or the structure’s Madelung energy goes up. This stops the ε phase shift from happening, as shown by X-ray diffraction that changes with temperature. When MA and FA are mixed together, the addition of MA creates a 3D network of layered octahedra by cutting the amount of shared iodide ions from three to one. The octahedra are not exactly lined up at room temperature, but every second octahedral layer has a twist that is very close to the same in the c direction. As the temperature rises, the unit cell gets bigger, which helps line up the octahedra exactly along the c-axis while keeping the tetragonal shape.
Many researchers use temperature-dependent X-ray diffraction to look into how the phases of LHP change from one to another. When the tetragonal phase changes into the cubic structure, some peaks drop from XRD patterns. At the same time, some double peaks join into single peaks. When the temperature changes, the XRD shows a shift in the peak. This shift tells us about the phase transformation and the thermal expansion factors, which help us figure out how the materials react to heat stress.
At the temperature changes that happen in a working solar cell, the phase change is identified to 54°C with a 1°C error. Two other techniques used to study the phase change are time-of-flight neutron powder diffraction and high precision synchrotron X-ray powder diffraction. The X-ray results for d6^MAPbI3 showed that the cubic and tetragonal phases existed together over a large temperature range (nearly 30 K), which means that this phase change happened in the first place. The change from an orthorhombic to a tetragonal phase was also first-order from Pnma to I4/mcm symmetry, and the phases existed at the same time.
The Pnma, on the other hand, is not a subgroup of I4/mcm, so there can’t be a continuous second-order phase shift. In order for a second-order phase transition to happen, the Pnma to I4/mcm transformation needs modes with two different irreducible representations to condense. This means that it has two main order parameters, which goes against one of the Landau conditions.
It is possible to learn a lot about lattice vibrations, temperature and pressure phase maps, crystallinity, structure changes in mixed halide perovskites, and how stable halide perovskites are when they are working in solar cells with Raman spectroscopy. It also lets us look into the vibrational features, electron-phonon interactions, dielectric screening, heat transport, and elastic features of MAPbI3 and molecules that are linked to it.
If the polarisability ± of the electron cloud changes during the shaking, a small amount of light will be spread close to the incoming monochromatic light. This is called the Raman Effect. You can think of polarisability as a scalar, and it means being able to make a dipole 5 E in a given electric field E. A basic understanding of polarisability needs a quantum mechanical picture. However, this overview only shows the inelastic scattering process and doesn’t go into more depth about the strength of the light that is scattered in an inelastic way.
Different types of lattice vibrations can be found in MAPbI3. These are the internal vibrations of the organic MA cations, which happen at frequencies between 300 and 3200 cm21; the libration and spinning modes of the MA cations, which happen at frequencies between 60 and 180 cm21; and the internal vibrations of the inorganic PbI3 network, which happen below 120 cm21. The normal modes of MAPbI3 are caused by the PbI3 network vibrating as well as the MA cations vibrating and how they connect with each other.
The vibrations of the PbI3 network are shown by the symmetry equations 5 7B1 u 1 6B2 u 1 7B3 u 1 5Ag 1 4B1 g 1 5B2 g 1 4B3 g 1 7Au. The g type (gerade, even) has an inversion symmetry of the phase, and the u type (ungerade, odd) has a phase change of the corresponding orbitals. The MA cation’s internal motions have a symmetry representation of A2 1 5A1 1 6E, with the E modes being twice as degenerate.
The MA cations’ modes seem to be grouped in fours of frequencies that are almost degenerate, which suggests that there isn’t much interaction between the cations. The MA cations can change shapes in symmetric or asymmetric ways. They can also stretch in symmetric or asymmetric ways, stretch in symmetric or asymmetric ways for CH and NH, and rock in asymmetric CH3-NH3 ways.
They think that the PbI3 network will be Raman-active, with the Ag, B1 g, B2 g, and B3 g symmetries also being Raman-active. The symmetries B1 u, B2 u, and B3 u are thought to be IR-active. People expect au modes to be quiet. We can figure out the molecular intramolecular motions of MA cations, but we still need to find out how their Raman and IR activity changes when they are included and how they adopt symmetry in the hybrid lead halide perovskites.
A study of the vibrational properties of artificial and mixed (layered) perovskites using infrared spectroscopy in the 700–3500 cm21 range can help with the assignment of the LHPs Raman spectrum. They are naturally complicated materials, and first-principles DFT calculations help show how different kinds of interactions and local structure disorder affect the features of the materials. Recently, an experimental and theoretical Raman vibrational study of MAPbI3 in the low-frequency range was used to find the bands related to the vibrations of the artificial and organic parts interacting with each other.
