Energy-Level Alignment at the Interface of Graphene Fluoride and

Article pubs.acs.org/JPCC

Energy-Level Alignment at the Interface of Graphene Fluoride and Boron Nitride Monolayers: An Investigation by Many-Body Perturbation Theory Qiang Fu,* Dmitrii Nabok,* and Claudia Draxl* Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin, Germany S Supporting Information *

ABSTRACT: Energy-level alignment at interfaces is important for understanding and optimizing optoelectronic and photocatalytic properties. In this work, we study the level alignment at the interface between graphene fluoride and boron nitride monolayers. These twodimensional (2D) semiconductors are representative wide-bandgap components for van der Waals (vdW) heterostructures. We perform a systematic study on the structural and electronic properties of their interface, by using density functional theory and the G0W0 method of many-body perturbation theory. We adopt this interface as a prototypical system to investigate the impact of polarization effects on band gap and level alignment. We find a small but still notable polarization-induced reduction of the materials’ band gap by 250 meV that we interpret and analyze in terms of an image-potential model. Such effects stem from nonlocal correlations between electrons and cannot be captured by semilocal or standard hybrid density functionals. Our work provides a lower limit of band-gap renormalization in 2D systems caused by polarization effects, and demonstrates the importance of many-body perturbation theory for a reliable prediction of energy-level alignment in 2D vdW heterojunctions.

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INTRODUCTION Energy-level alignment at interfaces, which specifies the relative positions of valence band maximum (VBM) and conduction band minimum (CBm) of one side relative to those of the other side, is one of the most important characteristics that influence interfacial optoelectronic properties. Energies and character of optical excitations as well as charge-injection barriers are largely determined by this alignment, and these properties are, in turn, critical for light-emission efficiency,1 solar-cell performance,2 or photocatalytic activity.3 So far, much effort has been devoted to different types of interfaces, like boundaries between organic4−7 or inorganic8,9 semiconductors, organic−metal interfaces,10−12 and hybrid inorganic−organic materials.13−15 These studies are not only interesting in terms of fundamental research but also important in view of practical applications. At an interface, intrinsic dipoles of its components and charge transfer between them can influence the vacuum energy level and thus the relative positions of VB and CB energies.1,15,16 Moreover, new covalent bonds may form and potentially modify the energetic positions of orbitals.17,18 In contrast, if the two components are connected via vdW forces only, i.e., without any dipole moment, charge transfer, or orbital overlap, one would expect the energy levels of the interface to appear as a superposition of VBs and CBs from the respective constituents, that is known as the Schottky-Mott limit.19,20 However, contrary to this intuition, the pristine energy levels © XXXX American Chemical Society

can still undergo significant changes upon interface formation.21−27 For example, the highest occupied molecular orbital− lowest unoccupied molecular orbital (HOMO−LUMO) gap of a benzene molecule has been theoretically predicted to reduce by 3.3 eV, when it is physisorbed on a graphite surface.22 The mechanism behind the gap renormalization was explained in terms of polarization effects. When an electron or hole is added to the adsorbed material − as realized in photoemission experiments − electrostatic interaction of the added charge will polarize the underlying substrate, i.e., creating an image charge. Thereby the LUMO/HOMO of the adsorbate is getting stabilized/destabilized, and thus, its band gap is reduced.22−25 Information on energy-level alignment can be either obtained experimentally by a series of spectroscopy probes or, alternatively, by first-principles calculations. For the latter approach, the most common method, density functional theory (DFT), may not provide a reliable description of the interfacial electronic structure. One of the reasons is that (semi)local functionals suffer from the so-called band-gap problem, due to a lack of the derivative discontinuity of exchange-correlation (xc) potential and the spurious self-interaction.28,29 Another reason is that the aforementioned band-gap renormalization − a nonlocal correlation effect − is not captured by such xc Received: February 20, 2016 Revised: April 20, 2016

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DOI: 10.1021/acs.jpcc.6b01741 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C functionals.22,25 Applying standard hybrid functionals cannot improve the description,24,30 because the electron correlation is still treated on a semilocal level. The GW approach of manybody perturbation theory,31 in contrast, is a powerful tool in this context.22,25,26 Currently, 2D materials have aroused great interest owing to their exceptional electronic and optical properties. 32−36 Fabrication of 2D heterostructures provides a promising approach for property tuning, through stacking of different 2D monolayers on top of each other.37−40 For junctions of two monolayers, excellent electronic and photocatalytic properties have been revealed by first-principles calculations, like a gap opening of graphene41,42 or enhanced visible-light absorption.41,43−45 In these investigations, the band gaps of the 2D components range from 0 eV (graphene) to about 5 eV (ZnO monolayer46). DFT at a level of semilocal or hybrid functionals has been the main method of computational investigations.41−45 For adsorbates on graphene, as mentioned above, it has been clearly shown that the polarizable gapless substrate does create an image charge.25,26 The questions here are whether such phenomenon can also occur in wide-bandgap monolayers, and if so, how pronounced the effect is. To address these questions, we perform G0W0 calculations on an interface between single-layer graphene fluoride (CF) and hexagonal boron nitride (h-BN). The two monolayers have large band gaps of about 7 eV and are only weakly bound via vdW interactions. A rectangular unit cell, as shown in Figure 1, is used to model CF, h-BN, and the hybrid junction, where hBN is placed on top of CF.

