1 Electrons, Excitons, and Phonons in Two-Dimensional Hybrid

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Perspective

Electrons, Excitons, and Phonons in Two-Dimensional Hybrid Perovskites: Connecting Structural, Optical, and Electronic Properties Daniel B Straus, and Cherie R. Kagan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00201 • Publication Date (Web): 26 Feb 2018 Downloaded from http://pubs.acs.org on February 26, 2018

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The Journal of Physical Chemistry Letters

Electrons, Excitons, and Phonons in Two-Dimensional Hybrid Perovskites: Connecting Structural, Optical, and Electronic Properties Daniel B. Strausa and Cherie R. Kaganabc* a

Department of Chemistry, bDepartment of Electrical and Systems Engineering, cDepartment of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104

Abstract Two-dimensional (2D) hybrid perovskites are stoichiometric compounds consisting of alternating inorganic metal-halide sheets and organoammonium cationic layers. This materials class is widely tailorable in composition, structure, and dimensionality and is providing an intriguing playground for the solid-state chemistry and physics communities to uncover structure-property relationships. In this Perspective, we describe semiconducting 2D perovskites containing lead and tin halide inorganic frameworks. In these 2D perovskites, charges are typically confined to the inorganic framework because of strong quantum and dielectric confinement effects, and exciton binding energies are many times greater than kT at room temperature. We describe the role of the heavy atoms in the inorganic framework, the geometry and chemistry of organic cations, and the “softness” of the organic-inorganic lattice on the electronic structure and dynamics of electrons, excitons, and phonons that govern the physical properties of these materials. TOC Graphic:

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Keywords: Ruddlesden-Popper, quantum well, quantum confinement, dielectric confinement, strain, electron-phonon coupling, charge transport

Organic-inorganic hybrid perovskites have been heavily investigated recently1–7 for their use in solar cells because in just a few years, the efficiency of perovskite-based solar cells has risen to rival commercial silicon solar cells.8 Hybrid perovskites comprise a metal (in recent work, typically Pb or Sn) atom in a corner-sharing octahedral halide cage, with a properly-sized9–12 positively charged organic (or cesium)13 cation occupying the interstitial space. Most solar cells are fabricated from three-dimensional (3D) perovskites that have a uniform structure throughout the material (Figure 1A). In these materials, the Goldschmidt tolerance parameter formalizes the restriction on overall size of the cation: if the cation is too large, a 3D perovskite lattice cannot crystallize.9,10 This restriction limits the degree of tunability that can be provided through cation modifications.14 Perovskite frenzy has brought renewed attention to two-dimensional (2D) analogues that were heavily studied in the 1990s-early 2000s. 2D hybrid perovskites spontaneously form if the length of the organic cation is increased (Figure 1B).11,12,15–17 2D perovskites are typically described as “perfect” quantum well superlattices because these materials have alternating organic and inorganic layers and are stoichiometric compounds that do not have the interfacial roughness common to molecular-beam epitaxially (MBE) grown quantum wells.18,19 Many 2D perovskites have a Type I band alignment of the organic and inorganic frameworks,20–22 with a few reports of Type II heterostructures realized through the introduction of conjugated organic cations.23,24 In addition, 2D perovskites show increased moisture stability compared to 3D analogues because of the inclusion of hydrophobic organic cations.25,26 The relaxation of the restriction on the length of the cation allows the properties of 2D perovskites to be tailored to a much greater degree because in addition to stoichiometric changes in metal and halide composition, there is a much wider range of acceptable organic cations11,24,27–30 and the thickness of the inorganic layers can be varied by controlling the number of inorganic layers n for each organic layer.1,26,31 In this Perspective, we


