ZnO101¯0 interface

Surface Science 618 (2013) 62–71

Contents lists available at ScienceDirect

Surface Science journal homepage: www.elsevier.com/locate/susc

First principles study of bonding, adhesion, and electronic structure at the Cu2O(111)/ZnOð1010Þ interface Leah Isseroff Bendavid a, Emily A. Carter b,⁎ a

Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544-5263, United States Department of Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics, and Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ 08544-5263, United States

b

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 12 June 2013 Accepted 25 July 2013 Available online 13 August 2013

adhesion energies of the Cu2O(111)/ZnOð1010Þ interface with varying Cu2O coating thickness. We first establish an accurate model of the ZnO substrate, validating DFT + U against the more accurate hybrid-DFT to calculate

Keywords: Density functional theory Adhesion energy Semiconductor interface Electronic properties Cuprous oxide Zinc oxide

the Cu2O(111) surface, characterizing the formation of surface copper dimers. The Cu2O(111)/ZnOð1010Þ interface is found to be only weakly interacting, with a DFT + U–derived adhesion energy of 0.85 ± 0.07 J/m2. Charge density analysis reveals that some interface stabilization occurs because of local Zn\O and Cu\O bonding interactions at the interface. We find that the overall impact of the ZnO substrate on the electronic structure of the Cu2O overlayer is to reduce the Cu2O band gap. © 2013 Elsevier B.V. All rights reserved.

Density functional theory (DFT)-based methods are used to understand atomic level interactions and calculate

properties of bulk wurtzite ZnO and the ZnOð1010Þ surface. DFT + U is then used to analyze the structure of

1. Introduction The reduction of CO2 to methanol is attractive as a renewable source of a fuel precursor and a means of reducing CO2 concentrations in the atmosphere. Methanol can be readily converted into gasoline by the well-known zeolite-based Mobil process [1–3]. Commercial production of methanol typically uses a Cu/ZnO catalyst with syngas and CO2 feeds [4]. While there is some uncertainty regarding the nature of the active site on the Cu/ZnO catalyst, oxidized Cu(I) sites are thought to promote catalytic activity and selectivity toward methanol production [4–7]. To increase catalytic activity and potentially create a photochemicallydriven catalyst, Cu2O has been proposed as an enhanced catalyst for methanol synthesis, as its surface contains Cu(I) ions that may strongly bind reactant molecules while acting as reduction sites [8,9]. Cu2O is also characterized by optical properties that may enable catalysis to be driven photochemically without an external bias, as has been employed in photocatalytic water splitting [10]. Early studies of the electrochemical activity of Cu2O for CO2 reduction have exhibited increased methanol yields and Faradaic efficiencies, but Cu2O also degrades in the process due to its simultaneous reduction to Cu [8,9]. Stabilization of Cu2O during catalysis is crucial for it to be a sustainable catalyst. Greater catalyst stability

⁎ Corresponding author. Tel.: +1 609 258 5391; fax: +1 609 258 5877. E-mail address: [email protected] (E.A. Carter). 0039-6028/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.susc.2013.07.027

was achieved recently using hybrid CuO–Cu2O semiconductor nanorod arrays [11]. Another method of stabilization derives motivation from the role of the ZnO substrate in the Cu/ZnO catalyst, where ZnO is presumed to stabilize the oxidized Cu(I) active sites [4–7]. Stabilization of a Cu2O catalyst might therefore be accomplished via the deposition of Cu2O on a ZnO substrate, which might act to stabilize the oxidized Cu(I) ions of Cu2O in a similar manner as in the Cu/ZnO catalyst. This demands a better understanding of the stability and electronic properties of the Cu2O/ZnO interface, which we undertake using methods based on firstprinciples density functional theory (DFT). A study of Cu2O/ZnO interfaces will also contribute insight into Cu2O/ZnO heterojunction solar cells. We chose to study the interface comprised of the two nonpolar, lowenergy surfaces of its components, where the surfaces considered are unreconstructed and bulk terminated (i.e., no surface vacancies). There are three stable phases for ZnO — rocksalt, zinc blende, and wurtzite. The wurtzite structure is the most stable under ambient conditions, and is therefore the relevant phase for our applications. Wurtzite ZnO is dominated by low index surfaces, specifically, the nonpolar ð1010Þ and ð1120Þ surfaces and the polar zinc-terminated (0001)– Zn and oxygen-terminated ð0001Þ–O basal plane surfaces. Early qualitative low-energy electron diffraction (LEED) experiments identified the nonpolar ð1010Þ surface as the most stable face [12], which was verified by a number of DFT-based calculations of surface cleavage energies [13–16]. Cu2O is stable in the cuprite crystal structure, and only the (111) and (100) surfaces have been characterized experimentally