For the CF and h-BN monolayers, the unit cell in z direction (perpendicular to the monolayers) contains enough vacuum to eliminate spurious interactions between periodic images (cell size c = 35 bohr). The PBE functional is applied in the DFT ground-state calculations.48 The atomic coordinates of each monolayer are relaxed until the maximum force is less than 2 × 10−4 hartree/bohr. To obtain the interface geometry, vdW interactions are accounted for by the vdW-DF functional,49 as implemented in the noloco code.50 This is used to determine the optimal distance between the two monolayers. We scan the potential energy surface (PES) by varying the distance between the h-BN monolayer and the nearest fluoride atoms in CF from 4.0 to 10.0 bohr, while keeping the geometry of each monolayer fixed. Accordingly, the unit-cell thickness c is increased to 40 bohr. The Brillouin zone is sampled by using a Γ-centered 5 × 9 × 1 grid. Convergence with the vacuum thickness, the basis sets, and the number of k-points is confirmed. One-shot G0W0 calculations are performed by using DFTPBE results as the starting point. The quasi-particle energies ϵqp nk are calculated in a perturbative way, according to KS KS KS KS xc KS ϵqp nk = ϵnk + Znk(ϵnk )⟨ψnk |Re{Σnk (ϵnk )} − Vnk |ψnk ⟩

(1)

KS KS Here, ϵnk and ψnk represent the DFT eigenvalues and eigenfunctions, Re{Σnk} is the real part of the self-energy and Vxc nk are the matrix elements of the xc potential in the underlying DFT calculation. Znk is the quasi-particle renormalization factor. The dielectric screening is calculated by using the randomphase approximation (RPA). For all frequency-dependent quantities, we employ a nonuniform grid of 16 points along the imaginary frequency axis. Convergence with the number of k-points as well as empty states is carefully checked, in order to ensure high quality of the calculations. For all systems, the Brillouin zone is sampled by using a Γ-centered 9 × 15 × 1 grid. An amount of 1000 empty states are considered in the respective summations for the calculations of the polarizability, the screened Coulomb potential, and the correlation selfenergy. In our systems, the quasi-particle energies turn out to be particularly sensitive to the number of empty states. More details are given in the Supporting Information. Attention must be also paid to the 2D nature of the systems under investigation when treated with three-dimensional periodic boundary conditions. Unlike DFT calculations with (semi)local density functionals, where overlap between charge densities of neighboring periodic images decay rapidly with the vacuum-layer thickness, in the G0W0 approach, artificial interactions between these periodic replica may show up in the nonlocal operators. As a result, G0W0 band gaps steadily increase with vacuum-layer thickness and hardly converge.51,52 Applying a truncation to the Coulomb potential is an effective approach for explicitly removing this type of artificial interactions, leading to well-converged G0W0 gaps with relatively small vacuum size.53,54 In this method, Coulomb interactions are cut off when the distance between two electrons, |r|, is larger than a threshold. In the 2D case, the truncated Coulomb potential, Vtrun c , is written as

Figure 1. Structures of the CF (left) and the h-BN (right) monolayers. The dotted rectangles represent the unit cells with lattice constant a. The gray, green, pink, and blue spheres represent carbon, fluorine, boron, and nitrogen atoms, respectively.

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COMPUTATIONAL DETAILS The calculations are performed using the full-potential allelectron code exciting.47 The wave functions are expanded in terms of the (linearized) augmented planewave plus localorbitals [(L)APW+lo] basis. In this method, the unit cell is divided into two regions. Within the so-called muffin-tin spheres, the wave functions are given as linear combinations of atom-centered functions. Muffin-tin radii, RMT, of 1.40, 1.35, 1.30, and 1.20 bohr, respectively, are used for B, C, N, and F. In the interstitial region, the wave functions are smoother and can be described by planewaves. We use an energy cutoff parameter of 5.0 bohr−1. For all four elements, the 1s electrons are treated as core states.

Vctrun(r) =

θ(zc − |z|) |r|

(2)

where |z| is the vertical distance between two electrons, and zc is the threshold for the Coulomb cutoff. Setting zc to be half of the cell size along z, it is then expressed as54 B


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The Journal of Physical Chemistry C

respectively. Interestingly, at the Γ point, the CB behaves like a delocalized nearly free-electron (NFE) state. It is very similar to the CB of the hydrogenated silicon carbide monolayer at Γ.59 According to the G0W0 calculations, the h-BN monolayer has an indirect band gap of 6.95 eV (K → Γ). In other words, the CBm is now formed by the NFE state. We will get back to this in more detail in the next section. The direct gap at K is calculated to be 7.60 eV (K → K). In a previous study,26 the corresponding gaps were found to be 6.58 (K → Γ) and 7.37 (K → K) eV. Our results are 0.37 (K → Γ) and 0.23 (K → K) eV larger than the values reported in ref 26, which may be attributed to the DFT starting point (PBE vs LDA), computational parameters or methodology (all-electron vs pseudopotential code). More details regarding the comparison can be found in the Supporting Information. The G0W0corrected IE and EA values of h-BN are calculated to be 7.41 eV (at K) and 0.47 eV (at Γ), respectively. CF/h-BN Interface. Before addressing the electronic structure, we briefly describe the interface geometry. The results of the PES scan obtained by the vdW-DF functional (black line) are shown in Figure 3. It is worth noting that the