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correlate the unique structural and optoelectronic properties in semiconducting 2D perovskites and discuss current and future applications for this diverse class of materials. We describe the structural properties of 2D perovskites at a level Figure 1: A) Schematic of a projection of the 3D hybrid perovskite, showing an inorganic network of corner sharing metal halide octahedra (red) with interstitial organic cations (blue, black). (green) Highlighting the restriction on cation size. B) Schematic of a projection down the c-axis of the 2D hybrid perovskite, showing the alternation of organic (blue, black) and corner-sharing inorganic (red) layers for 1 with inorganic layer thickness d and organic layer thickness L. (green) Highlighting the restriction solely on the cross-sectional area, but not the length of the organic cation. C) Energy diagram corresponding to the 2D structure in B). Labeling of the valence band VB, conduction band CB, electronic band gap Eg (grey) and the optical band gap Eexc (blue) of the inorganic framework, and the larger HOMO-LUMO gap of the organic cations (green). The organic framework (grey regions) has a dielectric constant ϵ2, which is smaller than the dielectric constant ϵ1 of the inorganic framework (red regions).

of detail needed to describe the correlation between their structure and physical properties. We point the reader to ref. 32, which describes the

structure

of

hybrid

perovskites

more

comprehensively, and for a greater focus on solar cells made from 2D perovskites, we suggest ref. 33. Excitons and Electronic Structure: Quantum and

dielectric confinement effects in 2D

perovskites increase the effective bandgap and the exciton binding energy (red, Figures 1B and C) compared to the 3D perovskites.34–37 For example, the exciton binding energy in 2D perovskites increases by more than an order of magnitude from ~10 meV in 3D perovskites38,39 to >150 meV in 2D perovskites with 1 (Figure 1C, dashed blue).35–37 Quantum

2 2 confinement in one dimension shifts the conduction and valence bands by

2, 2

, where and

are the mass of the electron and hole and d is the well thickness, and thereby increases the effective bandgap. It also increases the exciton binding energy such that the exciton binding energy of the 1s exciton is 2

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where , "# is the bulk exciton binding energy, $ is the dielectric constant (i.e.,

!

relative permittivity) of the inorganic framework, %& +

(

)

is the reduced exciton mass, * is

the free electron mass, and "# is the hydrogen Rydberg constant.40,41 is the dimensionality of the

system: in a bulk, non-confined material 3, and in a perfect 2D system 2, with a corresponding

exciton binding energy , 4 , . As the thickness d of the quantum well increases, increases from 2 and begins to approach 3. Dielectric confinement is an electrostatic phenomenon that results when a thin layer of material with dielectric constant $ is sandwiched between a material with dielectric

constant $ < $ . The electrostatic force between charges in the high dielectric constant ($ material

increases because the electric field generated by a charge extends into the lower dielectric constant ($ medium where it is screened less effectively.34,42,43 This phenomenon is also called the image-charge effect. The change in Coulomb forces in the high dielectric constant material renormalizes the energy levels, increasing both the electronic band gap as well as the exciton binding energy.44 Using first-order perturbation theory and an approximate model that assumes charge carriers are confined to the inorganic framework by an infinite barrier and assumes a two-band model with separable wavefunctions, the change in exciton binding energy Δ ≈ 2

$ $ 2 1 3 4#2 $ + $ $ $*

where q is the fundamental charge, $* the vacuum permittivity, and I is a factor that is approximately unity.40,41,45 These equations provide a simple framework to model confinement effects in 2D perovskites. However, they are inexact as it is not possible to define parent 3D organic and inorganic components from which to extrapolate their properties, as commonly done for MBE-grown semiconductor quantum well superlattices.46 To account for Coulomb interactions between the organic and inorganic constituents as well as spin-orbit coupling effects, detailed calculations of the band structure for 2D perovskites are needed.46