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71

[17]. Using DFT + U, we have shown elsewhere that the ideal bulkterminated (111) surface is lower in energy than the ideal (100) surface [18]. We therefore studied the Cu2O(111)/ZnOð1010Þ interface. Here we consider the stoichiometric Cu2O(111) surface, although future work will be needed to consider interfaces containing copper vacancies thought to be favorable on the (111) surface [18–21]. First row, mid-to-late transition-metal oxides are strongly correlated materials that are challenging to model with Kohn-Sham DFT, largely due to the self-interaction error of local and semilocal exchangecorrelation (XC) functionals. In modeling the Cu2O(111)/ZnOð1010Þ interface, it may be important to use variants of DFT that incorporate a fraction of exact nonlocal exchange, such as hybrid XC functionals [22–24], or that introduce a parameterized approximation to exact exchange, such as the DFT + U method [25,26]. DFT with the Heyd– Scuseria–Ernzerhof (HSE) screened exchange hybrid functional was previously employed in accurate modeling of bulk Cu2O, while the DFT + U method with the Perdew–Burke–Ernzerhof (PBE) generalized gradient expansion (GGA) XC functional [27,28] was identified as an alternative method for accurate structural predictions [29]. Bulk wurtzite ZnO has been studied using a number of DFT XC functionals, including the local density approximation (LDA) XC functional [30–32], PBE, the Tao–Perdew–Staroverov–Scuseria (TPSS) nonempirical meta-GGA functional [33,34], and HSE [16,35]. DFT-HSE predicted accurate lattice constants and bulk moduli, with improved electronic and optical properties in comparison to predictions with other functionals, and is therefore the best method with which to model ZnO. While DFT-HSE offers the ideal accuracy for both materials, it is unfeasible to use DFT-HSE when modeling large system sizes such as interfaces due to its computational cost. Here we explore the use of PBE + U as a less computationally expensive method than DFT-HSE that may offer similar accuracy in structural and electronic properties. Prior to simulating the interface, it is first necessary to have a model of the ZnO substrate that accurately describes its unique surface properties. The nonpolar ZnOð1010Þ surface is characterized by surface Zn–O dimers whose bulk fourfold coordination is reduced to threefold coordination. The nature of the surface dimer relaxation offers insight into the bonding character of the material [36]. If ZnO is dominated by ionic character, both atoms of the surface dimer would relax inward toward the bulk from their bulk-terminated positions and reduce the dimer bond length to obtain better screening. However, if the bonding is dominated by covalent character, the cation would surpass the anion in its inward relaxation so that it lies in a plane with its three anionic neighbors, effectively rehybridizing from sp3 to sp2. This would result in a strong tilt of the surface dimer with little change to the bond length. Fig. 1 shows the geometry of the surface dimer and the structural parameters used to describe its distortion. The nonpolar ZnOð1010Þ surface was characterized through LEED analysis by Duke et al., who showed that the surface is not reconstructed but undergoes significant inward relaxation of the surface dimer with the Zn\O bond rotating