4π [1 − e−kxyzc cos(kzzc)] (3) |k|2 This Coulomb truncation has been implemented in the exciting code and is used in the G0W0 calculations. Results of the G0W0 band gaps calculated with different vacuum thickness are given in the Supporting Information. Vctrun(k) =

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RESULTS AND DISCUSSION CF Monolayer. Different configurations of the CF monolayer were previously studied by DFT and G0 W 0 methods. It was found that the chair configuration, in which the fluoride atoms alternatively connect with the carbon atoms on both sides (shown in the left panel of Figure 1), is the most stable structure.55 Thus in our studies, only this chair configuration is considered. From the PBE calculations, we obtain a lattice parameter a/√3 of 2.606 Å and a Kohn−Sham band gap at the Γ point of 3.21 eV. The C−C and C−F bond lengths are calculated to be 1.584 and 1.373 Å, respectively. All these results agree very well with previous studies.55,56 It should be noted that in the following calculations, the lattice of CF is compressed by 3.4%, to 2.517 Å, in order to match the spacings of the h-BN monolayer. In this case, the band gap reduces to 3.07 eV. The C−C bond length is reduced to 1.536 Å, whereas the C−F distance becomes 1.374 Å, i.e., undergoes a very small change. The left panel of Figure 2 shows the probability density

Figure 3. Binding energy of the CF/h-BN interface as computed by the vdW-DF functional (black) in comparison to results from PBE (magenta), LDA (orange), and the DFT-D2 method (purple). The vertical dotted line indicates the optimal distance obtained from vdWDF and the horizontal line marks the zero-energy position. Figure 2. Probability density of the Kohn−Sham orbitals from the valence and conduction bands of CF at the Γ point (left) and of h-BN at the K point (right).

chair configuration of CF remains the most stable one at the interface (see Supporting Information). The optimal distance between CF and h-BN is found to be 6.0 bohr, and the corresponding binding energy is −0.17 eV. For sake of comparison, results from PBE (magenta), LDA60 (orange), and the semiempirical DFT-D2 method61 (purple) are also shown. As expected, PBE fails to give a local minimum, while LDA leads to smaller values of bond distance (5.5 bohr) and binding energy (−0.08 eV). The DFT-D2 method is close to LDA concerning the bond distance (5.5 bohr) and to vdW-DF in terms of the binding energy (−0.16 eV). In lack of experimental information, we adopt in the following the results from vdW-DF. We note, however, that the main message of this work would not be altered by using the DFT-D2 geometry. In the top panel of Figure 4, we plot the plane-averaged total charge density (ρtot) along the z direction, together with the charge density difference Δρ = ρtot − (ρCF + ρh‑BN), with ρCF and ρh‑BN being the plane-averaged charge densities of the pristine systems. One can see that the interaction between the two monolayers leads to an extremely small charge density redistribution, and the charge transfer between CF and h-BN is basically zero. This fact is also obvious from the electrostatic potential, displayed in the bottom panel of Figure 4, which has the same value on both sides of the interface. The position of

of the Kohn−Sham orbitals from both the VBM and the CBm. The ionization energy (IE) and the electron affinity (EA) are calculated to be 7.62 and 4.56 eV, respectively. The G0W0 calculation increases the band gap to 7.24 eV. The difference to previous results of about 7.4 eV55,56 is mainly due to the compressed lattice used in our calculations. Because the electron density and the electrostatic potential are not updated in G0W0 calculations, the vacuum energy level remains the same as obtained within DFT. The G0W0-corrected IE and EA values are then calculated to be 9.56 and 2.31 eV, respectively. h-BN Monolayer. From our PBE calculations, the optimized lattice constant of the h-BN monolayer is 2.517 Å, consistent with previous studies.57,58 We obtain a direct band gap of 4.65 eV at the K point, which also agrees well with literature values.26,57 An indirect gap of 4.67 eV exists between K and Γ, with the CB lying 24 meV higher at the Γ point. In the right panel of Figure 2, we present the probability density of the VB and the CB at K. The VB originates from π-states located at nitrogen atoms, and the CB comes from π-states of boron atoms. From the position of the DFT vacuum level, the IE and EA values (at K) are calculated to be 5.91 and 1.26 eV, C