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In conventional semiconductors, the valence band is made up of p-orbitals and the conduction band is made up of s-orbitals. This structure creates complexity in the valence band (e.g., heavy and light hole and spin-orbit bands), but not in the conduction band.47 In contrast, 3D and 2D hybrid perovskites have a valence band made up predominantly of halide p-orbitals hybridized with some metal s-orbital character, and a conduction band predominantly made of metal p-orbitals; in lead iodide hybrid perovskites, the relevant orbitals are I 5p, and Pb 6s and 6p.21,48,49 For a comprehensive discussion of the electronic structure of 3D and 2D perovskites, we refer the reader to Ref. 46, as the band structure depends on the details of the crystal structure of the perovskite. The band structure and density-of-states for

the

2D

hybrid

perovskite

4-fluorophenethylammonium

lead

iodide

(4FPEA2PbI4,

PEA=C6H5C2H4NH3+) is shown in Figure 2A, which notably shows complexity in the conduction band.49 The combination of this complex band structure and the incorporation of heavy Pb atoms (and to a lesser degree Sn atoms in analogous tin halide perovskites) generates significant spin-orbit coupling in the conduction band,21 with a calculated spin-orbit splitting Δ56 between the first two conduction band states of 1.2 eV in 4FPEA2PbI4 (green, Figure 2A).46,49,50 The large spin-orbit coupling and non-centrosymmetric structure of hybrid perovskites sets up the necessary condition for Figure 2: A) Calculated density-functional theory band structure of 4FPEA2PbI4 both without spin-orbit coupling (dashed lines) and with spin-orbit coupling (solid lines). (green) The spin-orbit splitting Δ56 . (Inset) Structure of 4FPEA2PbI4. Adapted from Ref. 50. B) 10 K absorption spectra of (i) (C10H21NH3)2PbI4, (ii) PEA2PbI4, and (iii) PEA2MAPb2I7. Reprinted figure with permission from Ref. 36. Copyright 1992 by the American Physical Society.

spin-dependent properties and the possibility of exotic Rashba and Dresselhaus effects.48–52 In the Rashba or Dresselhaus effect, charge carriers experience an effective magnetic field, and the non-centrosymmetric potential can cause one

spin orientation to be stabilized.51 Recently, a “giant” Rashba splitting was claimed to be observed in phenethylammonium lead iodide (PEA2PbI4), indicating the potential for 2D perovskites in spintronics applications.53 5 ACS Paragon Plus Environment


The correlation between crystal and electronic structures and its influence on optical properties has been most widely explored. We describe the structure-property relationship as the geometry and chemistry of the organic cation and the composition and dimensionality of the inorganic framework are tailored in 2D perovskites. Length of the Organic Cation: 2D perovskites can be synthesized with different chain length L alkylammonium cations. The length L of typical alkylammonium cations CmH2m+1NH3+ where m ≥ 4 has a negligible effect on the optical properties of the perovskite.15 For example, 1.6 K optical absorption spectra of cleaved single crystals of (CmH2m+1NH3)2PbI4 with m = 4, 8, 9, 10, and 12, in which the interlayer Pb-Pb distance (L + d, Figures 1B and C) varies from 15.17 Å to 24.51 Å, show a similar 320±30 meV exciton binding energy.15 Temperature-dependent photoluminescence (PL) measurements show thermally-activated quenching of the free-exciton luminescence intensity with an activation energy near room temperature of 370±50 meV in single crystals of the same materials.15 This higher temperature activation energy has been compared with the low temperature exciton binding energy in support of the insensitivity of the optical properties to alkyl chain length; however, these values may vary as these 2D perovskites undergo a structural phase transition (discussed later in this perspective) between temperatures of 250 K and 310 K that depends on m and correlates with melting of the amine (e.g., m = 4, 8, 9, and 10 are in the low temperature phase and m = 12 is in the high temperature phase), and as the crystals can degrade under illumination during measurements.15 Dielectric Constant of the Organic Cation ($2 ): While simply changing the length L of the organic cation has little effect on the electronic and optical properties, changing the dielectric constant of the organic cation $2 , e.g., by choosing aromatic instead of aliphatic amines, significantly decreases the exciton binding energy in 1 2D perovskites. For instance 10 K absorption spectra of single crystals show a decrease in exciton binding energy from 320 meV in (C10H21NH3)2PbI4 (Figure 2B(i)) to 220 meV in PEA2PbI4 (Figure 2B(ii)), consistent with PEA+ having a higher dielectric constant $2 than alkyl amines including C10H21NH3+.36 The activation energy for PL quenching in PEA2PbI4 single crystals is 6 ACS Paragon Plus Environment