63

with respect to the ideal surface plane [37]. They observed a relatively small tilt angle, θ, of 11.5 ± 5°, implying that chemical bonding in ZnO is primarily ionic with some covalent contributions, in agreement with the description of ZnO as being at the borderline between ionic and covalent solids [38]. Early theoretical calculations of the ZnO ð1010Þ surface used an empirical periodic tight-binding (TB) model, which predicted an overestimated tilt angle of 17.2° [39]. Later first-principles periodic Hartree–Fock (HF) [40], DFT-LDA [41], and DFT-B3LYP [14] calculations predicted much lower tilt angles of 2.48°, 3.59°, and 5.20°, respectively. Their underestimation of the tilt angle was explained as most likely due to unconverged geometries, as these calculations used thin slabs, frozen middle layers, or restricted the relaxation of Zn surface atoms to perpendicular to the surface [16]. More accurate tilt angles of 10.7° and 10.1° were calculated with DFT-LDA and DFT-PBE, respectively, when thicker slabs were used and the atoms in all layers were fully relaxed, illustrating the importance of a fully converged model [16]. Here we study how PBE + U and DFT-HSE compare to earlier theoretical approaches in the modeling of the ZnO surface, and further analyze the character of its chemical bonding. It is also necessary to develop an accurate model of the Cu2O(111) surface. Schulz and Cox characterized the Cu2O(111) surface using LEED and X-ray and ultraviolet photoemission spectroscopies, leading to proposed models of an ideal stoichiometric O-terminated (1 × 1) surface and a reconstructed (√3 × √3)R30° surface with 1/3 monolayer of oxygen vacancies [42]. They did not report the nature of surface relaxation in either termination, prompting further examination of the structure of the ideal Cu2O(111) surface via theory. DFT-PBE calculations of the ideal surface showed negligible surface relaxation, with a slight contraction of the bonds at the surface and minimal extension of some subsurface bonds to create a more compact surface trilayer [19,43,44]. We use PBE + U in this study, as it showed greater accuracy than DFT-PBE in predicting the ground state properties of bulk Cu2O [29]. While it would have been best to compare the PBE + U model of the surface to DFT-HSE, this comparison is not feasible due to computational expense, as the Cu2O(111) slab is too large to be relaxed with the more expensive hybrid functional. Instead we analyze the Cu2O(111) surface structure predicted with the PBE + U model and compare it to earlier results with DFT-PBE. Very little is known about the Cu2O(111)/ZnOð1010Þ interface, as most previous work has focused on copper oxide coatings on the ZnO(0001) surface, probably because there is evidence that the O-terminated ZnO(0001) surface is the most catalytically active face in methanol synthesis from syngas [45]. Cu2O(111) overlayers have been experimentally observed on Zn-terminated ZnO(0001) [46,47], and DFT-PBE has been used to characterize the most stable Cu-oxide surface structures on ZnO(0001) [48]. This study will therefore provide insight into a previously uncharacterized interface. We first compare the performance of PBE + U and DFT-HSE for bulk and surface calculations of ZnO to evaluate the viability of PBE + U for modeling the Cu2O(111)/ZnOð1010Þ interface. Our investigation of the ZnOð1010Þ surface not only establishes a viable model for the ZnO sub-

d

z2

z1

strate to be used in the interface, but also contributes to understanding its unique bonding character and structural properties. We also use PBE + U to analyze the structure of the unsupported Cu2O(111) surface and to evaluate its stability. After we validate the performance of PBE + U and develop a suitable model for both the substrate and coating, we then study the energetics and electronic structure of the Cu2O(111)/ZnOð1010Þ interface for various coating thicknesses. 2. Methods

Fig. 1. Diagram of the surface geometry and independent structural parameters used to describe the distortion of the surface dimer on ZnOð1010Þ. Red and gray spheres represent the O and Zn ions, respectively.

