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Cite This: J. Phys. Chem. C 2018, 122, 16715−16726

Graphene Oxide/Perovskite Interfaces For Photovoltaics Nourdine Zibouche,† George Volonakis,† and Feliciano Giustino*,†,‡ †

Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, U.K. Cornell University, Ithaca, New York 14853, United States

‡

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S Supporting Information *

ABSTRACT: Graphene-based materials hold a promising prospect for their utilization in perovskite solar cell devices as electron-extraction or holetransport layers. Here, we investigate the role of oxidized graphene when interfaced with the perovskite MAPbI. Using first-principles calculations based on density functional theory, we study the change in the structural and electronic properties of the heterostructures with the oxidation level. We show that, depending on the concentration of the epoxy functional groups, only reduced graphene oxide would be advantageous for the extraction of photogenerated charge carriers. For oxygen concentration up to 33%, both hole and electron carriers could be extracted, whereas for concentrations between 33 and 66%, electron transfer is favored. For concentrations above 66%, it should not be possible to extract carriers. Moreover, the analysis of the charge density rearrangement at the interface due to the oxidization of graphene shows that the interfacial dipole decreases with the increase in the oxygen content. Finally, we report the modification of the band gap and the work-function in the oxidized graphene for different rearrangements of the epoxy groups on the graphene sheet. This study shows that the reduced graphene oxide with specific oxidation levels could effectively be incorporated as a selective contact in heterojunction devices for applications in perovskite solar cells.

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INTRODUCTION The field of materials for photovoltaics (PVs) has recently been enriched by the discovery of organic−inorganic halide perovskites as light absorbers and electron/hole transporters.1−4 The superior properties of these PV materials include long diffusion lengths of the charge carriers,5,6 high absorption coefficients,7,8 direct and tunable band gaps, 9 relatively high carrier mobilities,10,11 and low-cost fabrication techniques based on solution processing.12 The current perovskite solar cells (PSCs) have reached an unprecedented power-conversion efficiency (PCE) above 22%,13 thus becoming potential alternatives to silicon14 and other thin films15,16 for the next generation of PV devices. However, the use of PSCs is hindered by the degradation of the perovskite when exposed to illumination and moisture, especially at high temperatures.17,18 Other degradation mechanisms have also been reported, and are associated with the interfaces between the different layers that compose the PSCs.17,18 To overcome the stability issue, several approaches have been investigated, including chemical modifications in the bulk or at the surface of the perovskite layer by substitutions19,20 or cross-linking additives,21,22 encapsulation,17,23 substitution, or doping of the charge-collecting and -transporting layers,24−26 or by incorporation of a buffer layer between the perovskite and the charge-transport interfaces.27,28 The interfacial interactions between different layers of the PSC are also of paramount importance for the device operation because they play a key role in the charge extraction and transfer to the electrodes, but also in the stability of the PSC device as a © 2018 American Chemical Society

whole. In this regard, several reports have explored different materials alongside the perovskite layer as charge collection or transport layers.29−31 One promising route toward applications is the incorporation of graphene and graphene-related materials in the PSC devices.32−34 Several reports have demonstrated the multifunctionalities of graphene-based materials in solar cell applications due to their outstanding optical and electrical properties. It has been shown that graphene and its related materials could be employed as transparent electrodes, transport and light-harvesting layers, and Schottky junctions, only to name a few.33,35−40 In PSCs, graphene-based materials are mainly explored as potential electron-extraction materials (EEM) and hole-transport materials (HTM).41−45 This also includes other forms of carbon materials, such as fullerenes and nanotubes, that have been incorporated as charge carrier extraction and injection or as additives, which led to the improvement in the performance of the PCS devices.40,46−48 Wang and co-workers combined graphene nanoflakes along with TiO2 as an EEM in a perovskite solar cell. The inclusion of graphene led to an increase in the PCE from 10 to 15.6% compared to the device without graphene.49 Mirfasih and co-workers have shown that using graphene scaffolds as an interface layer between the electrontransporting and -absorbing materials in a PSC improves the Received: April 5, 2018 Revised: June 5, 2018 Published: July 1, 2018 16715

