ACUERDOS DE COOPERACIÓN

Historically, perovskites are named after Lev Perovsky, a Russian mineralogist. This class of compounds has the same type of crystal structure as CaTiO3. In general, their formula is

AMX3 where A and M are cations and X an anion. The ideal perovskite has a simple cubic

crystal structure in which corner sharing octahedral networks MX6 have a M-X-M 180° bond

angle and A ions in the interstices (Figure 7.2, α-CsPbI3).211 The archetype cubic structure

lowers its symmetry when temperature or pressure changes are applied, in ways which depend on each compound. In particular, halide perovskites change the angle between M-X-M from the ideal 180° (as in the undistorted perovskite denoted as the α-phase), yielding the β-phase after the first phase transition, the γ-phase after the second and finally the non- perovskite structure δ-phase (Figure 7.2).212 _{For what concerns the electronic structure, halide}

perovskites are generally direct-gap semiconductors, meaning the valence band (VB) maximum and conduction band (CB) minimum occur at the same point of the Brillouin zone211 _{(see chapter 2.1 for a general introduction). This explains the high extinction}

coefficient of this material, which can absorb photons without the need of a phonon assisted transition. State of the art approach is to calculate the band structure using many body perturbation theory with GW approximation including spin-orbit coupling, which influences the band energies.213 The density of states in perovskites shows that the VB is dominated by the halide p-orbitals while the CB has mainly Pb 6p character (Figure 7.3).25,214 _{The bandgap}

energy, which is about 1.6 eV for CH3NH3PbI3, can be easily tuned by changing the

methylammonium cation or simply the halide anion. The latter, because it is directly involved in the band formation, can easily be explained by the different electronegativity of the halides.

Geometric and electronic structure

65

Figure 7.2 - A case study of the phase transition scheme as observed with synchrotron powder diffraction (λ = 0.413906 Å) for the CsPbI3 compound. Initially, the room temperature stable δ-phase (yellow) converts to the black perovskite α-phase upon heating above 360 °C. On cooling, the perovskite structure remains kinetically stabilized converting to the black perovskite β- and γ-phases at 260 and 175 °C, respectively. Full conversion of the γ- to the initial yellow δ-phase occurs after ∼48h. Taken from ref.212_.

The bandgap energy increases proportionally with the halide electronegativity, therefore in the order Cl->Br->I-.215 The reason for the bandgap tuning by the organic part, of which the partial density of states appears several eV below the valence band maximum25,211 (Figure 7.3), is purely structural. Indeed, through structural and Coulombic interactions, it can deform the perovskite lattice and lead to a bandgap change.212 _{Particularly, it is the octahedral tilting}

which is influenced by different cations and is responsible for the changes in the electronic structure close to the band edges, as demonstrated by a study212 comparing optical absorption and structural data.

Interestingly, the CH3NH3+ ions are free to rotate between the octahedral cages at room

temperature and this seems to have profound consequences on the electronic structure.216

Indeed, orientations in which cations lower the symmetry of the structure change the bandgap from direct to indirect (Figure 7.4).

Regarding the exciton binding energy (Eb), a general rule in semiconductor physics indicates

that it is directly proportional to the bandgap energy of the material,217 meaning that CH3NH3PbBr3 (bandgap energy of ~ 2.3) has a higher Eb than CH3NH3PbI3 (bandgap energy

of ~ 1.6). The experimental values of Eb measured for CH3NH3PbI3 at room temperature

Lead Halide Perovskites

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Figure 7.3 - Total density of states (DOS) of CH3NH3PbI3 in the cubic structure (a) and partial DOS for CH3NH3+ _{(b), Pb} (c) and I (e) obtained by first-principles calculations using generalized gradient approximation (GGA) for the exchange correlation. The zero in DOS is referred to the valence band maximum. The Pb partial DOS is enlarged by five times for a clear indication of the s orbital contribution. Taken from ref.25_.

Figure 7.4 - Band structure of the fully relaxed CH3NH3PbI3 crystal obtained using first-principles calculations with generalized gradient approximation (GGA). The bands are shown for molecule orientations along (a) (111) and (b) (011) direction. The insets show a magnification of the bands (which have been shifted in energy for convenience) around the bandgap and highlight the changes in the VB maximum and CB minimum caused by rotation of CH3NH3+_{. Note that for the} (011) orientation the bandgap becomes indirect. Taken from ref.216_.

It is important to understand the nature of the charge carriers upon photoexcitation for photovoltaic devices but the thermal energy at room temperature (i.e. 25 meV) is within the range of experimental values found for Eb and it is therefore not easy to predict the behavior

Geometric and electronic structure

67 in this material. Recently, Grancini et al.57 rationalized this problem of finding a univocal value for the exciton binding energies in HOIPs. Indeed, they found that the electron-hole interaction in CH3NH3PbI3 and CH3NH3PbBr3 is sensitive to the microstructure of the

material and therefore fabrication procedures influence the Eb, which explains the different

experimental values found in the literature.

From a point of view of defects in the material, taking into account the low processing temperature used for the synthesis of halide perovskites, a high concentration of intrinsic structural defects is intuitively expected, such as vacancies and/or interstitial atoms. In reality, the small Urbach tail energy (~15 meV),219,220 _{which can easily compete in sharpness}

with high temperature processed semiconductors commonly used in photovoltaics (Figure 7.5), points to a low density of traps221 (estimated ~1010 cm-3 in single crystals).222 Moreover, a computational study using density functional theory223 showed that even upon formation of intrinsic defects, gap states which could act as deep traps are absent in the DOS. These results explain at least partially the fact that the perovskites can be efficient semiconductors even when grown using simple solution processes.

Figure 7.5 - Absorption coefficient for a thin film of CH3NH3PbI3 compared with other semiconductors used in photovoltaics applications. The sharpness of the absorption edge (highlighted by a black line) is inversely proportional to the Urbach tail energy of which a low value, indicates high crystalline quality of the material and therefore low presence of defects. Surprisingly, the low temperature processed CH3NH3PbI3 film shows an Urbach tail similar to the one of GaAs, a monocrystalline direct semiconductor of very high electrical quality. Taken from ref.220_.

Interestingly, CH3NH3PbI3 can be either n- or p- self-doped by changing the ratio of

methylammonium halide (CH3NH3I) to lead iodine (PbI2), which are the synthetic precursors

of this perovskite.224 This means that tuning film composition by changing film formation method and process conditions, changes the electronic properties of CH3NH3PbI3. The main

defects playing a role in the ambipolar self-doping behavior are Pb2+ vacancies for the p- type; and I- vacancies and CH3NH3+ interstitials for the n-type.25,224 The sister perovskite

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is observed under thermal equilibrium growth conditions.225 This is because the formation energy of a CH3NH3+ interstitial is too high due to the smaller lattice constant when compared

to CH3NH3PbI3. Therefore, the only intrinsic defects in CH3NH3PbBr3 are Pb vacancies.