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found to be 220±30 meV. The electronic band gap also decreases,36 in accord with dielectric confinement.44 The local environment of the perovskite sample also affects the exciton binding energy. A recent study on butylammonium lead iodide (BA2PbI4, BA=C4H9NH3+) single crystals found an exciton binding energy of 370 meV that is enhanced substantially to 490 meV upon exfoliation and transfer such that the perovskite layer is bounded by silica (ϵ 2.13) on one side and air (ϵ 1) on the other.54 The increase in dielectric confinement created by the sample environment should also increase the band gap of the exfoliated layer compared to that of the crystal, though this is hard to directly compare at low temperatures

because

substrate

interactions

suppress the phase transition.54 Cross-sectional Area of the Organic Cation: 2D perovskites form if the length of the organic cation is increased, however there is a restriction Figure 3: A) Schematic showing distortion in the metalhalide framework to accommodate an organic cation with a larger cross-sectional area. B) Experimental energies of the excitonic absorption in PEA2SnI4-based 2D perovskites with functionalized cations that exhibit solely in-plane distortion (blue) and a combination of in- and out-of-plane distortion (red). Data from Ref. 27.

on their cross-sectional area such that they fit within

the

interstitial

space

between

the

inorganic octahedra (Figure 1B, green). For example, in 2D lead iodide perovskites, the maximum cross-sectional area is on the order of

40 Å2.12 The limited cross-sectional area available to host the organic cation can also be harnessed to tailor the optical properties of the perovskite by straining the inorganic framework. Increasing the crosssectional area of the organic cation will change the orientation of the cations in the organic framework, and for the perovskite to crystallize, the inter-octahedral metal-halide-metal bond angle must change to accommodate the larger cation (Figure 3A), though it is possible for the cation to be too large for a perovskite structure to form.11 Reduction of the metal-halide-metal bond angle from the ideal 180° alters the band structure and increases the band gap of the perovskite.27 This effect has been seen experimentally in 2D tin-halide perovskites.27–29 Experimental exciton resonances in SnI4-based 2D perovskites with



functionalized aromatic moieties and ethylammonium tethers are plotted against the Sn-I-Sn bond angle in Figure 3B.27 Strain effects are also reported in 2D lead halide perovskites. A recent study found that in 2D lead halide perovskites containing aromatic cations, the length of the alkyl tether connecting the ammonium cation to the aromatic moiety has a much larger effect on the band gap than the number of aromatic rings on the cation.19 A methyl tether results in more strain and a smaller Pb-X-Pb (X=Cl, Br, I) bond angle than an ethyl tether.19 We are not aware of any studies quantitatively probing the effect of strain on the exciton binding energy. However, akin to strain engineering in conventional Si electronics55 and in 3D perovskites56 which warps the light and heavy hole bands, we expect strain in 2D perovskites will modify the band structure, changing the carrier effective masses and therefore the exciton binding energy. Mixed Cation Systems: The properties of 2D hybrid perovskites can be further tuned through mixedcation systems. For instance, perovskites have been fabricated using multiple cations that differ in crosssectional area or dielectric constant. Xu and Mitzi demonstrated that by tailoring the ratio of A = 2,3,4,5,6-pentafluorophenethylammonium (5FPEA) and A = 2-napthyleneethylammonium (NEA) cations in A2SnI4 2D perovskites, the energy of the excitonic resonance can be continuously tuned from 572 nm (pure 5FPEA) to 602 nm (pure NEA).57 They also fabricated thin films of a perovskite containing five different cations that form a single-phase film and suggested that incorporating multiple cations may prove beneficial in perovskite-based devices because adding cations containing thiols or hydroxyls, for example, could favorably interact with substrates, contacts, or other interfaces while also maintaining the broad optical tunability.57