DOI: 10.1021/acs.jpcc.8b03230 J. Phys. Chem. C 2018, 122, 16715−16726

Article

The Journal of Physical Chemistry C

Figure 1. Layered structures forming the heterojunctions. (a) An example of the MAPbI3/GO heterostructure, where C, O, Pb, I, and MA are, respectively, the atoms of carbon, oxygen, lead, iodine, and methylammonium (CH3NH3) organic molecule. (b) MAPbI3 unit cell excluding the MA molecules in the left side, the dashed lines and the small size sphere represent, respectively, the image bonds and the image atoms in the periodic cell. The sublattice PbI2 at the interface is highlighted with the dashed red rhombus and presented separately in the right side. The angles A, A′, B, and B′ viewed along the x-direction and C, C′, D, and D′ along the y-direction represent the angles in the PbI2 sublattice having I atoms as vertices. (c) Graphene supercell, with the cyan area representing the rectangular unit cell of pristine graphene. (d) Fully oxidized graphene model (GO-100%O). The dark-pink stripe shows the armchair sites and the O atoms are indicated by the red sites. (e) Reduced graphene-oxide model with 66% of O atoms (rGO-66%O). (f) Reduced graphene-oxide model with 33% of O atoms (rGO-33%O).

density redistribution at the interface, which causes the decrease in the interfacial dipole. Moreover, the interfacial ferroelectric distortion observed in the heterojunction between MAPbI3 and pristine graphene55 is not present in the case of partially oxidized graphene.

device performance by 27%, as well as the stability compared to the conventional one.50 Di Carlo and co-workers showed that reduced graphene oxide (rGO), when used as an HTM to replace the conventional Spiro-OMeTAD, prevents the recombination of photogenerated charges and yields an increase in PCE by 36 and 26% under shelf and light-soaking tests, respectively.51 In a more recent work, they have also investigated the role of graphene and graphene oxide (GO) in PSCs under different degradation environments. The devices with both graphene and GO exhibited a better charge extraction and a slower degradation mechanisms, leading to an overall increase in the device performance and stability.52 rGO was also found to enhance the photovoltaic performance of the PSC when integrated in mesoporous TiO2 to form an EEM. On the contrary, when incorporated in the perovskite light-absorbing layer or in the Spiro-OMeTAD HTM, the PCSs show a decrease in the efficiency.53 For a more exhaustive overview on the role of graphene-based materials in the PSCs, we refer the reader to refs 36, 54. In spite of all the aforementioned studies, the role of graphene materials, in particular rGO, in PV devices is yet not completely understood, especially at the microscopic level. Here, we perform a systematic computational study on the interface between oxidized graphene and the organic−inorganic perovskite MAPbI3, where MA is the CH3NH3 cation, methylammonium. We investigate, by means of first-principles calculations based on density functional theory (DFT), the influence of the oxygen concentration on the electronic properties of the heterostructure. We show that the band alignment profile suggests that rGO can be employed as a recombination layer or as an electron-extraction layer, depending on the reduction level, whereas highly oxidized graphene is unsuitable for charge extraction. We also show that the increase in the oxygen content in oxidized graphene leads to a charge

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MODELS AND METHODS Models. The interface models considered in this work are composed of a MAPbI3 slab, and a graphene monolayer functionalized with epoxy (O) groups, at concentrations of 0, 33, 66, and 100%. MAPbI3 crystallizes in the tetragonal phase under room-temperature conditions, with experimental lattice parameters of a = b = 8.85 Å and c = 12.64 Å.56−58 It has been shown that (110) and (001) surfaces are the most favorable nonpolar surface of MAPbI3.59 In addition, in ref 55 it was shown that the electronic properties and the level alignment between pristine graphene and MAPbI3 are qualitatively the same. Therefore, the perovskite layer considered in this study is constructed by cutting the three-dimensional (3D) crystal along the crystalline plane (110), resulting in the PbI2 termination shown in Figure 1a,b. This termination is the most stable nondefective (110) surface termination,60 which is consistent with the experimental observations.61 The lattice parameters of the slab are a = 12.52 Å and b = 12.64 Å. The thickness of the slab is the same with the one used in ref 55, for which the electronic properties of the graphene/MAPbI3 interface are converged. Furthermore, the calculated electronic band gap of the chosen MAPbI3 slab is within 0.06 eV of bulk MAPbI3, which allows a proper description of the electronic properties of the interfaces investigated here. To minimize the mismatch between the GO and MAPbI3 structures, the proposed GO models in Figure 1c−f are constructed starting from a 5 × 3 supercell of a rectangular 16716