The Vienna Ab-initio Simulation Package (VASP version 5.2.2) [49] was used to perform all DFT and DFT + U calculations. Blöchl's allelectron, frozen-core projector augmented wave (PAW) method [50]

64

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71

was used to represent nuclei and core electrons (an [Ar] core for both Cu and Zn, and a [He] core for O) and all PAW potentials were obtained from the VASP package, using the standard PAW potential for O. The formalism of Dudarev et al. [51] was used with the PBE XC functional [27,28] for DFT + U [25,26]. For calculations with the HSE functional [22–24], the screening parameter was set to the recommended value of 0.2 Å−1 [52]. All calculations were performed spin-polarized in order to allow for the possibility of localized dangling bonds to form at surfaces and interfaces. However, we find no net magnetization in any of the systems studied here, so in fact these particular cases could have been calculated without including spin-polarization. The ZnO unit cell is comprised of two Zn atoms and two O atoms arranged in the wurtzite crystal structure (space group P63mc, No. 186). Calculations for the ZnO unit cell used 64 bands and a planewave kinetic energy cutoff of 700 eV. A 4 × 4 × 3 Γ-point-centered k-point mesh was used (14 irreducible k-points), which converged the total energy to within 1 meV/atom and the band (eigenvalue) gap to within 5 meV. For DFT-HSE calculations, the full 4 × 4 × 3 k-point mesh was used to evaluate the Hartree–Fock kernel. The Brillouin zone was integrated using the tetrahedron method with Blöchl corrections [53]. The atomic positions and unit cell structure were optimized with both DFT-HSE and DFT + U, converged to a force threshold of 0.03 eV Å−1. Bulk moduli were calculated by fitting a computed energy-volume curve to the Murnaghan equation of state [54]. Surfaces and interfaces were studied by constructing slabs with 13 Å of vacuum separating surfaces from their periodic images. Slabs modeling the clean ZnOð1010Þ surface, containing one Zn atom and one O atom per layer, were either constructed from PBE + U or HSE bulk primitive cell geometries (U–J = 4 eV for PBE + U, based on results from bulk ZnO, vide infra), followed by full ionic relaxation with the corresponding method to a converged force threshold of 0.03 eV Å−1. Slab lattice constants parallel to the surface were kept fixed to theoretical bulk values. The number of layers in the clean ZnO slab was tested for convergence of surface properties before being used as the substrate for the interface. 64 bands were used in calculations of the six-layer slabs, 96 bands for the eight-layer slabs, and 128 bands for the 10- and 12-layers slabs. A Γ-point-centered k-point mesh of 4 × 3 × 1 was used in all cases. All other computational parameters were the same as in the bulk calculations. The slab modeling the Cu2O(111) surface was constructed from the PBE + U bulk primitive cell geometry (U–J = 6 eV, based on results from bulk Cu2O [29]). The slab was comprised of five trilayers, where each trilayer consists of a layer of oxygen atoms sandwiched between two layers of Cu atoms, corresponding to a total of 30 atoms. This slab thickness converged the surface energy to within 10 mJ/m2. 176 bands and a Γ-point-centered k-point mesh of 4 × 4 × 1 was used, which converged the total energy to within 1 meV/atom. The surface energy, γ, is obtained from a slab containing two identical surfaces, via γ¼

  1 N Eslab − s Ebulk ; 2A Nb

mismatch. The ZnO ð1010Þ surface has orthogonal lattice vectors, where u =3.252 Å and v = 5.222 Å when constructed from the PBE + U bulk geometry. The Cu2O(111) surface is a parallelogram with an angle of 120° and lattice vectors u = v = 6.044 Å, obtained from previous PBE + U calculations [29]. To match the ZnOð1010Þ surface, the Cu2O surface vectors were redefined to be orthogonal (shown in Fig. 2), where u = 6.044 Å and v = 10.469 Å. We introduce a set of strain variables which have been defined for the matching of orthogonal cells [55]:

