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Principles of Chemical Bonding and Band Gap Engineering in Hybrid Organic–Inorganic Halide Perovskites
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Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, U.K.
*E-mail: [email protected]; Twitter: @lonepair.
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The Journal of Physical Chemistry C

Cite this: J. Phys. Chem. C 2015, 119, 11, 5755–5760
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https://doi.org/10.1021/jp512420b
Published February 6, 2015

Copyright © 2015 American Chemical Society. This publication is licensed under CC-BY.

Abstract

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The performance of solar cells based on hybrid halide perovskites has seen an unparalleled rate of progress, while our understanding of the underlying physical chemistry of these materials trails behind. Superficially, CH3NH3PbI3 is similar to other thin-film photovoltaic materials: a semiconductor with an optical band gap in the optimal region of the electromagnetic spectrum. Microscopically, the material is more unconventional. Progress in our understanding of the local and long-range chemical bonding of hybrid perovskites is discussed here, drawing from a series of computational studies involving electronic structure, molecular dynamics, and Monte Carlo simulation techniques. The orientational freedom of the dipolar methylammonium ion gives rise to temperature-dependent dielectric screening and the possibility for the formation of polar (ferroelectric) domains. The ability to independently substitute on the A, B, and X lattice sites provides the means to tune the optoelectronic properties. Finally, ten critical challenges and opportunities for physical chemists are highlighted.

Copyright © 2015 American Chemical Society

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Introduction

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Hybrid organic–inorganic halides have been of interest since the start of the 20th century; (1) however, the first report of a perovskite-structured hybrid halide appears to have been by D. Weber in 1978. (2, 3) In the same journal volume, he reported both CH3NH3PbX3 (X = Cl, Br, I) and the CH3NH3SnBr1–xIx solid solution. In the subsequent decades, these materials were studied in the context of their solid-state chemistry and physics, (4-6) with the first solar cell reported in 2009. (7) The resulting explosion of research effort and success in the photovoltaic applications of these materials has been the subject of many review papers and commentaries. (8-14)
Hundreds of materials have been tried and tested for use as light absorbing layers in solar cells, so one question has been frequently posed: what makes hybrid halide perovskites special? The question is difficult to answer with certainty as our understanding of the physical properties of these materials, including how the solar cells operate, continues to evolve. One of the unique features of this class of material is their large dielectric constants (ϵ0 > 20), compared to conventional semiconductors (ϵ0 < 20), which include a rotational component associated with molecular dipole relaxation.
The aim of this Feature Article is to step back and recount the fundamental physical chemistry underpinning the performance—and potential limitations—of hybrid perovskite materials. The work discussed here is primarily from our research group; (13, 15-21) however, many others have contributed to the computational studies in the area. Simulations on the electronic structure, alloy formation, and lattice defects have been the subject of recent review papers. (22-25)
We previously produced a gentle introduction to the fundamental chemistry of hybrid perovskites, (17) which is not duplicated here. Instead, we first discuss the principles of chemical bonding in these systems, followed by approaches to tune the electronic structure, and finally outline ten outstanding challenges in the field.

Figure 1

Figure 1. Schematic of the perovskite crystal structure with respect to the A, B, and X lattice sites. The redox chemistry of the component ions can be used to influence the valence and conduction band energies and orbital composition, and hence the stability of electrons and holes in the material. (26) Note that for larger molecular A sites layered perovskites are formed. (27, 28) Beyond halide perovskites, a wider range of stoichiometries and superstructures are known, e.g., the Ruddlesden–Popper, Aurivillius, and Dion–Jacobson phases.

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Chemical Bonding

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The chemical bonding in hybrid perovskites with ABX3 stoichiometry (shown in Figure 1) can be separated into three distinct components. It should be noted that these materials are organic–inorganic but not organometallic—following the IUPAC definition—as there is no direct bond between a metal and carbon atom. In the context of metal–organic frameworks, they are considered to be I3O0 materials (29) due to the combination of a three-dimensional inorganic network with a zero-dimensional (molecular) organic component.

a Metal Halide Framework

The bonding within the BX3– anionic framework is unambiguously heteropolar (mixed ionic/covalent interactions). The formal oxidation states of Pb(+2) and I(−1), resulting from the chemical composition, are a good approximation of the chemical species here. Electrostatic interactions dominate between ions with net charge. As usual, the quantification of partial charges remains ill-defined due to the collective nature of the periodic electronic wave function. (30, 31) The Born effective charges in halide perovskites are large (the value for Pb can exceed 4), (32) consistent with high ionicity.
The lattice energy (defined with respect to the ions held infinitely far apart) and electrostatic site potentials are listed for a range of perovskite stoichiometries in Table 1. In comparison to the three types of oxide (group VI anion) perovskite, for the halide (group VII anion) perovskite the electrostatic stabilization is notably reduced. The lattice energy is just −29.71 eV per ABX3 cell, with an electrostatic potential on the anion site ca. 50% of the group VI anions. Due to this weaker potential alone, lower ionization potentials (workfunctions) are expected for halide perovskites compared to, for example, metal oxides. (33, 34) A second consequence is that lattice vacancies are facile to form (21) and do not result in deep ionization levels. In contrast, for rocksalt-structured metal halides, the halide is in an octahedral coordination environment with a large confining electrostatic potential. In such cases, a halide vacancy will trap electrons with ionization levels deep in the band gap: an F-center.
For CH3NH3PbI3, the formal electronic configurations of Pb 6s26p0 and I 5p6 are apparent from the electronic band structure, where the upper valence band is formed from the I p orbitals and the lower conduction band is formed from the unoccupied Pb p orbitals. There is an admixture of Pb s in the valence band, but here the cationic lone pair electrons are stereochemically inactive, (35) at least in the equilibrium structural configuration. Polar instabilities of the Pb(II) ion are common in ferroelectric and multiferroic oxide perovskites. (36)
Strong hybridization (orbital overlap) along the octahedral framework results in light electron (0.15 me) and hole (0.12 me) effective masses a fraction of the free electron mass. (19) These light carrier masses provide the means for high-mobility band transport in high-quality materials. The high atomic numbers of lead and iodine suggest that relativistic effects are important for an accurate determination of the electronic structure. (19) Many-body electron–electron interactions have been shown to be important. These factors combine to make high-quality electronic structure studies, such as relativistic GW theory, computationally and methodologically challenging. While density functional theory calculations can now be performed routinely on system sizes of up to 100 s of atoms, for relativistic quasi-particle self-consistent GW theory CH3NH3PbI3 represents the most complex system studied to date. Note that this approach is superior to non-self-consistent G0W0 methods but still neglects electron–phonon coupling, which may be important for these structurally soft materials.
Table 1. Lattice Energy (eV/cell) and Site Madelung Potentials (in units of V) for a Range of ABX3 Perovskite Compositions (Cubic Lattice, a = 6 Å) Assuming the Formal Oxidation State of Each Speciesa
stoichiometryElatticeVA (V)VB (V)VX (V)
I–V–VI3–140.48–8.04–34.5916.66
II–IV–VI3–118.82–12.93–29.7115.49
III–III–VI3–106.92–17.81–24.8214.33
I–II–VII3–29.71–6.46–14.857.75
a

The potentials are aligned to a common vacuum level at 0 V. The hybrid halide perovskites are of type I–II–VII3. Reprinted with permission from ref 17. Copyright 2014 American Chemical Society.

b Intermolecular Interaction

Methylammonium is a closed-shell 18-electron cation. (In contrast to several erroneous statements in the published literature, CH3NH3+ is not a free radical.) The CH3NH3+ molecules in neighboring cages are ∼6 Å apart. The large permanent electric dipole (2.29 D with respect to the center of charge of the ion) results in an estimated electrostatic point dipole–dipole interaction energy of 25 meV. (16) For two static dipoles, the interaction tails off as (1/r3); however, the screening effect of two freely rotating dipoles shortens this Keesom force (one component of the van der Waals interaction) to (1/r6).
As the dipole–dipole interaction energy is comparable to available thermal energy at room temperature, we expect a complex ferroelectric behavior. Monte Carlo simulations have shown that for a fixed lattice a striped antiferroelectric alignment of dipoles is favored at low temperatures, which become increasingly disordered and finally paraelectric at high temperatures. (17) At room temperature, there is significant local structure which can be linked with regions of high and low electrostatic potential. Even for a single-crystal film the topology of the electrostatic potential resembles a bulk heterojunction more familiar to organic photovoltaics. Larger polar domain structures have recently been observed from piezoelectric force microscopy, which may be associated with effects from local chemical and lattice strain. (37) Tunable ferroelectric polarization has also been predicted to occur in the Sn analogues. (38)
The orientation of molecular dipoles is involved in the unusual dielectric response of CH3NH3PbI3. At high (optical) frequencies, there exists the standard electronic response of the system to an applied electric field. At lower (THz) frequencies, an additional vibrational response from lattice phonons gives rise to the static dielectric constant of 25 (previously computed from density functional perturbation theory). (19) The molecular response occurs at even lower frequencies (GHz regime), which can be associated with rotational order. Toward audio frequencies a “colossal” permittivity emerges, which can be linked to ionic and/or electronic conductivity: the Maxwell–Wagner effect. These contributing factors are summarized in Figure 2.

Figure 2

Figure 2. Schematic of the ordering of molecular dipoles in the presence of an external electric field, as well as the four regimes in the dielectric response from lowest frequency (electronic excitations) to highest frequency (space charges and electronic or ionic conductivity). Each process will have a characteristic relaxation time and can combine to give a complex temporal response to an external perturbation.