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corresponding Kohn−Sham gap is even less (about 20 meV). One exception is the CB of h-BN at the Γ point, i.e., the aforementioned NFE-like state. It experiences an upshift of 313 meV. In Figure 6, we plot its probability density. One can see that in the monolayer, the density is located on both sides of the h-BN plane, whereas at the interface, though retaining its delocalized NFE-like character, it is located only on one side, opposite to the CF plane. This redistribution of the probability density is reflected in an upshift of the energetic position. At the G0W0 level, the VBM of CF moves up by 94 meV, whereas its CBm moves down by 143 meV. Consequently, their energetic distance (formerly band gap) is reduced by 237 meV. For the h-BN monolayer, the VBM increases by 148 meV, and its CBm, interestingly, also moves up (by 164 meV), leading to a slight increase of their distance (K → Γ) by 16 meV. This is related to the fact that on the G0W0 level, the CBm of h-BN is provided by the NFE-like state. In contrast, the CB position at the K point decreases by 119 meV. Hence, the corresponding direct gap (K → K) on the BN side is reduced by 267 meV. In Table 2, we list the above-described shifts of energy levels upon interface formation at both the DFT (column 2) and the G0W0 (column 3) level, together with their difference, denoted by δ (column 4). In absence of polarization (image-charge) effects, the difference δ should be exactly zero. Thus, we can read from the actual values how important the nonlocal correlation effects are. For both the CF and the h-BN sides, it leads to an increase of VB as well as a decrease of CB by roughly 0.13 eV. Thus, the band-gap reduction caused by the polarization effects is about 250 meV. Interestingly, even for the NFE-like state, the corresponding level shift is still in the same range (−0.149 eV), indicating that the extent of renormalization may not depend on the nature of orbitals. To substantiate our claim of nonlocal correlations being the cause of this effect, we further analyze the G0W0 self-energies. These quantities have contributions from exchange and correlation, denoted by Σ x and Σ c , respectively. The corresponding matrix elements at the DFT level are expressed as Vx and Vc. Denoting Σα − Vα with the subscript α being x or c, we list in Table 2 their changes for both VB and CB upon interface formation

Figure 4. (Top) Plane-averaged total charge density (black) and charge density difference (gray). (Bottom) Electrostatic potential of the CF/h-BN interface along the vertical direction. The dotted line represents the position of the interface.

the vacuum level can therefore be regarded to be the same for all systems (set to 0 eV). In other words, in principle the energy-level alignment can be derived from their corresponding IE and EA values.62 The energy-level alignment at the CF/h-BN interface, obtained from both DFT and G0W0, is sketched in Figure 5. For comparison, the energetic positions of the respective VBM and CBm of the two individual monolayers are also shown. The DFT band structure and density of states of the interface as well as of the two components are displayed in the Supporting Information. The VBM of the interface is that of the h-BN monolayer, while the CBm is provided by CF. This reflects a type-II alignment, with a band gap of 1.31 eV (K → Γ) and of 4.81 eV (K → Γ) at the DFT and the G0W0 level, respectively. The various gaps are collected in Table 1. Upon interface formation, the respective VBM and CBm positions of both CF and h-BN shift very little (maximum of 30 meV) at the DFT level. Moreover, since the VBM and the CBm move in the same direction, the change of the

Δ(Σα − Vα) = (Σα − Vα)interface − (Σα − Vα)monolayer (4)

Figure 5. Energy-level alignment of the CF/h-BN interface from DFT (left panel) and G0W0 calculations (right panel). For comparison, the positions of the VB and CB in each individual monolayer (CF: green; h-BN: blue) are shown. The respective k-point is indicated for each level. The vacuum level is set to 0 eV. D


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Table 1. Band Gaps (in eV) of CF and h-BN (Both in the Pristine Monolayers and at the Interface) and Those of the CF/h-BN Interface, as Obtained by the PBE and G0W0 Calculationsa PBE

G0W0@PBE

3.07 (Γ → Γ) 3.08 (Γ → Γ)

7.24 (Γ → Γ) 7.01 (Γ → Γ)

4.65 (K → K)/4.67 (K → Γ) 4.64 (K → K)/4.97 (K → Γ)

7.60 (K → K)/6.95 (K → Γ) 7.33 (K → K)/6.96 (K → Γ)

1.31 (K → Γ)

4.81 (K → Γ)

CF (monolayer) CF (at interface) h-BN (monolayer) h-BN (at interface) CF/h-BN a

Note that the CF lattice is compressed by 3.4%. The K point in all cases refers to the coordinates defined by the hexagonal unit cell.

Figure 6. Probability density of the Kohn−Sham orbital of the NFElike state at Γ computed for the h-BN monolayer (left) and the CF/hBN interface (right).

Table 2. Differences in VB and CB Position between the Interface and the Respective Pristine System, as Obtained by DFT [ΔE (DFT)] and G0W0 [ΔE (G0W0)], as well as Their Difference Denoted by δa CF

ΔE (DFT)

ΔE (G0W0)

δ

Δ(Σx - Vx)

Δ(Σc -Vc)

VB at Γ CB at Γ

−0.033 −0.018

0.094 −0.143

0.127 −0.125

−0.006 0.030

0.138 −0.159

ΔE (DFT)

ΔE (G0W0)

δ

Δ(Σx - Vx)

Δ(Σc -Vc)

0.022 0.313 0.012

0.148 0.164 −0.119

0.126 −0.149 −0.131

−0.003

0.168

−0.014

−0.143

h-BN VB at K CB at Γ CB at K

Figure 7. Estimated energy-level shift of CB as a function of thickness t for a set of effective dielectric constants εeff (1.4−2.6). The inset shows a schematic of the image-potential model.