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Diammonium Cations: In addition to cations that contain a single positively charged nitrogen atom, diammonium cations can be employed to remove the van der Waals gap and directly link layers together. Diammonium cations have been extensively studied in 2D perovskite systems containing metals such as Cd and Cu,16 but only limited studies have been carried out on Pb and Sn perovskites.11,32 If the cations are assumed to be rigid, monoammonium cations will result in a

Figure 4: Schematic showing idealized structure for an n = 1 2D perovskite containing a diammonium cation, with inorganic layer thickness d and organic layer thickness L.

staggered structure where metal atoms in adjacent inorganic layers are offset by the metal-halide bond

length (e.g., Figure 1B), but diammonium cations would result in an eclipsed structure because of the rigid linkers (Figure 4).16 In reality, cations are not rigid, so this general principle does not always hold.11 The 2D diammonium lead iodide perovskites NH3(CH2)mNH3PbI4 (m = 4, 6, 8) have been recently synthesized and characterized.58 These perovskites exhibit the typical corner-sharing perovskite structure, though the inorganic framework is slightly corrugated,58 which likely originates from the geometrical constraints imposed by the diammonium cation. As m increases from 4 to 6 to 8, the band gap increases.58 The authors hypothesized that the increase in band gap may be related to an increase in quantum confinement (i.e., a reduction in tunneling between inorganic layers) with longer cations;58 an increase in dielectric confinement would have a similar effect. The interlayer distance (d + L) in NH3(CH3)mNH3PbI4 for 4 ≤ m ≤ 8 ranges from 10.38 Å to 13.73 Å,58 which are all shorter than the 15.17 Å interlayer distance for the BA2PbI4 compound.15 Even though (CmH2m+1NH3)2PbI4 (m ≥ 4) do not show an increase in quantum or dielectric confinement effects with increasing m, it is possible that for NH3(CH3)mNH3PbI4 (m = 4, 6, 8) the alkyl diammonium cations are short enough that adjacent inorganic layers are somewhat



electronically coupled. The increase is likely not caused by greater strain because the Pb-I-Pb bond angle decreases only slightly as m increases.58 We are not aware of any detailed studies of tunneling or of the reduction in dielectric confinement as the distance between adjacent inorganic layers in 2D perovskites decreases. However, the use of even shorter diammonium cations (m = 2, 3) is expected to result in stronger coupling between adjacent inorganic layers and provide further flexibility in tuning the bandgap and exciton binding energy of 2D perovskites and perhaps allow for the generation of indirect excitons.59 In the Cu-based 2D perovskite NH3C2H4NH3CuBr4, the interlayer Br-Br distance (L) is 3.602 Å, which is almost 0.3 Å smaller than two times the van der Waals radius of Br, and in NH3C3H6NH3CuBr4, the interlayer Br-Br distance is 4.063 Å, only slightly larger than the sum of Br van der Waals radii.11,60 However, an investigation into the effects of very short cations must be done carefully because lattice distortions introduced by short diammonium cations may be significant enough to dominate reductions in quantum and dielectric confinement. More complicated diammonium Pb and Sn halides have also been synthesized. A tin iodide perovskite (CH3)3NCH2CH2NH3SnI4 has been formed, where the cation contains one primary and one quaternary amine headgroup.61 This cation results in a short iodine-iodine distance of 4.19 Å between adjacent inorganic layers (compared to 16.30 Å in PEA2SnI4)62 as well as an average Sn-I-Sn bond angle of 166.9° and an excitonic absorption transition of 630 nm, compared to 156.5° and 609 nm in PEA2SnI4.61 The lower energy excitonic transition has been attributed to interactions between iodine atoms in adjacent layers as well as a reduction in strain, indicated by the larger bond angle.27,61 The electronic band gap has not been reported,61 so we are unable to dissect the exciton binding energy and band gap separately. Cationic Phase Transitions: We already described examples above where, in addition to tuning the length and dielectric constant, for some organic cations the perovskite undergoes a phase transition upon cooling.15,63,64 We highlight these phase transitions here as they drive changes in band structure that complicate the evaluation of temperature-dependent optical properties.46 The influence of the structural 10 ACS Paragon Plus Environment