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c. Molecule–Framework Interaction

The dominant bonding between the molecule (A site) and framework is electrostatic in nature. CH3NH3+ is a positively charged ion inside a negatively charged cage, so there is a strong electrostatic potential (∼8 V; Table 1) holding the molecule at its lattice site.
An additional electrostatic contribution to the chemical bonding between the molecular dipole and the PbI6 octahedra is the charge–dipole interaction, which is dependent on the dipole orientation. There is also the effect of primary polarization. Given the appreciable polarizability of the I– ions (ca. 7 × 10–24 cm3), an induced dipole interaction is expected (the so-called Debye force). Due to these interactions, a correlation is expected between molecular orientation and octahedral deformation in molecular dynamic simulations; (17) more in-depth studies are ongoing. The molecular dipole–framework interaction has also been discussed in terms of hydrogen bonds; however, both interactions are electrostatic in nature and are difficult to distinguish between. The significant mobility of the cations (including hydrogen atoms) at room temperature (16) does suggest that a dipole interaction is a more appropriate and general description.
The van der Waals interaction collectively describes the intermolecular (Keesom force) and molecule–framework (Debye force) interactions discussed above. It should be noted, however, that the term “van der Waals” is sometimes used synonymously with “London dispersion”. Within density functional theory, there are now many flavors of dispersion-corrected exchange-correlation functional, which aim to recover a description of the London force (secondary polarization) associated with dynamic correlation. By taking a first-generation generalized-gradient functional (e.g., PBE (39)) which overestimates equilibrium bond lengths by 1–2%, the addition of a weakly attractive r–6 potential will result in better agreement with experimental structures. It does not require that these interactions are “London dispersion” in nature. Our approach has been to employ a functional optimized for solids (e.g., PBEsol (40) or HSE06 (41)), which quantitatively describes structural parameters of dense materials without system-specific parametrization. In addition to improved lattice parameters, PBEsol also describes the vibrational properties of solid-state systems more accurately. (42)
From this discussion, it is clear that a variety of interactions give rise to the properties of the hybrid perovskites important to their photovoltaic performance. In particular, the combination of the light carrier effective masses provided by the metal halide framework and the strong dielectric screening—including the molecule–framework and intermolecular interactions—favors free carrier generation over excitons (bound electron–hole pairs) upon illumination.

Band Gap Engineering

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It is possible to chemically substitute on all of the perovskite lattice sites, and appropriate examples of each can be found in the literature. It is important to recognize the chemical distinction between the three approaches.
In the limit of a small perturbation, the physical response to a hydrostatic volume change can be described by the band gap deformation potential (43)(1)which for CH3NH3PbI3 is positive (αVR = 2.45 eV). (17) As the fundamental band gap is determined at the boundary of the Brillouin zone (R for the pseudocubic structure), the out-of-phase band-edge states are stabilized as the lattice expands. Temperature-dependent photoluminescence indicates a decrease in band gap with decreasing temperature (lattice contraction) from 1.61 eV at 300 K to 1.55 eV at 150 K, which is at the onset of a phase change. (44) The chemical effects of substitution will generally exceed this physical volume effect, as discussed below.

Figure 3

Figure 3. Calculated natural band offsets of CH3NH3PbI3 and related materials based on density functional calculations (with quasi-particle corrections). Interfacial or surface electric dipoles (or quadrupoles) are not considered here. Adapted with permission from ref 17. Copyright 2014 American Chemical Society.

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A-Site Substitution

The A site of CH3NH3PbI3 does not directly contribute to the frontier electronic structure, but it can have an indirect influence by changing the crystal structure (Figure 3).
Following eq 1, lower band gap values should be observed for smaller molecular cations. The replacement of CH3NH3+ by NH4+ in the perovskite lattice reduces the band gap by 0.3 eV. (19) The smallest possible counterion is a proton (H+); HPbI3 has a theoretical cubic perovskite lattice parameter of 6.05 Å and an associated band gap of less than 0.3 eV. (17)
The limitation of this logic (hydrostatic deformation) is the relationship between the size of the ion and the local structure. For example, in reality both NH4PbI3 and HPbI3 adopt alternative chain or layer structures due to a mismatch in ionic radius. (45, 46) The geometric constraints for the formation of a stable perovskite lattice are summed up in the radius ratio rules, which have been recently extended to hybrid perovskites. (47) An A-site ion too small for the BX3 framework results in an instability of the octahedral networks with respect to tilting, which can change the electronic properties (e.g., a transition from an antiferroelectric to ferroelectric phase).
CH3NH3PbI3 has a Goldschmidt tolerance factor of 0.91 (unstable with respect to tilting). NH4PbI3 has a tolerance factor of 0.76, and an alternative nonperovskite structure is favored. More asymmetric molecular ions (e.g., formamidinium, NH2CHNH2+ or FA) can also result in “built-in” structural distortions due to their deviation from spherical symmetry. The chemical and physical strains associated with the molecular substitution cannot be neglected when considering band gap engineering. (48)
The choice of A-site ions that are too large for the BX3 framework can result in layered perovskite structures (e.g., Ruddlesden–Popper type An–1A2′BnX3n+1 phases). The quantum confinement associated with these layered structures has itself attracted significant interest. (27, 28)

B-Site Substitution

Substitution on the B site can be used to directly alter the conduction band. Isovalent substitution of Pb for Sn has been successfully reported; (49) however, Sn(II) is less chemically stable in an octahedral environment. (50) Oxidation to Sn(IV) results in the low performance and high carrier concentrations found for the Sn halide perovskites. The stability of Ge(II) is further reduced, owing to its lower binding energy 4s2 electrons and is unlikely to result in a candidate photovoltaic material.
The so-called “double” perovskites are well-known for metal oxides. Here the B site is substituted by two aliovalent ions (one higher and one lower oxidation state)(2)An example here would be the substitution of Pb(II) by Bi(III) and Tl(I), which is likely to reduce the electronic band gap due to the lower binding energy of the Bi 6p orbitals and the fluctuations in electrostatic potential caused by the combination of monovalent and trivalent ions. An advantage of this approach is that controlled substitutions beyond the 1:1 stoichiometry could be used to influence the n-type (excess Bi) or p-type (excess Tl) carrier concentrations.

X-Site Substitution

For CH3NH3PbI3, the anion (X site) dictates the valence band energy. (15) The observed band gap changes upon halide substitution are influenced by the electronic states of the anion; i.e., from Cl to Br to I the valence band composition changes from 3p to 4p to 5p with a monotonic decrease in electron binding energy (lower ionization potential). The valence band energy varies by as much as 0.6 eV between the methylammonium chloride and iodide perovskites. This holds true for other choices of the molecular ion: the substitution of Br by I in FAPbX3 decreases the optical band gap from 2.23 to 1.48 eV. (51)
The successful incorporation of the tetrafluoroborate polyanion into the perovskite structure has been recently reported. (52) We have shown, however, that both BF4– and PF6– do not hybridize significantly with Pb, which results in an increase in the band gaps and a decrease in the band widths. (20) Such substations, if stable structures were formed, could be exploited to produce a novel high-k dielectric with potential applications in transistors or memristors.

Conclusion and Challenges

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In addition to their application in photovoltaics, hybrid halide perovskites display a rich physical chemistry. We have discussed the salient features of their chemical bonding and routes to tuning the properties beyond the widely studied methylammonium lead iodide.
Hybrid halide perovskites still pose many fundamental challenges relating to their physical chemistry and chemical physics. Ten issues of current interest include:
1.

Local structure — the average crystal structure inferred from standard X-ray diffraction experiments is likely to be far from the local structure of the perovskite framework.

2.

Dynamic disorder — knowledge is required of the time scales associated with molecular motion and how this changes from single crystals to thin films and with the method of preparation.

3.

Lattice point defects — there have been reports of n-type, p-type, and intrinsic semiconducting samples of CH3NH3PbI3. What causes this behavior, and how can the semiconductivity be controlled?

4.

Ionic conductivity — many perovskite materials support vacancy-mediated ion diffusion. Is iodine, methylammonium, or hydrogen mass transport contributing to low-frequency impedance spectra?

5.

Surface and interfaces — the chemical nature of extended defects is poorly understood, in particular the interface between the perovskite and the hole transport layer.

6.

Ferroelectricity — simulations demonstrate short-range ferroelectric order at room temperature; however, external electric fields and internal strains will change this behavior.

7.

Grain boundaries and domain walls — the perovskite microstructure may provide alternative pathways for conductivity and electron–hole separation or recombination. What is their form and abundance?

8.

Increased stability — the long-term air instability of these materials is in part associated with the volatility of the molecular components. The development of alternative ions without labile protons would be advantageous.

9.

Pb-free compositions — a major goal remains to identify a (stable) Pb-free material that maintains the same exceptional performance as CH3NH3PbI3 in solar cells. The difficulty is in maintaining a small band gap with lighter metals.

10.

Device models — there are standard electron transport models for p–n junction devices and extensions to bulk heterojunctions; however, there is no band transport model that encompasses the complex behavior of the hybrid perovskites including current–voltage hysteresis.

Author Information

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  • Corresponding Author
    • Aron Walsh - Centre for Sustainable Chemical Technologies and Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, U.K.;  Email: [email protected]
    • Notes
      The authors declare no competing financial interest.

    Biography

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    Prof. Aron Walsh holds the Chair of Materials Theory in the Centre for Sustainable Chemical Technologies at the University of Bath. He was awarded his BA and Ph.D from Trinity College Dublin (Ireland), completed a postdoctoral position at the National Renewable Energy Laboratory (USA), and held a Marie Curie fellowship at University College London (UK). His research combines computational technique development and applications at the interface of solid-state chemistry and physics.

    Acknowledgment

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    I thank J. M. Frost, K. T. Butler, F. Brivio, R. X. Yang, L. A. Burton, D. O. Scanlon, and C. H. Hendon who performed the original simulations discussed in this work, M. van Schilfgaarde for useful discussions on many-body physics, and L. M. Peter for insights into experimental aspects. I acknowledge funding from the Royal Society, the ERC (Grant 277757), and EPSRC Grants EP/J017361/1, EP/K016288/1, and EP/M009580/1.