nl

δ1 ¼

la1 −nb1 ka −mb2 mk ; δ2 ¼ 2 nb1 mb2

ð2Þ

where k, l, m, and n are integers multiplying primitive cells in each lattice direction, a1 and a2 are the lengths of the basis vectors spanning the Cu2O unit cell, and b1 and b2 are the lengths of the basis vectors spanning the ZnO unit cell (Fig. 2). These strain variables are minimized with respect to k, l, m, and n for each of the two possible orientations of the lattice vectors, constrained to a small enough periodicity to maintain computational feasibility. The optimal interface unit cell had the orientation a1 = 6.044 Å, a2 = 10.469 Å, b1 = 3.252 Å, and b2 = 5.222 Å, with l = 1, k = 1, n = 2, and m = 2, which resulted in a −7.1% strain in the b1 direction and a 0.24% strain in the b2 direction. This level of strain is higher than optimal but it is impossible to reduce further without the model becoming computationally unwieldy. (Further reduction of the magnitude of the strain in the b1 direction would have necessitated l = 4 and n = 7, yielding a strain of +6.2%. In the model of the interface with the thickest coating, this cell would comprise 464 atoms.) With this level of periodicity, there were 12 atoms per Cu2O trilayer (where each trilayer consists of eight Cu atoms sandwiched by two layers of two O atoms) and eight atoms per ZnO layer, totaling 124 atoms in the interface with the thickest coating, maintaining computational feasibility. We considered a number of lateral positions for the overlayer to identify the alignment that enables favorable chemical bonding between atoms at the interface. This allows for maximal chemical interaction energy between the two surfaces. Lateral translations of a single Cu2O overlayer in its bulk structure 1.980 Å above the bulk-terminated ZnO surface layer were sampled along each direction at defined intervals, calculating the total energy without structural optimization to determine the lowest energy initial structure as a starting point for building interfaces of all thicknesses. The ZnO substrate consisted of eight atomic layers, chosen based on its convergence of surface properties for the clean surface (vide infra). The number of Cu2O overlayers was then varied from one to five trilayers to study the effect of the coating thickness on adhesion energies and electronic properties.

ð1Þ

where Eslab is the total energy of a stoichiometric slab, Ebulk is the total energy of a bulk formula unit, Ns is the number of atoms in the slab, Nb is the number of atoms in the bulk formula unit, A is the unit surface area, and the factor 1/2 is used because the slab has two surfaces. To construct the Cu2O(111)/ZnOð1010Þ interface, the interface unit cell must be defined to minimize lattice mismatch while remaining both computationally feasible and experimentally relevant. The interface is assumed to be coherent, enforced by periodic boundary conditions, and is kept fixed at ZnO bulk lattice parameters to mimic a thin Cu2O coating that adheres epitaxially to a semi-infinite substrate. This results in a tensile or compressive stress in the Cu2O overlayer, which can be reduced by periodically repeating cells to minimize lattice

b2

a2

b1 a1 Cu2O overlayer

ZnO substrate

Fig. 2. Interface lattice matching of the Cu2O overlayer unit cell spanned by the vectors a1 and a2 and the ZnO substrate unit cell spanned by the vectors b1 and b2. Red, gray, and pink spheres represent O, Zn, and Cu atoms, respectively.

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71 Table 1 Bulk properties of wurtzite ZnO, calculated with DFT-HSE and PBE + U (with varying values of U–J) and compared to experiment. a and c are the unit cell lattice parameters. u is an internal coordinate of the wurtzite structure, where u is the length of the Zn\O bond parallel to the c-axis divided by the c lattice parameter. B0 is the bulk modulus, Eg is the eigenvalue gap from theory or the optical gap from experiment, and the final column is the energy at the center of the Zn 3d band. Functional a (Å)

c (Å)

u

B0 (GPa)

Eg (eV) Zn 3d (eV)

PBE + PBE + PBE + PBE + HSE Exp.

5.249 5.222 5.177 5.120 5.233 5.207–5.210a

0.3808 0.3809 0.3809 0.3808 0.3814 0.3825a

129 130 132 133 142 136–183a

1.01 1.28 1.57 1.90 2.50 3.30b

a b c

2 4 6 8

3.276 3.252 3.227 3.191 3.267 3.248–3.250a

−5.40 −5.96 −6.61 −7.31 −5.92 −7.5 ± 0.2c

Ref. [58–61]. Ref. [62]. Ref. [63].