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phase transition on band gap is readily seen by eye at temperatures between 235 and 310 K in alkylammonium lead halide perovskites [(CmH2m+1NH3)2PbI4, m = 4, 8, 9, 10, and 12] as a change in color from orange at high temperature to yellow at low temperature.15 Notably, this phase transition is absent for (C6H13NH3)2PbI4.15 In addition, no phase transition is observed in PEA2PbI4,36 demonstrating the influence of the cation on the thermodynamic properties of 2D hybrid perovskites. Interactions between 2D perovskites and the surrounding environment also affect phase transitions. The interaction of an exfoliated sheet with a silica substrate suppresses the freezing/melting phase transition in BA2PbI4,54 and this distinction must be taken into account when comparing the temperature-dependent optical properties of exfoliated sheets and larger single crystals. Halide and Metal Substitutions: The band gap of 2D perovskites can be tuned through halide substitution. Replacing iodide with bromide or chloride results in an increase in the band gap,11,19,32,65 as it does in 3D hybrid perovskites, and is consistent with lowering of the valence band maximum that has predominantly halide p-character.66 Mixed halide systems can also be used to further tailor the optical and electronic properties. By using two halides in PEA-based 2D perovskites and varying the proportion z in (PEA2PbX4(1-z)Y4z, X, Y = Cl, Br, I), the band gap can be continuously tuned.67 We are not aware of quantitative studies of the halide-dependent exciton binding energy in 2D perovskites. As ,

4 , 4 "# , the exciton binding energy will change in proportion to the exciton effective

!

mass and in inverse proportion to the square of the dielectric constant. Although studies of effective mass do not conclusively show a difference between lead iodide and lead bromide perovskites,38,68,69 as iodide is replaced by bromide and then chloride and the band gap increases, % and 9 and therefore EB are anticipated to increase for perovskites with similar crystal and band structures.70 Increases in the carrier effective masses will also reduce the carrier mobility. In the 3D perovskites, the dielectric constants trend as $:;?@ < $:; 175 Um in Solution-Grown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967–970.

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TOC Graphic 50x50mm (600 x 600 DPI)

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Figure 1: A) Schematic of a projection of the 3D hybrid perovskite, showing an inorganic network of corner sharing metal halide octahedra (red) with interstitial organic cations (blue, black). (green) Highlighting the restriction on cation size. B) Schematic of a projection down the c-axis of the 2D hybrid perovskite, showing the alternation of organic (blue, black) and corner-sharing inorganic (red) layers for n=1 with inorganic layer thickness d and organic layer thickness L. (green) Highlighting the restriction solely on the cross-sectional area, but not the length of the organic cation. C) Energy diagram corresponding to the 2D structure in B). Labeling of the valence band VB, conduction band CB, electronic band gap Eg (grey) and the optical band gap Eexc (blue) of the inorganic framework, and the larger HOMO-LUMO gap of the organic cations (green). The organic framework (grey regions) has a dielectric constant ϵ2, which is smaller than the dielectric constant ϵ1 of the inorganic framework (red regions). 44x23mm (600 x 600 DPI)



Figure 2: A) Calculated density-functional theory band structure of 4FPEA2PbI4 both without spin-orbit coupling (dashed lines) and with spin-orbit coupling (solid lines). (green) The spin-orbit splitting ∆_SO. (Inset) Structure of 4FPEA2PbI4. Adapted from Ref. 50. B) 10 K absorption spectra of (i) (C10H21NH3)2PbI4, (ii) PEA2PbI4, and (iii) PEA2MAPb2I7. Reprinted figure with permission from Ref. 36. Copyright 1992 by the American Physical Society. 45x25mm (600 x 600 DPI)