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      A review. Organolead-halide-perovskite-based solar cells have recently received significant attention due to their excellent photovoltaic performance and low cost. The general formula of this perovskite light harvester is RPbX3, where R and X stand for a monovalent org. cation and halide anion, resp. Structures of the perovskite solar cell are designed based on the function of the perovskite. Organolead halide perovskites can be used either as sensitizers or n- or p-type light harvesters. Rapid progress was made over the past year since the 1st report on long-term, durable, 9.7% efficiency perovskite solar cells based on MeNH3PbI3-sensitized TiO2 in 2012. As a result, power conversion efficiencies ≤16% have been achieved. Further improvement is expected from this material in terms of understanding charge accumulation and transport properties. Organolead halide perovskite is now regarded as a promising solar cell material, opening new horizons in solar cell research.
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      Jung, H. S.; Park, N.-G. Perovskite Solar Cells: From Materials to Devices Small 2015, 11, 10– 25
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      Perovskite Solar Cells: From Materials to Devices
      Jung, Hyun Suk; Park, Nam-Gyu
      Small (2015), 11 (1), 10-25CODEN: SMALBC; ISSN:1613-6810. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review of fundamentals of perovskite materials including opto-electronic and dielec. properties to give a better understanding and insight into high-performing perovskite solar cells. Perovskite solar cells based on organometal halide light absorbers have been considered a promising photovoltaic technol. due to their superb power conversion efficiency (PCE) along with very low material costs. Since the 1st report on a long-term durable solid-state perovskite solar cell with a PCE of 9.7% in 2012, a PCE ≤19.3% was demonstrated in 2014, and a certified PCE of 17.9% was shown in 2014. Such a high photovoltaic performance is attributed to optically high absorption characteristics and balanced charge transport properties with long diffusion lengths. Nevertheless, there are lots of puzzles to unravel the basis for such high photovoltaic performances. The working principle of perovskite solar cells was not well established by far, which is the most important thing for understanding perovskite solar cells. Various fabrication techniques and device structures are described toward the further improvement of perovskite solar cells.
    13. 13
      Butler, K. T.; Frost, J. M.; Walsh, A. Ferroelectric Materials for Solar Energy Conversion: Photoferroics Revisited Energy Environ. Sci. 2015,  DOI: 10.1039/C4EE03523B
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      Egger, D. A.; Edri, E.; Cahen, D.; Hodes, G. Perovskite Solar Cells: Do We Know What We Do Not Know? J. Phys. Chem. Lett. 2015, 6, 279– 282
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      Perovskite Solar Cells: Do We Know What We Do Not Know?
      Egger, David A.; Edri, Eran; Cahen, David; Hodes, Gary
      Journal of Physical Chemistry Letters (2015), 6 (2), 279-282CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      There is no expanded citation for this reference.
    15. 15
      Brivio, F.; Walker, A. B.; Walsh, A. Structural and Electronic Properties of Hybrid Perovskites for High-efficiency Thin-film Photovoltaics from First-principles APL Mater. 2013, 1, 042111
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      15
      Structural and electronic properties of hybrid perovskites for high-efficiency thin-film photovoltaics from first-principles
      Brivio, Federico; Walker, Alison B.; Walsh, Aron
      APL Materials (2013), 1 (4), 042111/1-042111/5CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
      The performance of perovskite solar cells recently exceeded 15% solar-to-electricity conversion efficiency for small-area devices. The fundamental properties of the active absorber layers, hybrid org.-inorg. perovskites formed from mixing metal and org. halides [e.g., (NH4)PbI3 and (CH3NH3)PbI3], are largely unknown. The materials are semiconductors with direct band gaps at the boundary of the first Brillouin zone. The calcd. dielec. consts. and band gaps show an orientation dependence, with a low barrier for rotation of the org. cations. Due to the elec. dipole of the methylammonium cation, a photoferroic effect may be accessible, which could enhance carrier collection. (c) 2013 American Institute of Physics.
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      Frost, J. M.; Butler, K. T.; Walsh, A. Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells APL Mater. 2014, 2, 081506
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      Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells
      Frost, Jarvist M.; Butler, Keith T.; Walsh, Aron
      APL Materials (2014), 2 (8), 081506/1-081506/10CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
      We report a model describing the mol. orientation disorder in CH3NH3PbI3, solving a classical Hamiltonian parametrised with electronic structure calcns., with the nature of the motions informed by ab initio mol. dynamics. We investigate the temp. and static elec. field dependence of the equil. ferroelec. (mol.) domain structure and resulting polarisability. A rich domain structure of twinned mol. dipoles is obsd., strongly varying as a function of temp. and applied elec. field. We propose that the internal elec. fields assocd. with microscopic polarisation domains contribute to hysteretic anomalies in the current-voltage response of hybrid org.-inorg. perovskite solar cells due to variations in electron-hole recombination in the bulk. (c) 2014 American Institute of Physics.
    17. 17
      Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells Nano Lett. 2014, 14, 2584– 2590
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      Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells
      Frost, Jarvist M.; Butler, Keith T.; Brivio, Federico; Hendon, Christopher H.; van Schilfgaarde, Mark; Walsh, Aron
      Nano Letters (2014), 14 (5), 2584-2590CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      The performance of organometallic perovskite solar cells has rapidly surpassed that of both conventional dye-sensitized and org. photovoltaics. High-power conversion efficiency can be realized in both mesoporous and thin-film device architectures. The authors address the origin of this success in the context of the materials chem. and physics of the bulk perovskite as described by electronic structure calcns. In addn. to the basic optoelectronic properties essential for an efficient photovoltaic device (spectrally suitable band gap, high optical absorption, low carrier effective masses), the materials are structurally and compositionally flexible. As the authors show, hybrid perovskites exhibit spontaneous elec. polarization; the authors also suggest ways in which this can be tuned through judicious choice of the org. cation. The presence of ferroelec. domains will result in internal junctions that may aid sepn. of photoexcited electron and hole pairs, and redn. of recombination through segregation of charge carriers. The combination of high dielec. const. and low effective mass promotes both Wannier-Mott exciton sepn. and effective ionization of donor and acceptor defects. The photoferroic effect could be exploited in nanostructured films to generate a higher open circuit voltage and may contribute to the current-voltage hysteresis obsd. in perovskite solar cells.
    18. 18
      Butler, K. T.; Frost, J. M.; Walsh, A. Band Alignment of the Hybrid Halide Perovskites CH3NH3PbCl3, CH3NH3PbBr3 and CH3NH3PbI3 Mater. Horiz. 2015,  DOI: 10.1039/C4MH00174E
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      Brivio, F.; Butler, K. T.; Walsh, A.; van Schilfgaarde, M. Relativistic Quasiparticle Self-consistent Electronic Structure of Hybrid Halide Perovskite Photovoltaic Absorbers Phys. Rev. B 2014, 89, 155204
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      19
      Relativistic quasiparticle self-consistent electronic structure of hybrid halide perovskite photovoltaic absorbers
      Brivio, Federico; Butler, Keith T.; Walsh, Aron; van Schilfgaarde, Mark
      Physical Review B: Condensed Matter and Materials Physics (2014), 89 (15), 155204/1-155204/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Solar cells based on a light absorbing layer of the organometal halide perovskite CH3NH3PbI3 have recently surpassed 15% conversion efficiency, though how these materials work remains largely unknown. We analyze the electronic structure and optical properties within the quasiparticle self-consistent GW approxn. While this compd. bears some similarity to conventional sp semiconductors, it also displays unique features. Quasiparticle self-consistency is essential for an accurate description of the band structure: Band gaps are much larger than what is predicted by the local-d. approxn. (LDA) or GW based on the LDA. Valence band dispersions are modified in a very unusual manner. In addn., spin-orbit coupling strongly modifies the band structure and gives rise to unconventional dispersion relations and a Dresselhaus splitting at the band edges. The av. hole mass is small, which partially accounts for the long diffusion lengths obsd. The surface ionization potential (work function) is calcd. to be 5.7 eV with respect to the vacuum level, explaining efficient carrier transfer to TiO2 and Au elec. contacts.
    20. 20
      Hendon, C. H.; Yang, R. X.; Burton, L. A.; Walsh, A. Assessment of Polyanion (BF4− and PF6−) Substitutions in Hybrid Halide Perovskites J. Mater. Chem. A 2015,  DOI: 10.1039/C4TA05284F
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      Walsh, A.; Scanlon, D. O.; Chen, S.; Gong, X. G.; Wei, S.-H. Self-Regulation Mechanism for Charged Point Defects in Hybrid Halide Perovskites Angew. Chem., Int. Ed 2015, 54, 1791– 1794
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      Self-regulation mechanism for charged point defects in hybrid halide perovskites
      Walsh, Aron; Scanlon, David O.; Chen, Shiyou; Gong, X. G.; Wei, Su-Huai
      Angewandte Chemie, International Edition (2015), 54 (6), 1791-1794CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Hybrid halide perovskites such as methylammonium lead iodide (CH3NH3PbI3) exhibit unusually low free-carrier concns. despite being processed at low-temps. from soln. We demonstrate, through quantum mech. calcns., that an origin of this phenomenon is a prevalence of ionic over electronic disorder in stoichiometric materials. Schottky defect formation provides a mechanism to self-regulate the concn. of charge carriers through ionic compensation of charged point defects. The equil. charged vacancy concn. is predicted to exceed 0.4 % at room temp. This behavior, which goes against established defect conventions for inorg. semiconductors, has implications for photovoltaic performance.
    22. 22
      Yin, W.; Yang, J.; Kang, J.; Yan, Y.; Wei, S.-H. Halide Perovskite Materials for Solar Cells: A Theoretical Review J. Mater. Chem. A 2015,  DOI: 10.1039/C4TA05033A
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      Giorgi, G.; Yamashita, K. Organic-Inorganic Halide Perovskites: An Ambipolar Class of Materials with Enhanced Photovoltaic Performances J. Mater. Chem. A 2015,  DOI: 10.1039/C4TA05046K
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      De Angelis, F. Modeling Materials and Processes in Hybrid/Organic Photovoltaics: From Dye-Sensitized to Perovskite Solar Cells Acc. Chem. Res. 2014, 47, 3349– 3360
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      Even, J.; Pedesseau, L.; Katan, C. Theoretical Insights into Multibandgap Hybrid Perovskites for Photovoltaic Applications SPIE Photonics Eur. 2014, 9140, 91400Y
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      Catlow, C. R. A.; Sokol, A. A.; Walsh, A. Microscopic Origins of Electron and Hole Stability in ZnO Chem. Commun. 2011, 47, 3386– 3388
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      Microscopic origins of electron and hole stability in ZnO
      Catlow, C. Richard A.; Sokol, Alexey A.; Walsh, Aron
      Chemical Communications (Cambridge, United Kingdom) (2011), 47 (12), 3386-3388CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
      We present a fundamental method to assess the doping limits of hetero-polar materials; applied to the case of ZnO, we show clearly that electrons are stable and holes are unstable under the limits of thermodn. control.
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      Calabrese, J.; Jones, N.; Harlow, R.; Herron, N.; Thorn, D.; Wang, Y. Preparation and Characterization of Layered Lead Halide Compounds J. Am. Chem. Soc. 1991, 113, 2328– 2330
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      Preparation and characterization of layered lead halide compounds
      Calabrese, J.; Jones, N. L.; Harlow, R. L.; Herron, N.; Thorn, D. L.; Wang, Y.
      Journal of the American Chemical Society (1991), 113 (6), 2328-30CODEN: JACSAT; ISSN:0002-7863.
      Mixing PbX2 with stoichiometric amts. of RNH3X and MeNH3X provided layered (RNH3)2(MeNH3)n-1PbnX3n+1 (R = nonyl, decyl, X = I, n = 1, 2; R = nonyl, decyl, X = Br, n = 1, 2, 3; R = phenethyl, X = I, n = 1, 2) having comparably sharp excitonic optical transitions. The layered structures of these compds. was confirmed by single crystal x-ray diffraction for (R'NH3)2PbI4 (R' = phenethyl, (n = 1, monolayer) (monoclinic space group C2/m, a 32.508(5), b 6.131(1), c 6.185(1) Å, β 93.80(1)°, R = 0.036, Rw = 0.037) and for (R'NH3)2(MeNH3)Pb2I7 (n = 2, bilayer) (triclinic space group P‾1, a 8.794(1), b 8.792(1), c 22.766(2) Å, α 94.02(1), β 97.02(1), γ 90.18(1)°, R = 0.059, Rw = 0.063). The presence of excitonic excited states suggests these materials may have large 3rd-order optical nonlinearities; photobleaching efficiencies of these excitonic transitions in thin films of the decylammonium-lead-iodide compds. are 1.5 × 10-7 cm2/W at 510 nm for n = 1, and 7.5 × 10-8 cm2/W at 570 nm for n = 2.
