Perovskite Interfaces For Photovoltaics

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Graphene-Oxide/Perovskite Interfaces For Photovoltaics Zibouche Nourdine, George Volonakis, and Feliciano Giustino J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03230 • Publication Date (Web): 01 Jul 2018 Downloaded from http://pubs.acs.org on July 1, 2018

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The Journal of Physical Chemistry

Graphene-Oxide/Perovskite Interfaces For Photovoltaics Nourdine Zibouche,

†

†

George Volonakis,

and Feliciano Giustino

∗,†,‡

†Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK ‡Cornell University, Ithaca, New York, 14853, USA E-mail: [email protected] Phone: +44 (0)1865 612792

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract Graphene-based materials hold a promising prospect for their utilization in perovskite solar cell devices as electron extraction or hole transport layers. Here we investigate the role of oxidized graphene when interfaced with the perovskite MAPbI3 . Using rst-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 of the oxygen content. Finally, we report the modication of the band-gap and the workfunction in the oxidized graphene for dierent rearrangements of the epoxy groups on the graphene sheet. This study shows that reduced graphene-oxide with specic oxidation levels could eectively be incorporated as a selective contact in heterojunction devices for applications in perovskite solar cells.

Introduction The eld of materials for photovoltaics (PVs) has recently been enriched by the discovery of organic-inorganic halide perovskites as light absorbers and electron/hole transporters.

14

The superior properties of these PV materials include long diusion lengths of the charge carriers,

5,6

high absorption coecients,

carrier mobilities,

10,11

7,8

direct and tunable band gaps,

9

relatively high

and low-cost fabrication techniques based on solution processing.

12

The current perovskite solar cells (PSCs) have reached an unprecedented power conversion eciency (PCE) above 22%,

13

thus becoming potential alternatives to silicon

2


14

and other

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thin-lms

15,16

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 dierent layers that compose the PSCs.

17,18

To

overcome the stability issue, several approaches have been investigated, including chemical modications in the bulk or at the surface of the perovskite layer by substitutions crosslinking additives,

21,22

and transporting layers,

encapsulation,

2426

17,23

19,20

or

substitution or doping of the charge collecting

or by incorporation of a buer layer between the perovskite

and the charge transport interfaces.

27,28

The interfacial interactions between dierent layers

of the PSC are also of paramount importance for the device operation, since 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 whole. In this regard, several reports have explored dierent materials alongside the perovskite layer as charge collection or transport layers.

2931

One promising route toward applications is the incorporation of graphene and graphenerelated materials in PSC devices.

3234

Several reports have demonstrated the multifunction-

alities 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.

33,3540

In PSCs, graphene-based materials are mainly explored

as potential electron extraction (EEM) and hole transport (HTM) materials.

4145

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.

40,4648

Wang and coworkers combined

graphene nanoakes along with TiO2 as an EEM in a perovskite solar cell. The inclusion of graphene led to an increase of PCE from 10% to 15.6% compared to the device without graphene.

49

Mirfasih and coworkers have shown that using graphene scaolds as an inter-

face layer between the electron transporting and absorbing materials in a PSC improves

3



Page 4 of 33

the device performance by 27% as well as the stability compared to the conventional one.

50

Di Carlo and coworkers showed that reduced graphene-oxide (rGO), when used as a 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 dierent degradation environments. The devices with both graphene and GO exhibited better charge extraction and 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 a 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 eciency.

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 mate-

rials, 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 CH3 NH3 cation, methylammonium. We investigate, by means of rst-principles calculations based on density functional theory, the inuence of the oxygen concentration on the electronic properties of the heterostructure.

We show that the band alignment prole 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 of the oxygen content in oxidized graphene leads to charge density redistribution at the interface, which causes the decrease of the interfacial dipole. Moreover, the interfacial ferroelectric distortion observed in the heterojunction between MAPbI3 and pristine graphene

55

is not present in the case of partially oxidized graphene.