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Figure 2. Change in the structure of MAPbI3 before (in blue) and after (in red) interfacing with the GO models. MAPbI3 structures (before/after) are relaxed with the lattice parameters of each GO model. Column a represents the unit cell of MAPbI3, column b represents the top view of the PbI2 sublattice at the interface, and column c represents the angles in the PbI2 sublattice along the x- and y-directions, as described in Figure 1b and in the main text. 16717


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case of the interface with pristine graphene.55 Therefore, in the following, we will not include vdW corrections.

unit cell of pristine graphene (cyan color in Figure 1c) as follows; first, by fully functionalizing the graphene sheet with oxygen atoms (100% O), which corresponds to a O:C ratio of 2:1 because here we only investigate the case of epoxy groups on graphene. To avoid the rippling of the graphene sheet, each side has equal number of O atoms uniformly distributed on the armchair sides, as depicted in Figure 1d with a dark-pink stripe. Then, the 66 and 33% models are obtained by removing O atoms to match the corresponding concentrations. To maintain a homogeneous arrangement of the O atoms and hence avoid the buckling of the graphene sheet in the rGO models, one and two O atoms every three are, respectively, removed along the zigzag direction for the 66% O and the 33% O models, as shown in Figure 2e,f. However, it is worth mentioning that in real rGOs, inhomogeneous phases of oxygen are formed on the graphene sheet due to the strong attractive interactions of the oxygen atoms at different graphene sides that lead to aggregation.62−64 This inhomogeneous distribution of the oxygen atoms can, thus, affect the electronic structure of rGO. The resulting interface models contain in total 168, 178, 188, and 198 atoms for pristine graphene, rGO-33%O, rGO-66%O, and GO-100%O, respectively. Methods. All the calculations are carried out using density functional theory (DFT)65 as implemented in the Quantum Espresso simulation package.66,67 The Kohn−Sham wavefunctions and energies are calculated using the local density approximation (LDA)68 in the Perdew−Zunger parametrization,69 using a plane-wave basis, with energy and charge density cutoffs of 40 and 320 Ry, respectively. Ultrasoft pseudopotentials70,71 are used to describe the core−valence interactions. The structural relaxation is performed until the force on each atom is smaller than 0.01 eV/Å. The Brillouin Zone integration is sampled following the Monkhorst−Pack scheme,72 using 4 × 4 × 1 and 8 × 8 × 1 k-point grids for the ionic optimization and the electronic structure calculations, respectively. To avoid spurious interactions between periodically repeated slabs, the vacuum region is set to be at least 20 Å, and we include dipole corrections to eliminate artificial electrostatic effects.73,74 It is well known that DFT underestimates band gaps. However, in the case of hybrid perovskites, DFT yields gaps close to experiments in the case of nonrelativistic calculations. This fortuitous result is due to the neglect of spin−orbit coupling (SOC).75−77 The inclusion of SOC in the case of MAPbI3 underestimates the band gap by as much as 1 eV.75−77 To obtain more accurate band gaps and hence a better estimate of the energy-level alignment, the PBE0 hybrid functional78,79 can be employed. However, using PBE0 for such large interface systems is computationally prohibitive. To overcome this limitation, PBE0+SOC calculations are performed using Vienna ab initio simulation package code80−82 on the bulk structure of MAPbI3 and the individual GO models, and then the corrections are added on top of the respective LDA values for the valence band maxima (VBM) and the conduction band minima (CBM) of the interfaces. The induced strain effects in the electronic structure of the MAPbI3 slab of each model are taken into account by aligning the planar average of the electrostatic potential of their respective strained bulk structures to that of the unstrained bulk MAPbI3. All band edge levels are referenced to the experimentally estimated energy levels of MAPbI3.8383 We have examined the effect of van der Waals (vdW) corrections for the interface with a fully oxidized graphene. The details of the calculation are given in the Supporting Information (SI.1). We found that the electronic structure remains unaffected as in the