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      Mitzi, D. B.; Wang, S.; Feild, C. A.; Chess, C. A.; Guloy, A. M. Conducting Layered Organic-inorganic Halides Containing 110-Oriented Perovskite Sheets Science 1995, 267, 1473– 1476
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      Rao, C. N. R.; Cheetham, A. K.; Thirumurugan, A. Hybrid Inorganicorganic Materials: a New Family in Condensed Matter Physics J. Phys.: Condens. Matter 2008, 20, 083202
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      Catlow, C. R. A.; Stoneham, A. M. Ionicity in solids J. Phys. C: Solid State 1983, 16, 4321– 4338
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      Ionicity in solids
      Catlow, C. R. A.; Stoneham, A. M.
      Journal of Physics C: Solid State Physics (1983), 16 (22), 4321-38CODEN: JPSOAW; ISSN:0022-3719.
      A review, with many refs., of the use of the ideas of ionicity and covalency in quant. studies of the solid state.
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      Jansen, M.; Wedig, U. A Piece of the Picture-Misunderstanding of Chemical Concepts Angew. Chem., Int. Ed. 2008, 47, 10026– 10029
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      Brgoch, J.; Lehner, A. J.; Chabinyc, M. L.; Seshadri, R. Ab Initio Calculations of Band Gaps and Absolute Band Positions of Polymorphs of RbPbI3 and CsPbI3: Implications for Main-Group Halide Perovskite Photovoltaics J. Phys. Chem. C 2014, 18, 27721– 27727
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      Scanlon, D. O.; Dunnill, C. W.; Buckeridge, J.; Shevlin, S. A.; Logsdail, A. J.; Woodley, S. M.; Catlow, C. R. A.; Powell, M. J.; Palgrave, R. G.; Parkin, I. P. Band Alignment of Rutile and Anatase TiO2 Nat. Mater. 2013, 12, 798– 801
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      Band alignment of rutile and anatase TiO2
      Scanlon, David O.; Dunnill, Charles W.; Buckeridge, John; Shevlin, Stephen A.; Logsdail, Andrew J.; Woodley, Scott M.; Catlow, C. Richard A.; Powell, Michael. J.; Palgrave, Robert G.; Parkin, Ivan P.; Watson, Graeme W.; Keal, Thomas W.; Sherwood, Paul; Walsh, Aron; Sokol, Alexey A.
      Nature Materials (2013), 12 (9), 798-801CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      The most widely used oxide for photocatalytic applications owing to its low cost and high activity is TiO2. The discovery of the photolysis of water on the surface of TiO2 in 1972 launched four decades of intensive research into the underlying chem. and phys. processes involved. Despite much collected evidence, a thoroughly convincing explanation of why mixed-phase samples of anatase and rutile outperform the individual polymorphs has remained elusive. One long-standing controversy is the energetic alignment of the band edges of the rutile and anatase polymorphs of TiO2. We demonstrate, through a combination of state-of-the-art materials simulation techniques and X-ray photoemission expts., that a type-II, staggered, band alignment of ∼ 0.4eV exists between anatase and rutile with anatase possessing the higher electron affinity, or work function. Our results help to explain the robust sepn. of photoexcited charge carriers between the two phases and highlight a route to improved photocatalysts.
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      Walsh, A.; Butler, K. T. Prediction of Electron Energies in Metal Oxides Acc. Chem. Res. 2014, 47, 364– 72
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      Walsh, A.; Payne, D. J.; Egdell, R. G.; Watson, G. W. Stereochemistry of Post-transition Metal Oxides: Revision of the Classical Lone Pair Model Chem. Soc. Rev. 2011, 40, 4455– 4463
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      Stereochemistry of post-transition metal oxides: revision of the classical lone pair model
      Walsh, Aron; Payne, David J.; Egdell, Russell G.; Watson, Graeme W.
      Chemical Society Reviews (2011), 40 (9), 4455-4463CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review. The chem. of post transition metals is dominated by the group oxidn. state N and a lower N-2 oxidn. state, which is assocd. with occupation of a metal s2 lone pair, as found in compds. of Tl(I), Pb(II) and Bi(III). The preference of these cations for non-centrosym. coordination environments has previously been rationalized in terms of direct hybridization of metal s and p valence orbitals, thus lowering the internal electronic energy of the N-2 ion. This explanation in terms of an on-site second-order Jahn-Teller effect remains the contemporary textbook explanation. In this tutorial review, we review recent progress in this area, based on quantum chem. calcns. and X-ray spectroscopic measurements. This recent work has led to a revised model, which highlights the important role of covalent interaction with oxygen in mediating lone pair formation for metal oxides. The role of the anion p AO in chem. bonding is key to explaining why chalcogenides display a weaker preference for structural distortions in comparison to oxides and halides. The underlying chem. interactions are responsible for the unique physicochem. properties of oxides contg. lone pairs and, in particular, to their application as photocatalysts (BiVO4), ferroelecs. (PbTiO3), multi-ferroics (BiFeO3) and p-type semiconductors (SnO). The exploration of lone pair systems remains a viable a venue for the design of functional multi-component oxide compds.
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      Ramesh, R.; Spaldin, N. A. Multiferroics: Progress and Prospects in Thin Films Nat. Mater. 2007, 6, 21– 9
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      Multiferroics. progress and prospects in thin films
      Ramesh, R.; Spaldin, Nicola A.
      Nature Materials (2007), 6 (1), 21-29CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      A review. Multiferroic materials, which show simultaneous ferroelec. and magnetic ordering, exhibit unusual phys. properties, and in turn promise new device applications, as a result of the coupling between their dual order parameters. We review recent progress in the growth, characterization, and understanding of thin-film multiferroics. The availability of high-quality thin-film multiferroics makes it easier to tailor their properties through epitaxial strain, at.-level engineering of chem. and interfacial coupling, and is a prerequisite for their incorporation into practical devices. We discuss novel device paradigms based on magnetoelec. coupling, and outline the key scientific challenges in the field.
    37. 37
      Kutes, Y.; Ye, L.; Zhou, Y.; Pang, S.; Huey, B. D.; Padture, N. P. Direct Observation of Ferroelectric Domains in Solution-Processed CH3NH3PbI3 Perovskite Thin Films J. Phys. Chem. Lett. 2014, 5, 3335– 3339
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      Direct Observation of Ferroelectric Domains in Solution-Processed CH3NH3PbI3 Perovskite Thin Films
      Kutes, Yasemin; Ye, Linghan; Zhou, Yuanyuan; Pang, Shuping; Huey, Bryan D.; Padture, Nitin P.
      Journal of Physical Chemistry Letters (2014), 5 (19), 3335-3339CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      A new generation of solid-state photovoltaics is being made possible by the use of organometal-trihalide perovskite materials. While some of these materials are expected to be ferroelec., almost nothing is known about their ferroelec. properties exptl. Using piezoforce microscopy (PFM), here we show unambiguously, for the first time, the presence of ferroelec. domains in high-quality β-CH3NH3PbI3 perovskite thin films that have been synthesized using a new soln.-processing method. The size of the ferroelec. domains is found to be about the size of the grains (∼100 nm). We also present evidence for the reversible switching of the ferroelec. domains by poling with DC biases. This suggests the importance of further PFM investigations into the local ferroelec. behavior of hybrid perovskites, in particular in situ photoeffects. Such investigations could contribute toward the basic understanding of photovoltaic mechanisms in perovskite-based solar cells, which is essential for the further enhancement of the performance of these promising photovoltaics.
    38. 38
      Stroppa, A.; Di Sante, D.; Barone, P.; Bokdam, M.; Kresse, G.; Franchini, C.; Whangbo, M.-H.; Picozzi, S. Tunable Ferroelectric Polarization and Its Interplay with Spin-orbit Coupling in Tin Iodide Perovskites Nat. Commun. 2014, 5, 5900
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      Tunable ferroelectric polarization and its interplay with spin-orbit coupling in tin iodide perovskites
      Stroppa, Alessandro; Di Sante, Domenico; Barone, Paolo; Bokdam, Menno; Kresse, Georg; Franchini, Cesare; Whangbo, Myung-Hwan; Picozzi, Silvia
      Nature Communications (2014), 5 (), 5900CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      Ferroelectricity is a potentially crucial issue in halide perovskites, breakthrough materials in photovoltaic research. Using d. functional theory simulations and symmetry anal., we show that the lead-free perovskite iodide (FA)SnI3, contg. the planar formamidinium cation FA, (NH2CHNH2)+, is ferroelec. In fact, the perpendicular arrangement of FA planes, leading to a 'weak' polarization, is energetically more stable than parallel arrangements of FA planes, being either antiferroelec. or 'strong' ferroelec. Moreover, we show that the 'weak' and 'strong' ferroelec. states with the polar axis along different crystallog. directions are energetically competing. Therefore, at least at low temps., an elec. field could stabilize different states with the polarization rotated by π/4, resulting in a highly tunable ferroelectricity appealing for multistate logic. Intriguingly, the relatively strong spin-orbit coupling in noncentrosym. (FA)SnI3 gives rise to a co-existence of Rashba and Dresselhaus effects and to a spin texture that can be induced, tuned and switched by an elec. field controlling the ferroelec. state.
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      Perdew, J.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865– 3868
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      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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      Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces Phys. Rev. Lett. 2008, 100, 136406– 4
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      Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
      Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gabor I.; Vydrov, Oleg A.; Scuseria, Gustavo E.; Constantin, Lucian A.; Zhou, Xiaolan; Burke, Kieron
      Physical Review Letters (2008), 100 (13), 136406/1-136406/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Popular modern generalized gradient approxns. are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of d. gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approxn. that improves equil. properties of densely packed solids and their surfaces.
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      Heyd, J.; Scuseria, G. Efficient Hybrid Density Functional Calculations in Solids: Assessment of the Heyd Scuseria Ernzerhof Screened Coulomb Hybrid Functional J. Chem. Phys. 2004, 121, 1187
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      Skelton, J. M.; Parker, S. C.; Togo, A.; Tanaka, I.; Walsh, A. Thermal Physics of the Lead Chalcogenides PbS, PbSe, and PbTe from First Principles Phys. Rev. B 2014, 89, 205203
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      Thermal physics of the lead chalcogenides PbS, PbSe, and PbTe from first principles
      Skelton, Jonathan M.; Parker, Stephen C.; Togo, Atsushi; Tanaka, Isao; Walsh, Aron
      Physical Review B: Condensed Matter and Materials Physics (2014), 89 (20), 205203/1-205203/10, 10 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      The lead chalcogenides represent an important family of functional materials, in particular due to the benchmark high-temp. thermoelec. performance of PbTe. A no. of recent investigations, exptl. and theor., have aimed to gather insight into their unique lattice dynamics and electronic structure. However, the majority of first-principles modeling has been performed at fixed temps., and there has been no comprehensive and systematic computational study of the effect of temp. on the material properties. We report a comparative lattice-dynamics study of the temp. dependence of the properties of PbS, PbSe, and PbTe, focusing particularly on those relevant to thermoelec. performance, viz. phonon frequencies, lattice thermal cond., and electronic band structure. Calcns. are performed within the quasiharmonic approxn., with the inclusion of phonon-phonon interactions from many-body perturbation theory, which are used to compute phonon lifetimes and predict the lattice thermal cond. The results are critically compared against exptl. data and other calcns., and add insight to ongoing research on the PbX compds. in relation to the off-centering of Pb at high temps., which is shown to be related to phonon softening. The agreement with expt. suggests that this method could serve as a straightforward, powerful, and generally applicable means of investigating the temp. dependence of material properties from first principles.
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      Yamada, Y.; Nakamura, T. Near-band-edge Optical Responses of Solution-processed Organic-inorganic Hybrid Perovskite CH3NH3PbI3 on Mesoporous TiO2 Electrodes Appl. Phys. Express 2014, 7, 032302
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      Near-band-edge optical responses of solution-processed organic-inorganic hybrid perovskite CH3NH3PbI3 on mesoporous TiO2 electrodes
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    The Journal of Physical Chemistry C