4


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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.

5658

It has been

shown that (110) and (001) surfaces are the most favorable non-polar surface of MAPbI3 . In addition, in Ref.

55

59

it was shown that the electronic properties and level alignment be-

tween pristine graphene and MAPbI3 are qualitatively the same. Therefore, the perovskite layer considered in this study is constructed by cutting the 3D crystal along the crystalline plane (110), resulting in the PbI2 termination shown in Figure 1-a,b. This termination is the most stable non-defective (110) surface termination, mental observations.

61

60

which is consistent with experi-

The lattice parameters of the slab are

a

= 12.52 Å and

The thickness of the slab is the same with the one used in Ref. properties of the graphene/MAPbI3 interface are converged.

55

b

= 12.64 Å.

, for which the electronic

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. In order to minimize the mismatch between the GO and MAPbI3 structures, the proposed GO models in Figure 1-c,d,e,f are constructed starting from a

5×3

supercell of a

rectangular unit cell of pristine graphene (cyan color in Figure 1-c) as follows; rst, by fully functionalizing the graphene sheet with oxygen atoms (100% O), which corresponds to a O:C ratio of 2:1, since 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 1-d 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 and hence avoid the buckling of

5



Page 6 of 33

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 2-e,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 dierent graphene sides that lead to aggregation.

6264

This inhomogeneous distribution of

the oxygen atoms can, thus, aect 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 calculations are carried out using density functional theory (DFT) the Quantum Espresso simulation package.

66,67

69

as implemented in

The Kohn-Sham wave-functions and ener-

gies are calculated using the local density approximation (LDA) parametrization,

65

68

in the Perdew-Zunger

using a plane-wave basis, with energy and charge density cutos of 40

Ry and 320 Ry, respectively. Ultra-soft pseudopotentials (USPPs)

70,71

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 (BZ) 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 articial electrostatic eects. It is well known that DFT underestimates band gaps.

73,74

However, in the case of hybrid

perovskites, DFT yields gaps close to experiments in the case of non-relativistic calculations. This fortuitous result is due to the neglect of spin-orbit coupling (SOC).

7577

The inclusion of

SOC in the case of MAPbI3 , underestimates the band gap by as much as 1 eV.

7577

To obtain

more accurate band gaps and hence a better estimate of the energy level alignment, the PBE0 hybrid functional

78,79

can be employed. However, using PBE0 for such large interface systems

6


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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 the methylammonium (CH3 NH3 ) 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).

is computationally prohibitive. performed using VASP code

To overcome this limitation, PBE0+SOC calculations are

8082

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 (VBMs) and the conduction band minima (CBMs) of the interfaces. The induced strain eects in 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 .

7


83

We have examined


Page 8 of 33

the eect of van der Waals (vdW) corrections for the interface with fully oxidized graphene. The details of the calculation are given in the Supporting information (SI.1).

We found

that the electronic structure remains unaected as in the case of the interface with pristine graphene.

55

Therefore, in the following we will not include vdW corrections.

Discussion Graphene and its derivatives, including graphene-oxides and nanotubes, have exceptional mechanical properties.

32,8487

As reported in the literature, the Young's moduli of pristine

graphene, rGO and GO are in the order of 1.0 TPa,

84

0.25 TPa

88

and 0.21 TPa,

tively. In contrast, the Young's modulus of MAPbI3 is of 0.0142 TPa,

90

89

respec-

that 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, in order to exclude any spurious strain eects in the study of these heterojunctions, the geometries of GO models are fully optimized. First, these calculations show an increase of the lattice parameters with the oxidation level, reaching maximum values of 3% and 5% for

a and b of the fully oxidized model as com-

pared to pristine graphene. Second, the atomic coordinates of the MAPbI3 slab are relaxed using the lattice parameters of the GO models. Figure S1-a shows the mismatch between the lattice parameters of pristine MAPbI3 and the GO structures. The mismatch increases with the oxygen concentration in the GO models, ranging 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 S1-b. It can be seen that the band gap also increases as the lattice parameters of the corresponding GO models increase with the oxygen content. However, the direct band gap character of the MAPbI3 structure is preserved in all cases, as shown if Figure S2. The binding energies of the MAPbI3 /GO heterojunctions are calculated as the dierence