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DISCUSSION Graphene and its derivatives, including graphene oxides and nanotubes, have exceptional mechanical properties.32,84−87 As reported in the literature, the Young’s moduli of pristine graphene, rGO, and GO are in the order of 1.0,84 0.25,88 and 0.21 TPa,89 respectively. In contrast, the Young’s modulus of MAPbI3 is 0.0142 TPa,90 which is much smaller than that of graphene materials. Therefore, in combining GO models with the MAPbI3 slab to construct the heterostructures, we opt for stretching the MAPbI3 slab while maintaining the graphene oxide layer fully relaxed. Accordingly, to exclude any spurious strain effects in the study of these heterojunctions, the geometries of GO models are fully optimized. First, these calculations show an increase in the lattice parameters with the oxidation level, reaching maximum values of 3 and 5% for a and b of the fully oxidized model, respectively, as compared to pristine graphene. Second, the atomic coordinates of the MAPbI3 slab are relaxed using the lattice parameters of the GO models. Figure S1a shows the mismatch between the lattice parameters of pristine MAPbI3 and the GO structures. The mismatch increases with the increasing oxygen concentration in the GO models in the range between −2.5−3 and 0.5−3% for a and b, respectively. The corresponding strain-induced changes in the LDA band gap of the MAPbI3 layer are shown in Figure S1b. It can be seen that the band gap also increases as the lattice parameters of the corresponding GO models increase with the increasing oxygen content. However, the direct band gap character of the MAPbI3 structure is preserved in all the cases, as shown in Figure S2. The binding energies of the MAPbI3/GO heterojunctions are calculated as the difference between the total energy of the interface models and the total energy of each individual slab forming the interface per surface area. The corresponding values of these different heterojunctions are 8 meV/Å2 (0.30 eV per surface Pb atom), 9 meV/Å2 (0.36 eV per surface Pb atom), 8 eV/Å2 (0.32 eV per surface Pb atom), and 6 meV/Å2 (0.25 eV per surface Pb atom) for MAPbI3/graphene, MAPbI3/rGO-33% O, MAPbI3/rGO-66%O, and MAPbI3/GO-100%O, respectively. These binding energies are in the same range and indicate the favorable formation of these heterostructures when MAPbI3 and oxidized graphene are brought into contact. Note that binding energy of the MAPbI3/graphene is in good agreement with previous studies.55,91 The average interlayer distances at equilibrium between GO models and MAPbI3 slab are calculated as dC−Pb between the outermost C atoms of the rGO slab and the outermost Pb atoms of the MAPbI3 slab. The values of dC−Pb are 3.54, 3.95, 4.16, and 3.97 Å for graphene, rGO-33%O, rGO-66%O, and GO-100%O, respectively. For the case of rGO, the distances are larger than that for pristine graphene and GO. This could be explained by the fact that for the latter cases, the buckling of the graphene sheet is less pronounced than that in the rGO models. For the heterostructure with pristine graphene, the interlayer distance is in a good agreement with the previously reported ones.55,91,92 To qualitatively examine the structural changes in MAPbI3 when interfaced with the GO models, we look at the changes in the bond angles of the PbI2 sublattice closest to the interface, shown by the red rhombus in Figure 1b. These bond angles have I atoms as vertices and indicated by A, A′, B, and B′ viewed along the x-direction and C, C′, D, and D′ along the y-direction. Figure 2 shows the changes in the structure of MAPbI3 for each 16718


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Figure 3. Charge density differences along the interface of MAPbI3 and GO heterostructures. (a) MAPbI3/graphene and (b) MAPbI3/rGO-33%O. (c) MAPbI3/rGO-66%O and (d) MAPbI3/GO-100%O heterostructures. Red and blue refer to electron accumulation and depletion, respectively, for an isosurface value of 0.003 Å−3.

Figure 4. Charge density redistribution at the interface of the MAPbI3/rGO-33%O heterostructure. (a) A 3D view of the localized charge density in the vicinity of Pb and O atoms closest to each other. (b) Charge density difference with a two-dimensional (2D) cut along the plane defined by the dashed triangle in (a). (c) Two-dimensional cut highlighting the charge density redistribution along the line that connects Pb and O atoms in (b). Red and blue refer to the electron accumulation and depletion, respectively, with isosurface value of 0.003 Å−3.