    Cite this: J. Phys. Chem. C 2015, 119, 11, 5755–5760
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    https://doi.org/10.1021/jp512420b
    Published February 6, 2015

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    • Abstract

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      Figure 1

      Figure 1. Schematic of the perovskite crystal structure with respect to the A, B, and X lattice sites. The redox chemistry of the component ions can be used to influence the valence and conduction band energies and orbital composition, and hence the stability of electrons and holes in the material. (26) Note that for larger molecular A sites layered perovskites are formed. (27, 28) Beyond halide perovskites, a wider range of stoichiometries and superstructures are known, e.g., the Ruddlesden–Popper, Aurivillius, and Dion–Jacobson phases.

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      Figure 2

      Figure 2. Schematic of the ordering of molecular dipoles in the presence of an external electric field, as well as the four regimes in the dielectric response from lowest frequency (electronic excitations) to highest frequency (space charges and electronic or ionic conductivity). Each process will have a characteristic relaxation time and can combine to give a complex temporal response to an external perturbation.

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      Figure 3

      Figure 3. Calculated natural band offsets of CH3NH3PbI3 and related materials based on density functional calculations (with quasi-particle corrections). Interfacial or surface electric dipoles (or quadrupoles) are not considered here. Adapted with permission from ref 17. Copyright 2014 American Chemical Society.

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      Aron Walsh

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      Prof. Aron Walsh holds the Chair of Materials Theory in the Centre for Sustainable Chemical Technologies at the University of Bath. He was awarded his BA and Ph.D from Trinity College Dublin (Ireland), completed a postdoctoral position at the National Renewable Energy Laboratory (USA), and held a Marie Curie fellowship at University College London (UK). His research combines computational technique development and applications at the interface of solid-state chemistry and physics.