8


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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 dierent hetero-

2 2 junctions are of 8 meV/Å (0.30 eV per surface Pb atom), 9 meV/Å (0.36 eV per surface Pb atom), 8 eV/Å

2

(0.32 eV per surface Pb atom) and 6 meV/Å

2

(0.25 eV per surface Pb

atom) for MAPbI3 /graphene, MAPbI3 /rGO-33%O, MAPbI3 /rGO-66%O and MAPbI3 /GO100%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 a good agreement with

previous studies.

55,91

The average interlayer distances at equilibrium between GO models

and MAPbI3 slab are calculated as

dC−P b

between the outermost C atoms of the rGO slab

and the outermost Pb atoms of the MAPbI3 slab. The values of

dC−P b

are 3.54 Å, 3.95 Å,

4.16 Å, 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 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 bond angles of the PbI2 sublattice closest to the interface shown by the red rhombus in Figure 1-b. These bond angles have I atoms as vertices and indicated by A, A', B, and B' viewed along the the

y

x

direction and C, C', D, and D' along

direction. Figure 2 shows the changes in the structure of MAPbI3 for each 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 this order.

In the interface with graphene, the angles A and B are

9



Page 10 of 33

simultaneously enlarged by 7%, whereas A' and B' are decreased by 2% compared to the reference ones.

The angles C, C', D, and D' undergo only a slight decrease.

This means

that the graphene layer induces a attening and the 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 away from the original plane formed by the angle in the

x

direction

for all oxidized models. It can also be seen that as the O concentration increases, the more signicant are the deviations of the angles in the PbI2 sublattice. 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 ndings on the MAPbI3 /graphene heterostructures.

55,91,92

Figure 3-a shows the charge

density dierence at the interface between graphene and MAPbI3 . We see depletion of electron charge near the graphene sheet, and 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, specic 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 3-b,c,d for dierent O concentrations. Figure 4-a depicts, as an example, a 3D view of the localized charge

10


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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 Fig. 1(b) and in the main

text. 11



Figure 3: Charge density dierences along the interface of MAPbI3 and GO heterostructures. a) MAPbI3 /graphene, b) MAPbI3 /rGO33%O. c) MAPbI3 /rGO-66%O. d) MAPbI3 /GO100%O heterostructures. Red and blue colors refer to electron accumulation and depletion, −3 respectively, for an isosurface value of 0.003 Å .

density redistribution between the Pb and O atoms closest to each other along the interface with the rGO-33%O model. A cut of this charge density redistribution along the plane dened by the dashed black triangle in Figure 4-a and containing the closest Pb-O line is shown in Figure 4-b,c. It indicates that 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 bluecolored area indicates a signicant 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 dierent angles of

12


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Figure 4:

Charge density redistribution at the interface of the MAPbI3 /rGO33%O het-

erostructure. a) A 3D view of the localized charge density in the vicinity of Pb and O atoms closest to each other. b) Charge density dierence with a 2D cut along the plane dened by the dashed triangle in a). c) 2D cut highlighting the charge density redistribution along the line that connect Pb and O atoms in b).

Red and blue colors refer to the electron −3 accumulation and depletion, respectively, with isosurface value of 0.003 Å .

the PbI2 sublattice of each model in Figure S2. Furthermore, it is found that, due to the charge reorganization combined with the formation of 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 the Table S1. The structural changes caused in MAPbI3 by the increase of the concentration and the arrangement of the O atoms on the graphene sheet causes 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 at 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 agreement with experiments.