D′ undergo only a slight decrease. This means that the graphene layer induces the flattening and suppression of the octahedral tilting of the MAPbI3 at the interface. In the case of interfaces with oxidized models, the variations in the bond angles of the PbI2 sublattice essentially dependent on the rearrangement of the O atoms on the graphene sheet, leading to the distortion of the MAPbI3 structure at the interface. In particular, the O atoms tend to repel the I atoms and attract the Pb atoms as the distance between them becomes smaller. This causes a displacement of the I atoms and hence the changes in the bond angles. For example, the I atom forming the vertex of the angle B is pushed

interface model. The superimposed blue and red unit cells of MAPbI3 correspond, respectively, to the reference unit cell before interfacing with the GO model and the one after the combination with the GO model. The columns a, b, and c represent the MAPbI3 unit cell, the PbI2 sublattice, and the above-mentioned angles in the PbI2 sublattice, respectively. The rows from top to bottom represent the interfaces with pristine graphene, rGO-33%O, rGO-66%O, and GO-100%O, in that order. In the interface with graphene, the angles A and B are simultaneously enlarged by 7%, whereas A′ and B′ are decreased by 2% compared to the reference ones. The angles C, C′, D, and 16719


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Figure 5. Energy-level alignment within the MAPbI3/GO heterojunctions. Purple represents the valence and conduction bands of MAPbI3, dark gray represents the work-function of pristine graphene, and green represents the valence and conduction bands of the graphene-oxide models within the interfaces. The electrons and holes are represented by circled e− and h+, respectively. The red cross-lines in rGO-66%O and GO-100%O indicate a forbidden charge transfer. The inset highlights the interpolated band alignment between rGO-33%O and rGO-66%O, where the blue-shaded area corresponds to a type II heterojunction. The blue-squared dots represent the band edges of rGO with 53% O with respect to the band edges of MAPbI3.

Figure 6. Orbital characters of the band edges in our models: MAPbI3/graphene (left) and MAPbI3/rGO-33%O (right) interfaces. In both interfaces, the VBM and CBM of MAPbI3 are predominantly of 5p orbitals character of I atoms and 6p orbitals character of Pb atoms, respectively. The CBM and VBM of graphene are of p-type orbitals C atoms, whereas that of rGO-33%O are of hybridized p-type orbitals of C and O atoms. Red and blue refer to the electrons and holes waves-functions, respectively. (a) CBM and (b) VBM of MAPbI3 in MAPbI3/graphene. (c) CBM and (d) VBM of graphene in MAPbI3/graphene. (e) CBM and (f) VBM of MAPbI3 in MAPbI3/rGO-33%O. (g) CBM and (h) VBM of rGO-33%O in MAPbI3/rGO-33%O.

away from the original plane formed by the angle in the xdirection for all oxidized models. It can also be seen that as the O

concentration increases, the more significant are the deviations of the angles in the PbI2 sublattice. 16720