Following is the suggested assignment of the low frequency Raman spectrum of orthorhombic MAPbI3: in Fig. 2.7A and B, the dashed black lines show this. The peak at 9 cm21 is for Pb-I-Pb rocking modes with Ag symmetry, the peak at 26 cm21 is for Pb-I-Pb bending modes with Ag symmetry, the small peak at 32 cm21 is for Pb-I-Pb bending modes with B2 g symmetry, the peaks at 42 and 49 cm21 are for Pb-I-Pb bending modes with Ag (3) and B2 g (4) symmetry, respectively, the peak at 58 cm21 is for MA cations’ librational modes, the peak at 85 cm21 is for MA cations’ librational modes as well as Pb-I stretching modes with B3 g symmetry, the peak at 97 cm21 is for Pb-I stretching modes of Ag symmetry, and the small peak at 142 cm21 is for MA cations’ librational modes.
Resonance Raman spectroscopy of halide substituted hybrid perovskites
In metal halide perovskites (MHPs) with the formula CH3NH3PbI2X, changing the halide group affects the shape, the charge quantum yield, and the contact with the organic MA cation. Researchers using Raman spectroscopies and theoretical vibration calculations have confirmed earlier findings that iodide-chloride perovskites can separate into two phases. They also found that substituting halides with halides that have shorter bonds to Pb can move the charge away from the MA cation, which lets the MA cation move around more freely and creates a more flexible organic phase.
Raman spectroscopy using a 532 nm laser to excite the material is done within the absorption profile of MHP materials and under resonance conditions. This gives information on motions in the excited state and hints at how charges are separated and transferred. We looked at the fundamental vibrations in the isolated clusters and how the degenerate states split when different halogens are added. We did this by using low-frequency Raman measurements (down to 10 cm21) and nonperiodic DFT calculations, paying special attention to the order of the peaks to find out the Raman properties of MHPs.
The actual Raman spectrum for MAPbI3 shows vibration peaks at 40, (54), (63), 71, 94, 108, 135, and 145 cm21. For MAPbI2Cl, the peaks are at 40, NA, NA, 71, 97, 110, and 166 cm21, which is a broad peak. Raman peaks at 69–73, 94–97, and 108–110 cm21 are the biggest. Peaks at 40 and 54 cm21 are also strong, but they depend on the chemistry of the halides used during synthesis.
Periodic DFT formulas are a good way to model single-crystalline materials where the different ways the cations are arranged must be thought of as periodic. Cluster calculations can help us understand local effects in the artificial octahedron and the behaviour of the organic cation for materials that don’t behave in a periodic or crystalline way.
DFT calculations on mixed halide clusters like (MA)2PbI5Cl and (MA)2PbI4Cl2 have shown that adding one Cl atom doesn’t make a big difference in the estimated Raman vibrational spectra compared to the (MA)2PbI6 cluster, but adding two Cl atoms makes a bigger difference. These results are useful because they help us figure out how to find doped phases.
The main goal of the study is to describe perovskite solar cell materials using Raman spectroscopy and Raman spectra calculated by DFT. The Raman spectra show three main vibrational modes of bimethylammonium-installed octahedra, ideal and disturbed artificial Oh octahedra, and octahedra that have been messed up. Comparing mode M4 to mode M3 (green colour), mode N20’s Raman activity changes to a lower wavenumber. Mode M20’s activity changes to a higher wavenumber, which is also green.
By looking at the new wave patterns and changes in the relative intensities of the Raman activities of (MA)2PbI4Cl2 compared to the analogue that isn’t doped, it’s possible to find different stages or places where halides are substituting. More often than not, OMHPs with one or two Cl groups have lower Raman intensities for modes C3 and C4 (green and violet colours) compared to mode C0 (black colour).
We calculated the DFT Raman spectra for three vibrational modes and looked at the actual Raman signal of MAPbI3. It showed three shoulders or peaks in the 70–120 cm21 range, which were linked to modes A, B, and C. There are four more peaks that show up between 140 and 400 cm21. These are for MA rotation, MA wagging, and symmetric MA-MA stretch. You should only think of cluster analysis as a representation of the local modes of the crystalline system. However, it can be used to look into the specific effects of chloride on crystallisation or on effects caused by local charge delocalisation and transfer.
In MAPbI2Cl’s Raman spectrum, mode B (peak “b0”) shifts to a lower intensity, which is linked to disordered inorganic frameworks where higher Raman activities have been seen before because of stronger electron-phonon interactions between the central cationic metal and anionic oxygen. It works the same way for MAPbI3 and the sub-MAPbI3 crystal in MAPbI2Cl on modes A and C. It shows that the MAPbI3 sample is 1.3 times brighter at 143 cm21 than the MAPbI2Cl sample at B145 cm21 in the range of 136 to 150 cm21.