83,94

In the case of the MAPbI3 /graphene heterojunction, the energy dierences between the work-

13



Page 14 of 33

function of graphene and the band edges of MAPbI3 are found to be 0.4 eV and 1.22 eV for conduction band minimum (CBM) and 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 6-a,c. This is in accord with the previous studies in which graphene favours a formation of a In the present work, the Ref.

55

n-type

n-type

Schottky junction with the MAPbI3 .

55

Schottky barrier is found to be smaller than the one in

This could be explained by the dierent methods used in each study.

In Ref.

55

,

scissor-shifted GW was used to correct the band level prole, whereas in the present one, the PBE0 functional is adopted. In fact, it has been demonstrated that the two methods can provide dierent band osets.

95

In our case, PBE0 induces large VBM osets and small

CBM osets, while GW yields the opposite trend.

55

In Ref.

92

, the VBM and CBM osets

between graphene and MAPbI3 are 0.61 eV and 0.89 eV, which are, respectively, smaller and larger than our values. that in Ref.

92

92

The slight dierences in these values could be ascribed to the fact

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 ecient collection of electrons from the perovskite.

52

The interface model with 33%O exhibits a type-I semiconducting heterojunction, also know as straddling junction, since the band edges of the rGO model lie between that of MAPbI3 .

The VBM and CBM osets are of 0.38 and 0.98 eV, respectively.

character of these band edges consist of hybridized GO model (Figure 6-g,h), and

p-type

p-type

The orbital

orbitals of C and O atoms for the

orbitals of I and Pb atoms for MAPbI3 , as shown in

Figure 6-e,f. These energy barrier heights indicate that the rGO-33%O is not expected to act as a selective contact, since it can extract both electrons and holes from MAPbI3 . Therefore, in order to prevent their recombination, an additional component in the heterojunction that would operate as blocking layer is needed. The corresponding work-function for this model is

14


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Figure 5:

Energy level alignment within the MAPbI3 -GO heterojunctions.

Purple color

represents the valence and conduction bands of MAPbI3 , the dark gray represents the workfunction of pristine graphene, and the 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 .

found to be of 5.28 eV, which is consistent with recently reported experimental data yielding

∼5.30 eV for 33%O. 96 It has been shown by Yan and coworkers that solution-processed multilayer rGO in MAPbI3 solar cell exhibited more ecient hole extraction than single-layer rGO due the possible recombination of the charge carriers.

97

Although it is dicult to estimate the

oxidation level in rGO/GO from experiments for comparison, our results for O concentrations between 0% and 33% predict that rGO is expected to operate as recombination layer and hence could explain the low performance of rGO single-layer observed by Yan.

97

For 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 most part of it, situated below that of MAPbI3 . In this

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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 of rGO33%O are of hybridized

p-type

p-type

orbitals C atoms, whereas that

orbitals of C and O atoms. Red and blue colors 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 /rGO33%O. g) CBM and h) VBM of rGO33%O in MAPbI3 /rGO33%O.

intermediate concentration, MAPbI3 /rGO is expected to form a type-II staggered heterojunction, and therefore to act as a selective

n-type

contact, which extracts electrons while

blocking holes. To examine the validity of our ndings for this range of concentrations, i.e. between 33%O and 66%O, we performed complementary calculations for the concentration 53.33%, hereafter rGO-53%O. The model is shown in Figure S6. The CBM and VBM levels

16


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of the rGO-53%O with respect to that of MAPbI3 are shown by the 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 nd 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 osets are estimated to be 1.1/0.18 eV 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 ow from MAPbI3 towards the GO. These ndings suggest that rGO, with specic O concentrations, would be benecial 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 eciency.

5153

Several experimental and theoretical studies have reported that the work-function of rGO/GO depends on nature and arrangement of the functional groups and other parameters that could yield a variation of up to 2.5 eV.