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agreement with the experiments.83,94 In the case of the MAPbI3/ graphene heterojunction, the energy differences between the work-function of graphene and the band edges of MAPbI3 are found to be 0.4 and 1.22 eV for the conduction band minimum (CBM) and the valence band maximum (VBM), respectively. The VBM is mainly dominated by the 5p orbitals of the I atoms, whereas the CBM is of the 6p orbitals of Pb atoms, as shown in Figure 6a,c. This is in accord with the previous studies in which graphene favors the formation of a n-type Schottky junction with MAPbI3.55 In the present work, the n-type Schottky barrier is found to be smaller than the one in ref 55. This could be explained by the different methods used in each study. In ref 55, scissor-shifted GW was used to correct the band-level profile, whereas in the present study, the PBE0 functional is adopted. In fact, it has been demonstrated that the two methods can provide different band offsets.95 In our case, PBE0 induces large VBM offsets and small CBM offsets, whereas GW yields the opposite trend.55 In ref 92 the VBM and CBM offsets between graphene and MAPbI3 are 0.61 and 0.89 eV, which are, respectively, smaller and larger than our values.92 The slight differences in these values could be ascribed to the fact that in ref 92 they considered MAPbI3 slab along the (100) and also to the absence of spin−orbit interactions and hybrid method corrections in their study. Despite these variations in the n/p Schottky barriers, graphene could indeed be used as a selective extraction material of the photogenerated carriers. As shown by Di Carlo and coworkers, the combination of graphene with TiO2 leads to an efficient collection of electrons from the perovskite.52 The interface model with 33% O exhibits a type I semiconducting heterojunction, also known as straddling junction, because the band edges of the rGO model lie between those of MAPbI3. The VBM and CBM offsets are 0.38 and 0.98 eV, respectively. The orbital character of these band edges consists of hybridized p-type orbitals of C and O atoms for the GO model (Figure 6g,h) and p-type orbitals of I and Pb atoms for MAPbI3, as shown in Figure 6e,f. These energy barrier heights indicate that rGO-33%O is not expected to act as a selective contact because it can extract both electrons and holes from MAPbI3. Therefore, to prevent their recombination, an additional component in the heterojunction that would operate as a blocking layer is needed. The corresponding work-function for this model is found to be 5.28 eV, which is consistent with the recently reported experimental data yielding ∼5.30 eV for 33% O.96 It has been shown by Yan and co-workers that solutionprocessed multilayer rGO in MAPbI3 solar cell exhibited a more efficient hole extraction than single-layer rGO due the possible recombination of the charge carriers.97 Although it is difficult to estimate the oxidation level in rGO/GO from the experiments for comparison, our results for O concentrations between 0 and 33% predict that rGO is expected to operate as a recombination layer and hence could explain the low performance of the singlelayer rGO as observed by Yan.97 For the oxygen content above 33% and below 66%, a linear interpolation of the band edges versus oxygen concentration shows that the CBM of rGO mainly ranges between that of MAPbI3 and rGO-33%O, as indicated by the blue-shaded area in the inset of Figure 5. On the other hand, the VBM is, for the most part, situated below that of MAPbI3. In this intermediate concentration, MAPbI3/rGO is expected to form a type II staggered heterojunction, and, therefore, to act as a selective ntype contact, which extracts electrons while blocking holes. To examine the validity of our findings for this range of concentrations, i.e., between 33% O and 66% O, we performed

As reported in ref 55, the combination of MAPbI3 and graphene almost suppresses the tilting of the PbI6 octahedra in the MAPbI3 structure, which yields an interfacial ferroelectric distortion. The charge redistribution creates an interfacial dipole that could facilitate the extraction of the electrons from the perovskite. The present results also corroborate these findings on the MAPbI3/graphene heterostructures.55,91,92 Figure 3a shows the charge density difference at the interface between graphene and MAPbI3. We see depletion of electron charge near the graphene sheet and an electron accumulation near the innermost Pb layer of the MAPbI3 structure. This charge density rearrangement creates an interfacial dipole moment of 1.4 D, which corresponds to a potential drop of 0.54 eV. This dipole should exert a driving force to push the photogenerated electrons from the perovskite toward graphene. In the case of the heterojunctions with the oxidized models, specific patterns of charge rearrangements within the interfacial regions are also noticeable. These charge redistributions evolve to become more localized as the concentration of the oxygen atoms increases, particularly between Pb and O atoms at the interface, as shown in Figure 3b−d for different O concentrations. Figure 4a depicts, as an example, a 3D view of the localized charge density redistribution between the Pb and O atoms closest to each other along the interface with the rGO33%O model. A cut of this charge density redistribution along the plane defined by the dashed black triangle in Figure 4a and containing the closest Pb−O line is shown in Figure 4b,c. It indicates that the bonds between the Pb and O atoms closest to each other are expected to form. To understand the nature of bonding between the Pb and O atoms, we have calculated the electron localization function (ELF) as shown in Figure S3. We observe very high ELF values in the region around the Pb and O atoms. It is clear that the topology of the ELF gradient between Pb and O direction is not spherically symmetric, suggesting the formation of a bond between the Pb and the O atoms. Moreover, the blue area indicates a significant charge transfer between the Pb and O atoms, reminiscent of ionic bonding.93 In contrast to the heterojunction with graphene, the MAPbI3 layer does not display a suppression of the octahedral tilting, as can be seen in the different angles of the PbI2 sublattice of each model in Figure S2. Furthermore, it is found that due to the charge reorganization combined with the formation of the Pb−O bonds, the magnitude of the interfacial dipole moment decreases with the O content from 1.4 D in the case of graphene to 0.23 D in the fully oxidized graphene, as reported in Table S1. The structural changes caused in MAPbI3 by the increase in the concentration and the arrangement of the O atoms on the graphene sheet cause the suppression of the ferroelectric distortion observed in the case of pristine graphene. One exception is the case of the GO-100%O model, for which a dipole moment of 0.67 D is observed. This could be explained by the fact the O atoms in the interface are equidistant and homogeneously distributed between the graphene sheet and the perovskite, and consequently form a relatively uniform flat layer, which is expected to behave in a similar way as in the case of graphene. In fact, we can see in Figure S2 that the angles A, A′, B, C, C′, and D′ become larger than the reference ones. This means that the tilting of the octahedra is also suppressed, hence the interfacial ferroelectricity vanishes. The energy band lineup for all the studied interfaces, constructed relative to the vacuum level and including the PBE0 corrections as described in the Methods section, is shown in Figure 5. The PBE0 band gap of MAPbI3 is 1.62 eV, in close 16721