    • References

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        Two organolead halide perovskite nanocrystals, MeNH3PbBr3 and MeNH3PbI3, efficiently sensitize TiO2 for visible-light conversion in photoelectrochem. cells. When self-assembled on mesoporous TiO2 films, the nanocryst. perovskites exhibit strong band-gap absorptions as semiconductors. The MeNH3PbI3-based photocell with spectral sensitivity of up to 800 nm yielded a solar energy conversion efficiency of 3.8%. The MeNH3PbBr3-based cell showed a high photovoltage of 0.96 V with an external quantum conversion efficiency of 65%.
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        Review. Over the last 12 mo, we have witnessed an unexpected breakthrough and rapid evolution in the field of emerging photovoltaics, with the realization of highly efficient solid-state hybrid solar cells based on organometal trihalide perovskite absorbers. In this Perspective, the steps that have led to this discovery are discussed, and the future of this rapidly advancing concept have been considered. It is likely that the next few years of solar research will advance this technol. to the very highest efficiencies while retaining the very lowest cost and embodied energy. Provided that the stability of the perovskite-based technol. can be proven, we will witness the emergence of a contender for ultimately low-cost solar power.
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        A review. Organolead-halide-perovskite-based solar cells have recently received significant attention due to their excellent photovoltaic performance and low cost. The general formula of this perovskite light harvester is RPbX3, where R and X stand for a monovalent org. cation and halide anion, resp. Structures of the perovskite solar cell are designed based on the function of the perovskite. Organolead halide perovskites can be used either as sensitizers or n- or p-type light harvesters. Rapid progress was made over the past year since the 1st report on long-term, durable, 9.7% efficiency perovskite solar cells based on MeNH3PbI3-sensitized TiO2 in 2012. As a result, power conversion efficiencies ≤16% have been achieved. Further improvement is expected from this material in terms of understanding charge accumulation and transport properties. Organolead halide perovskite is now regarded as a promising solar cell material, opening new horizons in solar cell research.
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        A review of fundamentals of perovskite materials including opto-electronic and dielec. properties to give a better understanding and insight into high-performing perovskite solar cells. Perovskite solar cells based on organometal halide light absorbers have been considered a promising photovoltaic technol. due to their superb power conversion efficiency (PCE) along with very low material costs. Since the 1st report on a long-term durable solid-state perovskite solar cell with a PCE of 9.7% in 2012, a PCE ≤19.3% was demonstrated in 2014, and a certified PCE of 17.9% was shown in 2014. Such a high photovoltaic performance is attributed to optically high absorption characteristics and balanced charge transport properties with long diffusion lengths. Nevertheless, there are lots of puzzles to unravel the basis for such high photovoltaic performances. The working principle of perovskite solar cells was not well established by far, which is the most important thing for understanding perovskite solar cells. Various fabrication techniques and device structures are described toward the further improvement of perovskite solar cells.
      13. 13
        Butler, K. T.; Frost, J. M.; Walsh, A. Ferroelectric Materials for Solar Energy Conversion: Photoferroics Revisited Energy Environ. Sci. 2015,  DOI: 10.1039/C4EE03523B
        There is no corresponding record for this reference.
      14. 14
        Egger, D. A.; Edri, E.; Cahen, D.; Hodes, G. Perovskite Solar Cells: Do We Know What We Do Not Know? J. Phys. Chem. Lett. 2015, 6, 279– 282
        14
        Perovskite Solar Cells: Do We Know What We Do Not Know?
        Egger, David A.; Edri, Eran; Cahen, David; Hodes, Gary
        Journal of Physical Chemistry Letters (2015), 6 (2), 279-282CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
        There is no expanded citation for this reference.
      15. 15
        Brivio, F.; Walker, A. B.; Walsh, A. Structural and Electronic Properties of Hybrid Perovskites for High-efficiency Thin-film Photovoltaics from First-principles APL Mater. 2013, 1, 042111
        15
        Structural and electronic properties of hybrid perovskites for high-efficiency thin-film photovoltaics from first-principles
        Brivio, Federico; Walker, Alison B.; Walsh, Aron
        APL Materials (2013), 1 (4), 042111/1-042111/5CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
        The performance of perovskite solar cells recently exceeded 15% solar-to-electricity conversion efficiency for small-area devices. The fundamental properties of the active absorber layers, hybrid org.-inorg. perovskites formed from mixing metal and org. halides [e.g., (NH4)PbI3 and (CH3NH3)PbI3], are largely unknown. The materials are semiconductors with direct band gaps at the boundary of the first Brillouin zone. The calcd. dielec. consts. and band gaps show an orientation dependence, with a low barrier for rotation of the org. cations. Due to the elec. dipole of the methylammonium cation, a photoferroic effect may be accessible, which could enhance carrier collection. (c) 2013 American Institute of Physics.
      16. 16
        Frost, J. M.; Butler, K. T.; Walsh, A. Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells APL Mater. 2014, 2, 081506
        16
        Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells
        Frost, Jarvist M.; Butler, Keith T.; Walsh, Aron
        APL Materials (2014), 2 (8), 081506/1-081506/10CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
        We report a model describing the mol. orientation disorder in CH3NH3PbI3, solving a classical Hamiltonian parametrised with electronic structure calcns., with the nature of the motions informed by ab initio mol. dynamics. We investigate the temp. and static elec. field dependence of the equil. ferroelec. (mol.) domain structure and resulting polarisability. A rich domain structure of twinned mol. dipoles is obsd., strongly varying as a function of temp. and applied elec. field. We propose that the internal elec. fields assocd. with microscopic polarisation domains contribute to hysteretic anomalies in the current-voltage response of hybrid org.-inorg. perovskite solar cells due to variations in electron-hole recombination in the bulk. (c) 2014 American Institute of Physics.
      17. 17
        Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells Nano Lett. 2014, 14, 2584– 2590
        17
        Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells
        Frost, Jarvist M.; Butler, Keith T.; Brivio, Federico; Hendon, Christopher H.; van Schilfgaarde, Mark; Walsh, Aron
        Nano Letters (2014), 14 (5), 2584-2590CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
        The performance of organometallic perovskite solar cells has rapidly surpassed that of both conventional dye-sensitized and org. photovoltaics. High-power conversion efficiency can be realized in both mesoporous and thin-film device architectures. The authors address the origin of this success in the context of the materials chem. and physics of the bulk perovskite as described by electronic structure calcns. In addn. to the basic optoelectronic properties essential for an efficient photovoltaic device (spectrally suitable band gap, high optical absorption, low carrier effective masses), the materials are structurally and compositionally flexible. As the authors show, hybrid perovskites exhibit spontaneous elec. polarization; the authors also suggest ways in which this can be tuned through judicious choice of the org. cation. The presence of ferroelec. domains will result in internal junctions that may aid sepn. of photoexcited electron and hole pairs, and redn. of recombination through segregation of charge carriers. The combination of high dielec. const. and low effective mass promotes both Wannier-Mott exciton sepn. and effective ionization of donor and acceptor defects. The photoferroic effect could be exploited in nanostructured films to generate a higher open circuit voltage and may contribute to the current-voltage hysteresis obsd. in perovskite solar cells.
      18. 18
        Butler, K. T.; Frost, J. M.; Walsh, A. Band Alignment of the Hybrid Halide Perovskites CH3NH3PbCl3, CH3NH3PbBr3 and CH3NH3PbI3 Mater. Horiz. 2015,  DOI: 10.1039/C4MH00174E
        There is no corresponding record for this reference.
      19. 19
        Brivio, F.; Butler, K. T.; Walsh, A.; van Schilfgaarde, M. Relativistic Quasiparticle Self-consistent Electronic Structure of Hybrid Halide Perovskite Photovoltaic Absorbers Phys. Rev. B 2014, 89, 155204
        19
        Relativistic quasiparticle self-consistent electronic structure of hybrid halide perovskite photovoltaic absorbers
        Brivio, Federico; Butler, Keith T.; Walsh, Aron; van Schilfgaarde, Mark
        Physical Review B: Condensed Matter and Materials Physics (2014), 89 (15), 155204/1-155204/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
        Solar cells based on a light absorbing layer of the organometal halide perovskite CH3NH3PbI3 have recently surpassed 15% conversion efficiency, though how these materials work remains largely unknown. We analyze the electronic structure and optical properties within the quasiparticle self-consistent GW approxn. While this compd. bears some similarity to conventional sp semiconductors, it also displays unique features. Quasiparticle self-consistency is essential for an accurate description of the band structure: Band gaps are much larger than what is predicted by the local-d. approxn. (LDA) or GW based on the LDA. Valence band dispersions are modified in a very unusual manner. In addn., spin-orbit coupling strongly modifies the band structure and gives rise to unconventional dispersion relations and a Dresselhaus splitting at the band edges. The av. hole mass is small, which partially accounts for the long diffusion lengths obsd. The surface ionization potential (work function) is calcd. to be 5.7 eV with respect to the vacuum level, explaining efficient carrier transfer to TiO2 and Au elec. contacts.
      20. 20
        Hendon, C. H.; Yang, R. X.; Burton, L. A.; Walsh, A. Assessment of Polyanion (BF4− and PF6−) Substitutions in Hybrid Halide Perovskites J. Mater. Chem. A 2015,  DOI: 10.1039/C4TA05284F
        There is no corresponding record for this reference.
      21. 21
        Walsh, A.; Scanlon, D. O.; Chen, S.; Gong, X. G.; Wei, S.-H. Self-Regulation Mechanism for Charged Point Defects in Hybrid Halide Perovskites Angew. Chem., Int. Ed 2015, 54, 1791– 1794
        21
        Self-regulation mechanism for charged point defects in hybrid halide perovskites
        Walsh, Aron; Scanlon, David O.; Chen, Shiyou; Gong, X. G.; Wei, Su-Huai
        Angewandte Chemie, International Edition (2015), 54 (6), 1791-1794CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
        Hybrid halide perovskites such as methylammonium lead iodide (CH3NH3PbI3) exhibit unusually low free-carrier concns. despite being processed at low-temps. from soln. We demonstrate, through quantum mech. calcns., that an origin of this phenomenon is a prevalence of ionic over electronic disorder in stoichiometric materials. Schottky defect formation provides a mechanism to self-regulate the concn. of charge carriers through ionic compensation of charged point defects. The equil. charged vacancy concn. is predicted to exceed 0.4 % at room temp. This behavior, which goes against established defect conventions for inorg. semiconductors, has implications for photovoltaic performance.
      22. 22
        Yin, W.; Yang, J.; Kang, J.; Yan, Y.; Wei, S.-H. Halide Perovskite Materials for Solar Cells: A Theoretical Review J. Mater. Chem. A 2015,  DOI: 10.1039/C4TA05033A