the range of shifts as obtained from the G0W0 calculations. In this way, the effective dielectric constant is estimated to be 1.4− 1.6 for CF and 2.0−2.6 for h-BN. These values agree very well with available experiments, giving 1.2 for multilayer CF66 and 2−4 for an h-BN film.67 For 2D materials, the macroscopic dielectric screening is highly anisotropic, i.e., in principle it cannot be described by a simple dielectric constant.68,69 In a recent study, static dielectric functions were calculated for fifty-one 2D materials, with their band gaps ranging from 0 to 8 eV.69 These values are mostly about 2 for wide-bandgap monolayers (7−8 eV) over a large range of in-plain momentum, consistent with our estimation of εeff for CF and h-BN. In addition, a correlation relation was established between band gaps and dielectric functions. As one could expect, smaller gaps correspond to larger values of εeff.69 As clearly shown in Figure 7, increasing screening, i.e., εeff, leads to larger energy-level shifts. Consequently, the polarizationinduced band-gap reduction should be more notable for 2D vdW junctions with smaller gaps. In other words, the 250 meV revealed by our calculations may be regarded as a lower limit for such band-gap renormalization of 2D materials purely bound by vdW interactions.

a

The right side of the table provides the respective contributions from the exchange Δ(Σx − Vx) and the correlation Δ(Σc − Vc) parts. Note that these two terms do not sum up to δ, because in the former the QP renormalization factor is not taken into account. All values are given in eV.

It quantitatively reflects the cause of the band-gap reduction, since the correlation term clearly plays the dominant role. In addition, it explains why standard hybrid functionals, by mixing a portion of nonlocal Hartree−Fock exchange, cannot catch the polarization effects. These results are interpreted with a simple image-potential model,63−65 by considering the interaction between a point charge and a planar dielectric slab with a thickness t and an effective dielectric constant εeff (inset of Figure 7). This model is particularly suited for 2D materials exhibiting a finite thickness, and has been successfully applied for nanopeapod structures.64 In our investigations, the distance between the point charge and the slab is chosen to be 6.0 bohr, according to the optimal distance at the interface. The effective thickness t of the two monolayers is estimated from the density of the valence electrons (see Supporting Information), being 7.8 and 2.1 bohr for CF and h-BN, respectively. In Figure 7, we plot the so obtained energy-level shift of the CB as a function of t for a set of εeff. Note that the VB shift has the same size but opposite sign. The two dotted lines correspond to the thicknesses of CF and h-BN, and the gray region (−0.15 to −0.10 eV) indicates

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CONCLUSIONS In summary, by using many-body perturbation theory, we investigate possible polarization effects on the energy-level alignment of a prototypical weakly bonded interface, constituted by monolayers of graphene fluoride and boron nitride. Both of them are nonpolar and wide-bandgap E