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Figure 7. Variation in the band gap and the work-function for different configurations of the O atoms on the graphene sheet in rGO-33%O and rGO66%O models. (a) Band gap differences between the initial models and the other configurations for both rGO-33%O and rGO-66%O. (b) Workfunction differences between the initial models and the other configurations for both rGO-33%O and rGO-66%O. The values of the gaps and the workfunctions of the reference configurations are set to zero. The blue and the orange histograms refer to the models with concentrations of 33% O and 66% O, respectively. The configurations 1−11 are discussed in the Supporting Information and shown in Figures S4 and S5.

rGO-33%O model, the gap varies in the range of 0−0.46 eV, whereas the work-function increases by up to 0.15 eV as compared to the reference configuration. For the rGO-66%O case, the changes in the band gap and the work-function with respect to the initial configuration range between −0.3−0.2 and −0.3−0.4 eV, respectively. As it can be seen in Figure 7a,b, the largest changes in the band gap and work-function are found for configuration 11, which corresponds to having all the O atoms clustering together in the graphene sheet (see Figures S4-l and S5-l). Nevertheless, by including the largest values of these changes in the band gap and the work-function for the corresponding GO models would preserve the heterojunction types in the band alignment shown in Figure 5. This means that replacing the values of the initial models by the values of the clustered models for rGO (33 and 66%) to construct the bandlevel alignment as shown in Figure 5 will also yield to type I and type II heterojunctions between rGO and MAPbI3 for rGO-33% O and rGO-66%O, respectively. We mention that the variation in the total energies across the configurations is negligible, the largest difference being 5 meV/atom.

complementary calculations for the concentration 53.33%, hereafter rGO-53%O. The model is shown in Figure S6. The CBM and VBM levels of the rGO-53%O with respect to those of MAPbI3 are shown by blue-dashed lines in the inset of Figure 5. The CBM of rGO-53%O is located between the band edges of MAPbI3 and the VBM of rGO-53%O is below the VBM of MAPbI3. Consequently, rGO/MAPbI3 forms a type II staggered heterostructure at 53.33% O. This result clearly validates our prediction that rGO would operate as an electron-extraction material in this range of concentrations between 33 and 66% of oxygen. For O concentrations higher than 66%, we find again straddling heterojunctions. However, in contrast to the heterojunction with the rGO-33%O model, the situation is reversed as the band edges of MAPbI3 are now located between those of the GO model. The VBM/CBM offsets are estimated to be 1.1/0.18 and 1.83/2.26 eV for heterojunctions with the rGO66%O and GO-100%O models, respectively. These large energy barriers would prevent the photogenerated charges to flow from MAPbI3 toward GO. These findings suggest that rGO, with specific O concentrations, would be beneficial for the extraction of electrons. This is consistent with the recently reported experiments showing that when rGO was incorporated as an EEM, the PSC exhibited an improvement in its efficiency.51−53 Several experimental and theoretical studies have reported that the work-function of rGO/GO depends on the nature and arrangement of the functional groups and other parameters that could yield a variation of up to 2.5 eV.96,98,99 To take into account these effects in the calculated band alignment in the MAPbI3/rGO heterostructures, we further examine the change in the band gap and the work-function of rGO with respect to different arrangements of the O atoms on the graphene sheet. Because rGO is a highly disordered material, we have selected 11 different configurations for each concentration, i.e., for 33% O and for 66% O, as described in the Supporting Information (SI.2). The selected configurations are shown in the Supporting Information Figures S4 and S5. The variation in the band gap and the work-function in the models rGO-33%O and rGO-66%O with the rearrangement of the O atoms on the graphene sheet is shown in Figure 7. For the