When DFT calculations are done on OMHPs, they show how charges move from the HOMO to the LUMO (with LUMO 1 1 and LUMO 1 2). For example, the HOMO of 2MAPbI6 showed an I 5p π-bonding orbital while its LUMO, LUMO 1 1, and LUMO 1 2 were reduced to “Pb(6 s)I(5p)” σ-antibonding, “Pb(6p)I(5p)” σ-antibonding, and “Pb(6 s)I(5p)” σ-antibonding orbitals, respectively. The 143 cm21 mode was seen to be 7 times less intense in the MAPbI2Cl sample. This is because mode M of the internal MAPbI3 lost its polarisation.
Raman spectroscopy probing bleaching and recrystallization process of CH3NH3PbI3 film
Raman spectroscopy was used to look into how pyridine changes the structure of CH3NH3PbI3 plates and causes them to bleach and re-crystallize. The freshly made CH3NH3PbI3 film had the usual CH3NH3PbI3 properties, such as PbI bending at 71 cm21, PbI stretching at 94 cm21, and the CH3NH31 libration mode at 111 cm21. But at 50, 71, and 94 cm21, the white film had a lot less of the artificial cage patterns that were visible. This points to pyridine completely breaking down the PbI6 framework and the CH3NH3PbI3 crystal structure.
Over time, the pyridine peak goes away and the CH3NH3PbI3 peak gets stronger. This suggests that the perovskite structure is recrystallising and pyridine is intercalating in a way that can be undone. The fact that the CH3NH3 1 libration mode and bound pyridine mode both showed up at the same time shows that pyridine is interacting with the CH3NH31 groups to help them align and recrystallise into a more ordered phase. The recovered CH3NH3PbI3 film had a stronger Raman spectrum with bands at 71 cm21 (PbI bending), 94 cm21 (PbI stretching), 111 cm21 (CH3NH31 libration mode), and a new band at 145 cm21 that was caused by the ordering of CH3NH3 1 groups. This shows that the crystallinity has improved after the recrystallisation process.
You can get information about pyridine’s bonds when it interacts with CH3NH3PbI3. For the symmetric ring breathing mode with nitrogen, there is a change of 11 cm21. The pure pyridine, on the other hand, has fingerprint waves at 991 and 1029 cm21. When pyridine interacts with CH3NH3PbI3, the v(N˩) breathing mode moves from 991 to 1002 cm21, but the band at 1029 cm21 stays the same. This means that the nitrogen group on the pyridine ring probably forms a link with CH3NH3PbI3.
DFT calculations were also used to look into different bonding scenarios. They showed that the nitrogen is not fully bonded to a Lewis acid, but rather sterically limited where an iodide interaction competed with a pure Lewis pair interaction. Because of this, only partial bonding is present because of a disappointed Lewis pair effect. When there is a problem with bonding, pyridine would connect to iodine through hydrogen from protons that are alone or protons that are connected to the hydrogen in the CH3NH31 (MA1) ion, or to Pb21 surfaces that are uncovered and pyridine^(PbIn)(22n) plumbate complexes.
Because there is a lot of light in the measured spot, care needs to be taken with the levels used in confocal Raman spectroscopy in real life. Longer readings or greater intensity first improve the crystallinity of a bad starting material. This may be followed by a possible temperature phase change. Finally, the material breaks down into precursor salts like PbI2 and MAI in the case of MAPbI3.
Conclusions
X-ray diffraction (XRD) and Raman spectroscopy are important tools in current material science for studying how Liquid Hole (LHP) materials are structured and how they vibrate. These methods give details about the structure of crystals, their symmetries, displacements, flaws, micro-crystallinity, rotations, thermal expansion, phase changes, vibrations, effects from doping, and effects on local charge transfer. Raman spectroscopy is used along with XRD to characterise vibrations in both non-resonant and resonant states and help figure out how structure affects properties. These methods give chemical and crystalline features from sub-angstrom changes in the structure. This helps us understand molecular chemistry during the making process as well as the structure and properties of the LHP crystalline materials that are made. You can also use Raman spectroscopy to figure out how vibrations work in amorphous structures, molecular materials, gases, and solvents. It can figure out the chemical names and processes that happen during reactions and also see specifics about solid materials by looking at bonding interactions, orientations, symmetries, and phonon modes. A thorough study of the various strengths in resonance Raman readings can also be used to look into the main relationship between light and matter and the subsequent spreading of charges.
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