96,98,99

In order to take into account these eects 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 dierent arrangements of the O atoms on the graphene sheet. Since rGO is a highly disordered material, we have selected 11 dierent congurations for each concentration, i.e. for 33%O and for 66%O, as described in the Supporting information (SI.2). The selected congurations are shown in the supplemental Figures S4 and S5. The variation of the band gap and the work-function in the models rGO-33%O and rGO-66% with the rearrangement of the O atoms on the graphene sheet is shown in Figure 7.

For rGO-33%O model, the gap varies in the range of 00.46 eV, whereas the work-

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Page 18 of 33

Figure 7: Variation of the band gap and the work-function for dierent congurations of the O atoms on the graphene sheet in rGO-33%O and rGO-66%O models.

a) Band gap

dierences between the initial models and the other congurations for both rGO-33%O and rGO-66%O. b) Work-function dierences between the initial models and the other congurations for both rGO-33%O and rGO-66%O. The values of the gaps and the work-functions of the reference congurations are set to zero. The blue and the orange histograms refer to the models with concentrations of 33%O and 66%O, respectively. The congurations 111 are discussed in the Supporting information and shown in Supplemental Figures S4 and S5.

function increases by up to 0.15 eV as compared to the reference conguration.

For the

rGO-66%O case, the changes in the band gap and the work-function with respect to the initial conguration range between -0.30.2 eV and -0.30.4 eV, respectively. As it can be seen in Figure 7-a,b, the largest changes of the band gap and work-function are found for conguration 11, which corresponds to having all the O atoms clustering together in the graphene sheet (see Figure S4-l 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 band level alignment as shown in Figure 5 will also yield to a type-I and type-II heterojunctions between rGO and MAPbI3 for rGO-33%O rGO-66%O, respectively.

We mention that the variation in the total energies across congurations is

negligible, the largest dierence being of 5 meV/atom.

18


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Conclusions In summary, we investigated the interfaces between the perovskite MAPbI3 and grapheneoxide. We performed density functional theory calculations to examine the structural and electronic properties of the heterostructure with the variation of the oxygen content in oxidized graphene. We showed that the inclusion of oxygen highly aects 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 of the oxygen concentration.

The interfacial ferroelectric distortion ob-

served in the MAPbI3 /graphene and MAPbI3 /GO-100%O models can mainly be attributed to the attening 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 eect is suppressed due the negligible changes in the MAPbI3 structure. The analysis of the energy band alignment shows that reduced graphene-oxide would be more relevant for the extraction of charge carriers than highly oxidized and fully oxidized graphene.

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 osets than the conduction ones, therefore, a blocking layer is required to selectively extract the desired charge carriers. For concentrations between to 33% and 66%, a type-II staggered heterojunction can form between MAPbI3 and rGO, with suitable conduction band osets for the extraction of electrons. Higher oxygen concentrations would hinder any charge carrier extraction.

In addition, we showed that dierent rearrangements of the oxygen atoms in

oxidized graphene lead to variations of the work-function and the band osets.

Yet, the

type of the alignment found for MAPbI3 /rGO remains largely unaected. Overall, our work supports the potential use of rGO with suitable oxidation levels as a material for the charge carriers 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

19



Page 20 of 33

nature of GO and rGO structures that depend on the preparation conditions and other factors, including thickness/size of the akes, 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 dierent 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 ecient charge carriers extraction, and hence an improvement in the performance of the perovskite solar cell devices.

Acknowledgement The research leading to these results has received funding from the Graphene Flagship (Horizon 2020 Grant No.

785219 - GrapheneCore2), the Leverhulme Trust (Grant RL-

2012-001), and the UK Engineering and Physical Sciences Research Council (Grant No. EP/M020517/1). The authors acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility (http://dx.doi.org/10.5281/zenodo.22558) and the ARCHER UK 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.

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Figure 8: TOC graphic

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Perovskite Interfaces For Photovoltaics

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