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Alignment at Organic/Organic Interfaces: The Role of Structural Defects. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 115319. (6) Smets, Y.; Rietwyk, K. J.; Fingerle, M.; Schmitt, F.; Lach, S.; Ley, L.; Ziegler, C.; Pakes, C. I. Energy Level Alignment at the Porphyrin/ Cobaltocene Interface: From Transfer Doping to Cobalt Intercalation. Org. Electron. 2014, 15, 531−536. (7) Yonezawa, K.; Hinderhofer, A.; Hosokai, T.; Kato, K.; Makino, R.; Schreiber, F.; Ueno, N.; Kera, S. Structural Defects Control the Energy Level Alignment at Organic/Organic Interfaces. Adv. Mater. Interfaces 2014, DOI: 10.1002/admi.201400004. (8) Conesa, J. C. Modeling with Hybrid Density Functional Theory the Electronic Band Alignment at the Zinc Oxide-Anatase Interface. J. Phys. Chem. C 2012, 116, 18884−18890. (9) Scanlon, D. O.; Dunnill, C. W.; Buckeridge, J.; Shevlin, S. A.; Logsdail, A. J.; Woodley, S. M.; Catlow, C. R. A.; Powell, M. J.; Palgrave, R. G.; Parkin, I. P.; et al. Band Alignment of Rutile and Anatase TiO2. Nat. Mater. 2013, 12, 798−801. (10) Peisert, H.; Knupfer, M.; Fink, J. Energy Level Alignment at Organic/Metal Interfaces: Dipole and Ionization Potential. Appl. Phys. Lett. 2002, 81, 2400−2402. (11) Zhao, J.; Feng, M.; Dougherty, D. B.; Sun, H.; Petek, H. Molecular Electronic Level Alignment at Weakly Coupled Organic Film/Metal Interfaces. ACS Nano 2014, 8, 10988−10997. (12) Egger, D. A.; Liu, Z.-F.; Neaton, J. B.; Kronik, L. Reliable Energy Level Alignment at Physisorbed Molecule-Metal Interfaces from Density Functional Theory. Nano Lett. 2015, 15, 2448−2455. (13) Greiner, M. T.; Helander, M. G.; Tang, W. M.; Wang, Z. B.; Qiu, J.; Lu, Z. H. Universal Energy-Level Alignment of Molecules on Metal Oxides. Nat. Mater. 2011, 11, 76−81. (14) Feng, W.; Rangan, S.; Cao, Y.; Galoppini, E.; Bartynski, R. A.; Garfunkel, E. Energy Level Alignment of Polythiophene/ZnO Hybrid Solar Cells. J. Mater. Chem. A 2014, 2, 7034−7044. (15) Timpel, M.; Nardi, M. V.; Ligorio, G.; Wegner, B.; Pätzel, M.; Kobin, B.; Hecht, S.; Koch, N. Energy-Level Engineering at ZnO/ Oligophenylene Interfaces with Phosphonate-Based Self-Assembled Monolayers. ACS Appl. Mater. Interfaces 2015, 7, 11900−11907. (16) Hofmann, O. T.; Deinert, J. C.; Xu, Y.; Rinke, P.; Stähler, J.; Wolf, M.; Scheffler, M. Large Work Function Reduction by Adsorption of a Molecule with a Negative Electron Affinity: Pyridine on ZnO (1010). J. Chem. Phys. 2013, 139, 174701. (17) Yu, M.; Doak, P.; Tamblyn, I.; Neaton, J. B. Theory of Covalent Adsorbate Frontier Orbital Energies on Functionalized LightAbsorbing Semiconductor Surfaces. J. Phys. Chem. Lett. 2013, 4, 1701−1706. (18) Willenbockel, M.; Lüftner, D.; Stadtmüller, B.; Koller, G.; Kumpf, C.; Soubatch, S.; Puschnig, P.; Ramsey, M. G.; Tautz, F. S. The Interplay Between Interface Structure, Energy Level Alignment and Chemical Bonding Strength at Organic-Metal Interfaces. Phys. Chem. Chem. Phys. 2015, 17, 1530−1548. (19) Shen, C.; Kahn, A.; Hill, I. In Conjugated Polymer and Molecular Interfaces, 1st ed.; Salaneck, W. R., Seki, K., Kahn, A., Pireaux, J.-J., Eds.; Marcel Dekker, Inc.: New York, 2002; pp 351−400. (20) Schottky, W. Halbleitertheorie der Sperrschicht. Naturwissenschaften 1938, 26, 843−843. (21) Inkson, J. C. Many-Body Effect at Metal-Semiconductor Junctions. II. The Self Energy and Band Structure Distortion. J. Phys. C: Solid State Phys. 1973, 6, 1350−1362. (22) Neaton, J. B.; Hybertsen, M. S.; Louie, S. G. Renormalization of Molecular Electronic Levels at Metal-Molecule Interfaces. Phys. Rev. Lett. 2006, 97, 216405. (23) Thygesen, K. S.; Rubio, A. Renormalization of Molecular Quasiparticle Levels at Metal-Molecule Interfaces: Trends across Binding Regimes. Phys. Rev. Lett. 2009, 102, 046802. (24) Garcia-Lastra, J. M.; Rostgaard, C.; Rubio, A.; Thygesen, K. S. Polarization-Induced Renormalization of Molecular Levels at Metallic and Semiconducting Surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 245427. (25) Puschnig, P.; Amiri, P.; Draxl, C. Band Renormalization of a Polymer Physisorbed on Graphene Investigated by Many-Body

semiconductors, and the charge transfer between them is negligible. We find that despite these systems having large gaps, mutual polarization leads to a notable band-gap reduction of 250 meV. Our work provides a lower limit for such an effect, and indicates that for 2D materials with smaller band gaps, an even larger impact is to be expected. This effect, which stems from nonlocal electron correlations, cannot be captured by semilocal or standard hybrid density functionals, and thereby points to the importance of many-body perturbation theory for an accurate description of energy-level alignment at such interfaces.

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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.6b01741 Convergence tests of the G0W0 calculations with respect to the vacuum thickness, the number of k-points, and the number of empty states; comparison of the G0W0 band gap of h-BN with previous results; configuration of CF at the interface; band structures and densities of states; and estimation of the effective thickness for CF and h-BN. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(Q.F.) E-mail: [email protected]. Phone: +49 (0)30 2093 66450. *(D.N.) E-mail: [email protected]. Phone: +49 (0)30 2093 66364. *(C.D.) E-mail: [email protected]. Phone: +49 (0)30 2093 66363. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support by the German Research Foundation (DFG) through Collaborative Research Centers SFB-951 and SFB-658. Computing time granted by the North-German Supercomputing Alliance (HLRN) is appreciated. We thank Sven Lubeck for his implementation of the DFT-D2 method, and Benjamin Höffling, Olga Turkina, and Christian Vorwerk for critical reading of the manuscript. Q.F. thanks IRIS Adlershof for financial support, Sofo Jorge for helpful discussion, and Wahib Aggoune for assistance on colors.