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CONCLUSIONS In summary, we investigated the interfaces between the perovskite MAPbI3 and graphene oxide. We performed density functional theory calculations to examine the structural and electronic properties of the heterostructure with the variation in the oxygen content in oxidized graphene. We showed that the inclusion of oxygen highly affects the charge density distribution at the interface and becomes more localized in the vicinity of the Pb and O atoms, which could be interpreted as a bond formation between the latter atoms. The noticeable interfacial dipole moment in the MAPbI3/graphene heterostructure is found to decrease with the increase in the oxygen concentration. The interfacial ferroelectric distortion observed in the MAPbI3/ graphene and MAPbI3/GO-100%O models can mainly be attributed to the flattening of PbI2 sublattice and the suppression of the octahedra tilting at the interface. In the case of heterostructures with MAPbI3/rGO-33%O and MAPbI3/ rGO-66%O, this effect is suppressed due the negligible changes in the MAPbI3 structure. 16722


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Computing (ARC) facility (http://dx.doi.org/10.5281/zenodo. 22558) and the ARCHER U.K. National Supercomputing Service under the “T-Dops” project and the DECI resource “Cartesius” based in The Netherlands at SURFsara and “Abel” based in Oslo with support from the PRACE AISBL and MareNostrum at BSC-CNS, Spain (PRACE-15).

The analysis of the energy band alignment shows that the reduced graphene oxide would be more relevant for the extraction of charge carriers than the highly oxidized and fully oxidized graphenes. We expect that, for oxygen concentrations of up to 33%, the combination of MAPbI3 and rGO would form a type I straddling heterojunctions with smaller valence band offsets than the conduction ones; therefore, a blocking layer is required to selectively extract the desired charge carriers. For concentrations between 33 and 66%, a type II staggered heterojunction can form between MAPbI3 and rGO, with suitable conduction band offsets for the extraction of electrons. Higher oxygen concentrations would hinder any charge-carrier extraction. In addition, we showed that different rearrangements of the oxygen atoms in oxidized graphene lead to variations in the work-function and the band offsets. Yet, the type of alignment found for MAPbI3/rGO remains largely unaffected. Overall, our work supports the potential use of rGO with suitable oxidation levels as a material for the charge-carrier extraction and transport in perovskite solar cells, and as a potential complement to the TiO2 layer used for electron extraction in PSCs. Yet, because of the heterogeneous nature of GO and rGO structures that depend on the preparation conditions and other factors, including thickness/size of the flakes, temperature, and presence of defects, a clear understanding of their chemical and physical properties is still a challenge to be addressed. This is especially true when we consider the presence of different functional groups such as hydroxyls and carbonyls. Further studies are also needed to investigate the combination of rGO/GO and other layered materials as EEMs or HTMs, which could also lead to an efficient charge-carrier extraction, and hence an improvement in the performance of the perovskite solar cell devices.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b03230. Structural parameters and band gap of MAPbI3 in the heterostructure with the considered GO models (Figure S1); band structures of MAPbI3/GO interfaces (Figure S2); electron localization function (ELF) at MAPbI3/ rGO-33% O interface (Figure S3) (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +44 (0) 1865 612792. ORCID

Nourdine Zibouche: 0000-0001-8768-8271 George Volonakis: 0000-0003-3047-2298 Feliciano Giustino: 0000-0001-9293-1176 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research leading to these results has received funding from the Graphene Flagship (Horizon 2020 Grant No. 785219 GrapheneCore2), the Leverhulme Trust (Grant No. RL-2012001), and the U.K. Engineering and Physical Sciences Research Council (Grant No. EP/M020517/1). The authors acknowledge the use of the University of Oxford Advanced Research 16723


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