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Figure 3: A) Schematic showing distortion in the metal-halide framework to accommodate an organic cation with a larger cross-sectional area. B) Experimental energies of the excitonic absorption in PEA2SnI4-based 2D perovskites with functionalized cations that exhibit solely in-plane distortion (blue) and a combination of in- and out-of-plane distortion (red). Data from Ref. 27. 34x14mm (600 x 600 DPI)



Figure 4: Schematic showing idealized structure for an n = 1 2D perovskite containing a diammonium cation, with inorganic layer thickness d and organic layer thickness L. 82x82mm (600 x 600 DPI)


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Figure 5: A) Absorption and B) PL spectra of exfoliated sheets of BA¬2MAn-1PbnI3n+1 (n = 1 - 5). From Ref. 74. Reprinted with permission from AAAS. 38x17mm (600 x 600 DPI)



Figure 6: Reflection spectra of a single crystal of (C10H21NH3)2PbI4 at 1.6 K with light propagating A) orthogonal to the c-axis with polarizations E ∥ c and E ⊥ c and B) parallel to the c-axis with two different polarizations a’ and b’. Reprinted figure with permission from Ref. 15. Copyright 1990 by the American Physical Society. 36x16mm (600 x 600 DPI)


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Figure 7: A) PL map of an exfoliated (BA)2(MA)3Pb4I13 crystal showing sub-band gap PL at the crystal edges. B) Absorption and C) PL spectra of thin films of BA¬2MAn-1PbnI3n+1, n = 1-5 and 3D methylammonium lead iodide. Dashed lines indicate the position of the excitonic absorption or PL resonance in exfoliated single crystals (Figures 5A and B). From Ref. 74. Reprinted with permission from AAAS. 87x93mm (300 x 300 DPI)



Figure 8: Energy diagram for A) AEQTPbCl4 with a Type I heterojunction and B) AEQTPbI4 with a Type II heterojunction. Reprinted from Ref. 24. 60x43mm (600 x 600 DPI)


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Figure 9: Density-functional theory computed phonon modes in PEA2PbI4 below 50 meV. Top: electronphonon couplings for each phonon mode. Bottom: Contributions to each phonon mode from the Pb-I framework (blue) and organic cations (green). Reprinted from Ref. 18. 78x74mm (600 x 600 DPI)



Figure 10: A) 15K absorption (black) and PL (blue) spectra of a PEA2PbI4 thin film. PL × 60 (purple) highlights hot excitonic PL resonances α and β. B) Pseudocolor plot of time-resolved PL spectrum a PEA2PbI4 thin film. C) Schematic of relaxation processes in PEA2PbI4. Reprinted from Ref. 18. 71x62mm (600 x 600 DPI)


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Figure 11: A) Room temperature transient absorption spectrum of butylammonium lead iodide indicating that trap states are excitonic in nature. Reprinted from Ref. 31. B) 1.6 K PL spectra of (CmH2m+1)2PbI4¬ (m = 4, 8, 9, 10, 12) showing a sharp excitonic resonance at 2.56 eV and several sub-band gap PL resonances. Reprinted figure with permission from Ref. 15. Copyright 1990 by the American Physical Society. C) PL from a PEA2PbI4 thin film (black, from Ref. 18) and single crystal plotted on linear and (inset) logarithmic scale. D) White light emission from a single crystal of EDBEPbBr4. An image of the fluorescence from a single-crystal and a depiction of the crystal structure are inset. Adapted from Ref. 30. 68x56mm (600 x 600 DPI)



Figure 12: A) Schematic of a PEA2SnI4 thin film FET. B) Powder XRD pattern of a thin-film of PEA2SnI4 thin film. C) Transfer curve of a PEA2SnI4 FET. A-C from Ref. 101. Reprinted with permission from AAAS. D) Photocurrent of PEA2MAPb2I7 with photocurrent j ∥ c and j ⊥ c. Reprinted from Ref. 83, with permission from Elsevier. 81x79mm (600 x 600 DPI)


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1 Electrons, Excitons, and Phonons in Two-Dimensional Hybrid

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