        There is no corresponding record for this reference.
      23. 23
        Giorgi, G.; Yamashita, K. Organic-Inorganic Halide Perovskites: An Ambipolar Class of Materials with Enhanced Photovoltaic Performances J. Mater. Chem. A 2015,  DOI: 10.1039/C4TA05046K
        There is no corresponding record for this reference.
      24. 24
        De Angelis, F. Modeling Materials and Processes in Hybrid/Organic Photovoltaics: From Dye-Sensitized to Perovskite Solar Cells Acc. Chem. Res. 2014, 47, 3349– 3360
        There is no corresponding record for this reference.
      25. 25
        Even, J.; Pedesseau, L.; Katan, C. Theoretical Insights into Multibandgap Hybrid Perovskites for Photovoltaic Applications SPIE Photonics Eur. 2014, 9140, 91400Y
        There is no corresponding record for this reference.
      26. 26
        Catlow, C. R. A.; Sokol, A. A.; Walsh, A. Microscopic Origins of Electron and Hole Stability in ZnO Chem. Commun. 2011, 47, 3386– 3388
        26
        Microscopic origins of electron and hole stability in ZnO
        Catlow, C. Richard A.; Sokol, Alexey A.; Walsh, Aron
        Chemical Communications (Cambridge, United Kingdom) (2011), 47 (12), 3386-3388CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
        We present a fundamental method to assess the doping limits of hetero-polar materials; applied to the case of ZnO, we show clearly that electrons are stable and holes are unstable under the limits of thermodn. control.
      27. 27
        Calabrese, J.; Jones, N.; Harlow, R.; Herron, N.; Thorn, D.; Wang, Y. Preparation and Characterization of Layered Lead Halide Compounds J. Am. Chem. Soc. 1991, 113, 2328– 2330
        27
        Preparation and characterization of layered lead halide compounds
        Calabrese, J.; Jones, N. L.; Harlow, R. L.; Herron, N.; Thorn, D. L.; Wang, Y.
        Journal of the American Chemical Society (1991), 113 (6), 2328-30CODEN: JACSAT; ISSN:0002-7863.
        Mixing PbX2 with stoichiometric amts. of RNH3X and MeNH3X provided layered (RNH3)2(MeNH3)n-1PbnX3n+1 (R = nonyl, decyl, X = I, n = 1, 2; R = nonyl, decyl, X = Br, n = 1, 2, 3; R = phenethyl, X = I, n = 1, 2) having comparably sharp excitonic optical transitions. The layered structures of these compds. was confirmed by single crystal x-ray diffraction for (R'NH3)2PbI4 (R' = phenethyl, (n = 1, monolayer) (monoclinic space group C2/m, a 32.508(5), b 6.131(1), c 6.185(1) Å, β 93.80(1)°, R = 0.036, Rw = 0.037) and for (R'NH3)2(MeNH3)Pb2I7 (n = 2, bilayer) (triclinic space group P‾1, a 8.794(1), b 8.792(1), c 22.766(2) Å, α 94.02(1), β 97.02(1), γ 90.18(1)°, R = 0.059, Rw = 0.063). The presence of excitonic excited states suggests these materials may have large 3rd-order optical nonlinearities; photobleaching efficiencies of these excitonic transitions in thin films of the decylammonium-lead-iodide compds. are 1.5 × 10-7 cm2/W at 510 nm for n = 1, and 7.5 × 10-8 cm2/W at 570 nm for n = 2.
      28. 28
        Mitzi, D. B.; Wang, S.; Feild, C. A.; Chess, C. A.; Guloy, A. M. Conducting Layered Organic-inorganic Halides Containing 110-Oriented Perovskite Sheets Science 1995, 267, 1473– 1476
        There is no corresponding record for this reference.
      29. 29
        Rao, C. N. R.; Cheetham, A. K.; Thirumurugan, A. Hybrid Inorganicorganic Materials: a New Family in Condensed Matter Physics J. Phys.: Condens. Matter 2008, 20, 083202
        There is no corresponding record for this reference.
      30. 30
        Catlow, C. R. A.; Stoneham, A. M. Ionicity in solids J. Phys. C: Solid State 1983, 16, 4321– 4338
        30
        Ionicity in solids
        Catlow, C. R. A.; Stoneham, A. M.
        Journal of Physics C: Solid State Physics (1983), 16 (22), 4321-38CODEN: JPSOAW; ISSN:0022-3719.
        A review, with many refs., of the use of the ideas of ionicity and covalency in quant. studies of the solid state.
      31. 31
        Jansen, M.; Wedig, U. A Piece of the Picture-Misunderstanding of Chemical Concepts Angew. Chem., Int. Ed. 2008, 47, 10026– 10029
        There is no corresponding record for this reference.
      32. 32
        Brgoch, J.; Lehner, A. J.; Chabinyc, M. L.; Seshadri, R. Ab Initio Calculations of Band Gaps and Absolute Band Positions of Polymorphs of RbPbI3 and CsPbI3: Implications for Main-Group Halide Perovskite Photovoltaics J. Phys. Chem. C 2014, 18, 27721– 27727
        There is no corresponding record for this reference.
      33. 33
        Scanlon, D. O.; Dunnill, C. W.; Buckeridge, J.; Shevlin, S. A.; Logsdail, A. J.; Woodley, S. M.; Catlow, C. R. A.; Powell, M. J.; Palgrave, R. G.; Parkin, I. P. Band Alignment of Rutile and Anatase TiO2 Nat. Mater. 2013, 12, 798– 801
        33
        Band alignment of rutile and anatase TiO2
        Scanlon, David O.; Dunnill, Charles W.; Buckeridge, John; Shevlin, Stephen A.; Logsdail, Andrew J.; Woodley, Scott M.; Catlow, C. Richard A.; Powell, Michael. J.; Palgrave, Robert G.; Parkin, Ivan P.; Watson, Graeme W.; Keal, Thomas W.; Sherwood, Paul; Walsh, Aron; Sokol, Alexey A.
        Nature Materials (2013), 12 (9), 798-801CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
        The most widely used oxide for photocatalytic applications owing to its low cost and high activity is TiO2. The discovery of the photolysis of water on the surface of TiO2 in 1972 launched four decades of intensive research into the underlying chem. and phys. processes involved. Despite much collected evidence, a thoroughly convincing explanation of why mixed-phase samples of anatase and rutile outperform the individual polymorphs has remained elusive. One long-standing controversy is the energetic alignment of the band edges of the rutile and anatase polymorphs of TiO2. We demonstrate, through a combination of state-of-the-art materials simulation techniques and X-ray photoemission expts., that a type-II, staggered, band alignment of ∼ 0.4eV exists between anatase and rutile with anatase possessing the higher electron affinity, or work function. Our results help to explain the robust sepn. of photoexcited charge carriers between the two phases and highlight a route to improved photocatalysts.
      34. 34
        Walsh, A.; Butler, K. T. Prediction of Electron Energies in Metal Oxides Acc. Chem. Res. 2014, 47, 364– 72
        There is no corresponding record for this reference.
      35. 35
        Walsh, A.; Payne, D. J.; Egdell, R. G.; Watson, G. W. Stereochemistry of Post-transition Metal Oxides: Revision of the Classical Lone Pair Model Chem. Soc. Rev. 2011, 40, 4455– 4463
        35
        Stereochemistry of post-transition metal oxides: revision of the classical lone pair model
        Walsh, Aron; Payne, David J.; Egdell, Russell G.; Watson, Graeme W.
        Chemical Society Reviews (2011), 40 (9), 4455-4463CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
        A review. The chem. of post transition metals is dominated by the group oxidn. state N and a lower N-2 oxidn. state, which is assocd. with occupation of a metal s2 lone pair, as found in compds. of Tl(I), Pb(II) and Bi(III). The preference of these cations for non-centrosym. coordination environments has previously been rationalized in terms of direct hybridization of metal s and p valence orbitals, thus lowering the internal electronic energy of the N-2 ion. This explanation in terms of an on-site second-order Jahn-Teller effect remains the contemporary textbook explanation. In this tutorial review, we review recent progress in this area, based on quantum chem. calcns. and X-ray spectroscopic measurements. This recent work has led to a revised model, which highlights the important role of covalent interaction with oxygen in mediating lone pair formation for metal oxides. The role of the anion p AO in chem. bonding is key to explaining why chalcogenides display a weaker preference for structural distortions in comparison to oxides and halides. The underlying chem. interactions are responsible for the unique physicochem. properties of oxides contg. lone pairs and, in particular, to their application as photocatalysts (BiVO4), ferroelecs. (PbTiO3), multi-ferroics (BiFeO3) and p-type semiconductors (SnO). The exploration of lone pair systems remains a viable a venue for the design of functional multi-component oxide compds.
      36. 36
        Ramesh, R.; Spaldin, N. A. Multiferroics: Progress and Prospects in Thin Films Nat. Mater. 2007, 6, 21– 9
        36
        Multiferroics. progress and prospects in thin films
        Ramesh, R.; Spaldin, Nicola A.
        Nature Materials (2007), 6 (1), 21-29CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
        A review. Multiferroic materials, which show simultaneous ferroelec. and magnetic ordering, exhibit unusual phys. properties, and in turn promise new device applications, as a result of the coupling between their dual order parameters. We review recent progress in the growth, characterization, and understanding of thin-film multiferroics. The availability of high-quality thin-film multiferroics makes it easier to tailor their properties through epitaxial strain, at.-level engineering of chem. and interfacial coupling, and is a prerequisite for their incorporation into practical devices. We discuss novel device paradigms based on magnetoelec. coupling, and outline the key scientific challenges in the field.
      37. 37
        Kutes, Y.; Ye, L.; Zhou, Y.; Pang, S.; Huey, B. D.; Padture, N. P. Direct Observation of Ferroelectric Domains in Solution-Processed CH3NH3PbI3 Perovskite Thin Films J. Phys. Chem. Lett. 2014, 5, 3335– 3339
        37
        Direct Observation of Ferroelectric Domains in Solution-Processed CH3NH3PbI3 Perovskite Thin Films
        Kutes, Yasemin; Ye, Linghan; Zhou, Yuanyuan; Pang, Shuping; Huey, Bryan D.; Padture, Nitin P.
        Journal of Physical Chemistry Letters (2014), 5 (19), 3335-3339CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
        A new generation of solid-state photovoltaics is being made possible by the use of organometal-trihalide perovskite materials. While some of these materials are expected to be ferroelec., almost nothing is known about their ferroelec. properties exptl. Using piezoforce microscopy (PFM), here we show unambiguously, for the first time, the presence of ferroelec. domains in high-quality β-CH3NH3PbI3 perovskite thin films that have been synthesized using a new soln.-processing method. The size of the ferroelec. domains is found to be about the size of the grains (∼100 nm). We also present evidence for the reversible switching of the ferroelec. domains by poling with DC biases. This suggests the importance of further PFM investigations into the local ferroelec. behavior of hybrid perovskites, in particular in situ photoeffects. Such investigations could contribute toward the basic understanding of photovoltaic mechanisms in perovskite-based solar cells, which is essential for the further enhancement of the performance of these promising photovoltaics.
      38. 38
        Stroppa, A.; Di Sante, D.; Barone, P.; Bokdam, M.; Kresse, G.; Franchini, C.; Whangbo, M.-H.; Picozzi, S. Tunable Ferroelectric Polarization and Its Interplay with Spin-orbit Coupling in Tin Iodide Perovskites Nat. Commun. 2014, 5, 5900
        38
        Tunable ferroelectric polarization and its interplay with spin-orbit coupling in tin iodide perovskites
        Stroppa, Alessandro; Di Sante, Domenico; Barone, Paolo; Bokdam, Menno; Kresse, Georg; Franchini, Cesare; Whangbo, Myung-Hwan; Picozzi, Silvia
        Nature Communications (2014), 5 (), 5900CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