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REFERENCES

(1) Schlesinger, R.; Bianchi, F.; Blumstengel, S.; Christodoulou, C.; Ovsyannikov, R.; Kobin, B.; Moudgil, K.; Barlow, S.; Hecht, S.; Marder, S.; et al. Efficient Light Emission from Inorganic and Organic Semiconductor Hybrid Structures by Energy-Level Tuning. Nat. Commun. 2015, 6, 6754. (2) Chuang, C.-H. M.; Brown, P. R.; Bulović, V.; Bawendi, M. G. Improved Performance and Stability in Quantum Dot Solar Cells through Band Alignment Engineering. Nat. Mater. 2014, 13, 796−801. (3) Migani, A.; Mowbray, D. J.; Iacomino, A.; Zhao, J.; Petek, H.; Rubio, A. Level Alignment of a Prototypical Photocatalytic System: Methanol on TiO2(110). J. Am. Chem. Soc. 2013, 135, 11429−11432. (4) Lindell, L.; Ç akır, D.; Brocks, G.; Fahlman, M.; Braun, S. Role of Intrinsic Molecular Dipole in Energy Level Alignment at Organic Interfaces. Appl. Phys. Lett. 2013, 102, 223301. (5) Bussolotti, F.; Yang, J.; Hinderhofer, A.; Huang, Y.; Chen, W.; Kera, S.; Wee, A. T. S.; Ueno, N. Origin of the Energy Level F


Article

The Journal of Physical Chemistry C Perturbation Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 085107. (26) Hüser, F.; Olsen, T.; Thygesen, K. S. Quasiparticle GW Calculations for Solids, Molecules, and Two-Dimensional Materials. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 235132. (27) Jin, C.; Rasmussen, F. A.; Thygesen, K. S. Tuning the Schottky Barrier at the Graphene/MoS2 Interface by Electron Doping: Density Functional Theory and Many-Body Calculations. J. Phys. Chem. C 2015, 119, 19928−19933. (28) Kümmel, S.; Kronik, L. Orbital-Dependent Density Functionals: Theory and Applications. Rev. Mod. Phys. 2008, 80, 3−60. (29) Cohen, A. J.; Mori-Sánchez, P.; Yang, W. Challenges for Density Functional Theory. Chem. Rev. 2012, 112, 289−320. (30) Refaely-Abramson, S.; Sharifzadeh, S.; Jain, M.; Baer, R.; Neaton, J. B.; Kronik, L. Gap Renormalization of Molecular Crystals from Density-Functional Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 081204. (31) Hedin, L. New Method for Calculating the One-Particle Green’s Function with Application to the Electron-Gas Problem. Phys. Rev. 1965, 139, A796. (32) Mas-Ballesté, R.; Gómez-Navarro, C.; Gómez-Herrero, J.; Zamora, F. 2D Materials: To Graphene and Beyond. Nanoscale 2011, 3, 20−30. (33) Osada, M.; Sasaki, T. Two-Dimensional Dielectric Nanosheets: Novel Nanoelectronics from Nanocrystal Building Blocks. Adv. Mater. 2012, 24, 210−228. (34) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699− 712. (35) Butler, S. Z.; Hollen, S. M.; Cao, L.; Cui, Y.; Gupta, J. a.; Gutiérrez, H. R.; Heinz, T. F.; Hong, S. S.; Huang, J.; Ismach, A. F.; et al. Progress, Challenges, and Opportunities in Two-Dimensional Materials beyond Graphene. ACS Nano 2013, 7, 2898−2926. (36) Xu, M.; Liang, T.; Shi, M.; Chen, H. Graphene-like TwoDimensional Materials. Chem. Rev. 2013, 113, 3766−3798. (37) Geim, A. K.; Grigorieva, I. V. Van der Waals Heterostructures. Nature 2013, 499, 419−25. (38) Dean, C.; Young, A.; Wang, L.; Meric, I.; Lee, G.-H.; Watanabe, K.; Taniguchi, T.; Shepard, K.; Kim, P.; Hone, J. Graphene based Heterostructures. Solid State Commun. 2012, 152, 1275−1282. (39) Wang, H.; Liu, F.; Fu, W.; Fang, Z.; Zhou, W.; Liu, Z. TwoDimensional Heterostructures: Fabrication, Characterization, and Application. Nanoscale 2014, 6, 12250−12272. (40) Niu, T.; Li, A. From Two-Dimensional Materials to Heterostructures. Prog. Surf. Sci. 2015, 90, 21−45. (41) Du, A.; Sanvito, S.; Li, Z.; Wang, D.; Jiao, Y.; Liao, T.; Sun, Q.; Ng, Y. H.; Zhu, Z.; Amal, R.; et al. Hybrid Graphene and Graphitic Carbon Nitride Nanocomposite: Gap Opening, Electron-hole Puddle, Interfacial Charge Transfer, and Enhanced Visible Light Response. J. Am. Chem. Soc. 2012, 134, 4393−4397. (42) Hu, W.; Yang, J. First-Principles Study of Two-Dimensional van der Waals Heterojunctions. Comput. Mater. Sci. 2016, 112, 518. (43) Wu, F.; Liu, Y.; Yu, G.; Shen, D.; Wang, Y.; Kan, E. VisibleLight-Absorption in Graphitic g-C3N4 Bilayer: Enhanced by Interlayer Coupling. J. Phys. Chem. Lett. 2012, 3, 3330−3334. (44) Wang, J.; Guan, Z.; Huang, J.; Li, Q.; Yang, J. Enhanced Photocatalytic Mechanism for the Hybrid g-C3N4/MoS2 Nanocomposite. J. Mater. Chem. A 2014, 2, 7960. (45) Xu, L.; Huang, W.-Q.; Wang, L.-L.; Tian, Z.-A.; Hu, W.; Ma, Y.; Wang, X.; Pan, A.; Huang, G.-F. Insights into Enhanced Visible-Light Photocatalytic Hydrogen Evolution of g-C3N4 and Highly Reduced Graphene Oxide Composite: The Role of Oxygen. Chem. Mater. 2015, 27, 1612−1621. (46) Topsakal, M.; Cahangirov, S.; Bekaroglu, E.; Ciraci, S. FirstPrinciples Study of Zinc Oxide Honeycomb Structures. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 235119. (47) Gulans, A.; Kontur, S.; Meisenbichler, C.; Nabok, D.; Pavone, P.; Rigamonti, S.; Sagmeister, S.; Werner, U.; Draxl, C. Exciting: A

Full-Potential All-Electron Package Implementing Density-Functional Theory and Many-Body Perturbation Theory. J. Phys.: Condens. Matter 2014, 26, 363202. (48) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (49) Dion, M.; Rydberg, H.; Schröder, E.; Langreth, D. C.; Lundqvist, B. I. Van der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. (50) Nabok, D.; Puschnig, P.; Ambrosch-Draxl, C. noloco: An Efficient Implementation of van der Waals Density Functionals based on a Monte-Carlo Integration Technique. Comput. Phys. Commun. 2011, 182, 1657−1662. (51) Hüser, F.; Olsen, T.; Thygesen, K. S. How Dielectric Screening in Two-Dimensional Crystals Affects the Convergence of Excited-State Calculations: Monolayer MoS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 245309. (52) Berseneva, N.; Gulans, A.; Krasheninnikov, A. V.; Nieminen, R. M. Electronic Structure of Boron Nitride Sheets Doped with Carbon from First-Principles Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 035404. (53) Rozzi, C. A.; Varsano, D.; Marini, A.; Gross, E. K. U.; Rubio, A. An Exact Coulomb Cutoff Technique for Supercell Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 205119. (54) Ismail-Beigi, S. Truncation of Periodic Image Interactions for Confined Systems. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 233103. (55) Leenaerts, O.; Peelaers, H.; Hernández-Nieves, A. D.; Partoens, B.; Peeters, F. M. First-Principles Investigation of Graphene Fluoride and Graphane. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 195436. (56) Klintenberg, M.; Lebègue, S.; Katsnelson, M. I.; Eriksson, O. Theoretical Analysis of the Chemical Bonding and Electronic Structure of Graphene Interacting with Group IA and Group VIIA Elements. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 085433. (57) Şahin, H.; Cahangirov, S.; Topsakal, M.; Bekaroglu, E.; Akturk, E.; Senger, R. T.; Ciraci, S. Monolayer Honeycomb Structures of Group-IV Elements and III-V Binary Compounds: First-Principles Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 155453. (58) Peng, Q.; Ji, W.; De, S. Mechanical Properties of the Hexagonal Boron Nitride Monolayer: Ab initio Study. Comput. Mater. Sci. 2012, 56, 11−17. (59) Gori, P.; Pulci, O.; Marsili, M.; Bechstedt, F. Side-Dependent Electron Escape from Graphene- and Graphane-like SiC Layers. Appl. Phys. Lett. 2012, 100, 043110. (60) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13249. (61) Grimme, S. Semiempirical GGA-type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (62) Anderson, R. L. Experiments on Ge-GaAs Heterojunctions. Solid-State Electron. 1962, 5, 341−344. (63) Barrera, R. G.; Guzmán, O.; Balaguer, B. Point Charge in a Three-Dielectric Medium with Planar Interfaces. Am. J. Phys. 1978, 46, 1172−1179. (64) Milko, M.; Puschnig, P.; Draxl, C. Predicting the Electronic Structure of Weakly Interacting Hybrid Systems: The Example of Nanosized Peapod Structures. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 155416. (65) Pont, F. M.; Serra, P. Comment on ”Point Charge in a ThreeDielectric Medium with Planar Interfaces” [Am. J. Phys. 46, 1172− 1179 (1978)]. Am. J. Phys. 2015, 83, 475−476. (66) Ho, K.-I.; Huang, C.-H.; Liao, J.-H.; Zhang, W.; Li, L.-J.; Lai, C.S.; Su, C.-Y. Fluorinated Graphene as High Performance Dielectric Materials and the Applications for Graphene Nanoelectronics. Sci. Rep. 2014, 4, 5893. (67) Kim, K. K.; Hsu, A.; Jia, X.; Kim, S. M.; Shi, Y.; Dresselhaus, M.; Palacios, T.; Kong, J. Synthesis and Characterization of Hexagonal G


Article

The Journal of Physical Chemistry C Boron Nitride Film as a Dielectric Layer for Graphene Devices. ACS Nano 2012, 6, 8583−8590. (68) Cudazzo, P.; Tokatly, I. V.; Rubio, A. Dielectric Screening in Two-Dimensional Insulators: Implications for Excitonic and Impurity States in Graphane. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 085406. (69) Andersen, K.; Latini, S.; Thygesen, K. S. Dielectric Genome of van der Waals Heterostructures. Nano Lett. 2015, 15, 4616−4621.

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