        Ferroelectricity is a potentially crucial issue in halide perovskites, breakthrough materials in photovoltaic research. Using d. functional theory simulations and symmetry anal., we show that the lead-free perovskite iodide (FA)SnI3, contg. the planar formamidinium cation FA, (NH2CHNH2)+, is ferroelec. In fact, the perpendicular arrangement of FA planes, leading to a 'weak' polarization, is energetically more stable than parallel arrangements of FA planes, being either antiferroelec. or 'strong' ferroelec. Moreover, we show that the 'weak' and 'strong' ferroelec. states with the polar axis along different crystallog. directions are energetically competing. Therefore, at least at low temps., an elec. field could stabilize different states with the polarization rotated by π/4, resulting in a highly tunable ferroelectricity appealing for multistate logic. Intriguingly, the relatively strong spin-orbit coupling in noncentrosym. (FA)SnI3 gives rise to a co-existence of Rashba and Dresselhaus effects and to a spin texture that can be induced, tuned and switched by an elec. field controlling the ferroelec. state.
      39. 39
        Perdew, J.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865– 3868
        39
        Generalized gradient approximation made simple
        Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
        Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
        Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
      40. 40
        Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces Phys. Rev. Lett. 2008, 100, 136406– 4
        40
        Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
        Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gabor I.; Vydrov, Oleg A.; Scuseria, Gustavo E.; Constantin, Lucian A.; Zhou, Xiaolan; Burke, Kieron
        Physical Review Letters (2008), 100 (13), 136406/1-136406/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
        Popular modern generalized gradient approxns. are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of d. gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approxn. that improves equil. properties of densely packed solids and their surfaces.
      41. 41
        Heyd, J.; Scuseria, G. Efficient Hybrid Density Functional Calculations in Solids: Assessment of the Heyd Scuseria Ernzerhof Screened Coulomb Hybrid Functional J. Chem. Phys. 2004, 121, 1187
        There is no corresponding record for this reference.
      42. 42
        Skelton, J. M.; Parker, S. C.; Togo, A.; Tanaka, I.; Walsh, A. Thermal Physics of the Lead Chalcogenides PbS, PbSe, and PbTe from First Principles Phys. Rev. B 2014, 89, 205203
        42
        Thermal physics of the lead chalcogenides PbS, PbSe, and PbTe from first principles
        Skelton, Jonathan M.; Parker, Stephen C.; Togo, Atsushi; Tanaka, Isao; Walsh, Aron
        Physical Review B: Condensed Matter and Materials Physics (2014), 89 (20), 205203/1-205203/10, 10 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
        The lead chalcogenides represent an important family of functional materials, in particular due to the benchmark high-temp. thermoelec. performance of PbTe. A no. of recent investigations, exptl. and theor., have aimed to gather insight into their unique lattice dynamics and electronic structure. However, the majority of first-principles modeling has been performed at fixed temps., and there has been no comprehensive and systematic computational study of the effect of temp. on the material properties. We report a comparative lattice-dynamics study of the temp. dependence of the properties of PbS, PbSe, and PbTe, focusing particularly on those relevant to thermoelec. performance, viz. phonon frequencies, lattice thermal cond., and electronic band structure. Calcns. are performed within the quasiharmonic approxn., with the inclusion of phonon-phonon interactions from many-body perturbation theory, which are used to compute phonon lifetimes and predict the lattice thermal cond. The results are critically compared against exptl. data and other calcns., and add insight to ongoing research on the PbX compds. in relation to the off-centering of Pb at high temps., which is shown to be related to phonon softening. The agreement with expt. suggests that this method could serve as a straightforward, powerful, and generally applicable means of investigating the temp. dependence of material properties from first principles.
      43. 43
        Bardeen, J.; Shockley, W. Deformation Potentials and Mobilities in Non-Polar Crystals Phys. Rev. 1950, 549, 72
        There is no corresponding record for this reference.
      44. 44
        Yamada, Y.; Nakamura, T. Near-band-edge Optical Responses of Solution-processed Organic-inorganic Hybrid Perovskite CH3NH3PbI3 on Mesoporous TiO2 Electrodes Appl. Phys. Express 2014, 7, 032302
        44
        Near-band-edge optical responses of solution-processed organic-inorganic hybrid perovskite CH3NH3PbI3 on mesoporous TiO2 electrodes
        Yamada, Yasuhiro; Nakamura, Toru; Endo, Masaru; Wakamiya, Atsushi; Kanemitsu, Yoshihiko
        Applied Physics Express (2014), 7 (3), 032302CODEN: APEPC4; ISSN:1882-0786. (IOP Publishing Ltd.)
        We studied the near-band-edge optical responses of soln.-processed MeNH3PbI3 on mesoporous TiO2 electrodes, which is utilized in mesoscopic heterojunction solar cells. Photoluminescence (PL) and PL excitation spectra peaks appear at 1.60 and 1.64 eV, resp. The transient absorption spectrum shows a neg. peak at 1.61 eV owing to photobleaching at the band-gap energy, indicating a direct band-gap semiconductor. On the basis of the temp.-dependent PL and diffuse reflectance spectra, we clarified that the absorption tail at room temp. is explained in terms of an Urbach tail and consistently detd. the band-gap energy to be ∼1.61 eV at room temp.
      45. 45
        Fan, L.-Q.; Wu, J.-H. NH4PbI3 Acta Crystallogr., Sect. E 2007, 63, i189
        There is no corresponding record for this reference.
      46. 46
        Wang, F.; Yu, H.; Xu, H.; Zhao, N. HPbI3: A New Precursor Compound for Highly Efficient Solution-Processed Perovskite Solar Cells Adv. Funct. Mater. 2015,  DOI: 10.1002/adfm.201404007
        There is no corresponding record for this reference.
      47. 47
        Kieslich, G.; Sun, S.; Cheetham, T. Solid-State Principles Applied to Organic-Inorganic Perovskites: New Tricks for an Old Dog Chem. Sci. 2014, 5, 4712– 4715
        47
        Solid-state principles applied to organic-inorganic perovskites: new tricks for an old dog
        Kieslich, Gregor; Sun, Shijing; Cheetham, Anthony K.
        Chemical Science (2014), 5 (12), 4712-4715CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
        Hybrid org.-inorg. materials that adopt perovskite-like architectures show intriguing order-disorder phase transitions and exciting electronic properties. We extend the classical concept of ionic tolerance factors to this important class of materials and predict the existence of several hitherto undiscovered hybrid perovskite phases.
      48. 48
        Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric Engineering of Metal-halide Perovskites with Tunable Optical Band Gaps Nat. Commun. 2014, 5, 5757
        48
        Steric engineering of metal-halide perovskites with tunable optical band gaps
        Filip, Marina R.; Eperon, Giles E.; Snaith, Henry J.; Giustino, Feliciano
        Nature Communications (2014), 5 (), 5757CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
        Owing to their high energy-conversion efficiency and inexpensive fabrication routes, solar cells based on metal-org. halide perovskites have rapidly gained prominence as a disruptive technol. An attractive feature of perovskite absorbers is the possibility of tailoring their properties by changing the elemental compn. through the chem. precursors. In this context, rational in silico design represents a powerful tool for mapping the vast materials landscape and accelerating discovery. Here we show that the optical band gap of metal-halide perovskites, a key design parameter for solar cells, strongly correlates with a simple structural feature, the largest metal-halide-metal bond angle. Using this descriptor we suggest continuous tunability of the optical gap from the mid-IR to the visible. Precise band gap engineering is achieved by controlling the bond angles through the steric size of the mol. cation. On the basis of these design principles we predict novel low-gap perovskites for optimum photovoltaic efficiency, and we demonstrate the concept of band gap modulation by synthesizing and characterizing novel mixed-cation perovskites.
      49. 49
        Noel, N. K.; Stranks, S. D.; Abate, A.; Wehrenfennig, C.; Guarnera, S.; Haghighirad, A.; Sadhanala, A.; Eperon, G. E.; Pathak, S. K.; Johnston, M. B. Lead-Free Organic-Inorganic Tin Halide Perovskites for Photovoltaic Applications Energy Environ. Sci. 2014, 7, 3061– 3068
        49
        Lead-free organic-inorganic tin halide perovskites for photovoltaic applications
        Noel, Nakita K.; Stranks, Samuel D.; Abate, Antonio; Wehrenfennig, Christian; Guarnera, Simone; Haghighirad, Amir-Abbas; Sadhanala, Aditya; Eperon, Giles E.; Pathak, Sandeep K.; Johnston, Michael B.; Petrozza, Annamaria; Herz, Laura M.; Snaith, Henry J.
        Energy & Environmental Science (2014), 7 (9), 3061-3068CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
        Already exhibiting solar to elec. power conversion efficiencies of over 17%, org.-inorg. lead halide perovskite solar cells are one of the most promising emerging contenders in the drive to provide a cheap and clean source of energy. One concern however, is the potential toxicol. issue of lead, a key component in the archetypical material. The most likely substitute is tin, which like lead, is also a group 14 metal. While org.-inorg. tin halide perovskites have shown good semiconducting behavior, the instability of tin in its 2+ oxidn. state has thus far proved to be an overwhelming challenge. Here, we report the first completely lead-free, CH3NH3SnI3 perovskite solar cell processed on a mesoporous TiO2 scaffold, reaching efficiencies of over 6% under 1 sun illumination. Remarkably, we achieve open circuit voltages over 0.88 V from a material which has a 1.23 eV band gap.
      50. 50
        Walsh, A.; Watson, G. W. Influence of the Anion on Lone Pair Formation in Sn(II) Monochalcogenides: A DFT Study J. Phys. Chem. B 2005, 109, 18868– 18875
        There is no corresponding record for this reference.
      51. 51
        Eperon, G. E.; Stranks, S. D.; Menelaou, C.; Johnston, M. B.; Herz, L. M.; Snaith, H. J. Formamidinium Lead Trihalide: A Broadly Tunable Perovskite for Efficient Planar Heterojunction Solar Cells Energy Environ. Sci. 2014, 7, 982– 988
        51
        Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells
        Eperon, Giles E.; Stranks, Samuel D.; Menelaou, Christopher; Johnston, Michael B.; Herz, Laura M.; Snaith, Henry J.
        Energy & Environmental Science (2014), 7 (3), 982-988CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
        Perovskite-based solar cells have attracted significant recent interest, with power conversion efficiencies in excess of 15% already superceding a no. of established thin-film solar cell technologies. Most work has focused on a methylammonium lead trihalide perovskites, with a bandgaps of ∼1.55 eV and greater. Here, we explore the effect of replacing the methylammonium cation in this perovskite, and show that with the slightly larger formamidinium cation, we can synthesize formamidinium lead trihalide perovskites with a bandgap tunable between 1.48 and 2.23 eV. We take the 1.48 eV-bandgap perovskite as most suited for single junction solar cells, and demonstrate long-range electron and hole diffusion lengths in this material, making it suitable for planar heterojunction solar cells. We fabricate such devices, and due to the reduced bandgap we achieve high short-circuit currents of >23 mA cm-2, resulting in power conversion efficiencies of up to 14.2%, the highest efficiency yet for soln. processed planar heterojunction perovskite solar cells. Formamidinium lead triiodide is hence promising as a new candidate for this class of solar cell.
      52. 52
        Nagane, S.; Bansode, U.; Game, O.; Chhatre, S. Y.; Ogale, S. CH3NH3PbI(3−x)(BF4)x: Molecular Ion Substituted Hybrid Perovskite Chem. Commun. 2014, 50, 9741– 9744
        There is no corresponding record for this reference.