65

Table 3 Bader charges on the individual atoms of the ZnOð1010Þ slab, derived from PBE + 4 and DFT-HSE charge densities. The number in the atom name denotes the layer in which the atoms are located, with 1 representing the surface layer and 4 representing the middle layer. Bader charges from the bulk calculations (O-bulk and Zn-bulk) are reported for comparison. Atom

PBE + 4 charge

DFT-HSE charge

O1 Zn1 O2 Zn2 O3 Zn3 O4 Zn4 O-bulk Zn-bulk

−1.168 1.169 −1.195 1.210 −1.216 1.202 −1.206 1.206 −1.209 1.209

−1.257 1.259 −1.288 1.302 −1.307 1.292 −1.296 1.295 −1.306 1.306

The contributions to Eadh can be further divided into chemical interaction and relaxation energy components through To examine the stability of the interface, we calculate the ideal work of separation, Wsep, defined as Eadh ¼

W sep ¼

EZnO þ E′Cu2 O −ECu2 O=ZnO A

;

where EZnO is the energy of the clean, relaxed ZnO substrate, ECu2 O is the energy of the unsupported, relaxed Cu2O coating at the substrate (ZnO) lattice parameters, EZnO=Cu2 O is the energy of the ZnO/Cu2O interface, and A is the area of the interface. Another measure of interface stability is the adhesion energy, Eadh, defined as EZnO þ ECu2 O −ECu2 O=ZnO A

A

;

ð4Þ

which differs from Wsep only in ECu2 O , which is the energy of the unsupported, relaxed Cu2O coating at bulk Cu2O lattice parameters.

;

ð5Þ

ð3Þ 0

Eadh ¼

      EZnO −EZnO;int þ ECu2 O −ECu2 O;int þ EZnO;int þ ECu2 O;int −ECu2 O=ZnO

where EZnO,int and ECu2 O;int are the energies of the clean ZnO substrate and the unsupported Cu2O coating, respectively, frozen in the structure of the interface. This groups the components of the adhesion energy into three contributions: the penalties for restructuring the relaxed substrate and overlayer to form the interface, defined as the loss of the relaxation energies EZnO,relax and ECu2 O;relax , and the gain in the chemical interaction between the substrate and coating at the interface, ECu2 O=ZnO;inter , such that Eadh ¼ −

EZnO;relax þ ECu2 O;relax þ ECu2 O=ZnO;inter A

:

ð6Þ

Wsep, Eadh, EZnO,relax, ECu2 O;relax , and ECu2 O=ZnO;inter were calculated for all overlayer thicknesses.

Table 2 Properties of the ZnOð1010Þ surface calculated with DFT-HSE and PBE + 4 at various slab thicknesses, compared to other theoretical methods and experiment. Quantities reported are defined in Fig. 1. Vacant table entries indicate unreported data in previous studies. Method (# of layers)

Surface energy (J/m2)

z1 (Å)

z2 (Å)

θ (°)

d (Å)

Middle layer θ (°)

Middle layer d (Å)

HSE(6) HSE(8) HSE(10) HSE(12) PBE + 4(6) PBE + 4(8) PBE + 4(10) PBE + 4(12) LDA(8)a LDA(20)b PBE(20)b B3LYP(8)c HF + corr(4)d TB(8)e Exp.

0.98 0.99 0.99 0.98 0.90 0.91 0.90 0.90 – 1.15 0.80 1.15 1.35 – –

0.620 0.633 0.636 0.638 0.608 0.620 0.623 0.625 0.623 0.592 0.600 0.626 0.678 0.53 0.54 ± 0.1f

0.948 0.933 0.926 0.925 0.954 0.938 0.932 0.933 0.738 0.931 0.928 0.777 0.758 1.10 0.94 ± 0.1f

10.2 9.3 9.0 8.9 10.8 9.9 9.6 9.6 3.6 10.7 10.1 5.2 2.5 17.2 11.5 ± 5f

1.856 1.855 1.856 1.855 1.848 1.848 1.849 1.849 1.835 1.822 1.862 1.905 1.839 1.926 2.010f

3.8 1.9 1.0 0.6 3.7 1.8 1.1 0.6 – ~0 ~0 – – – 0

1.983 1.998 1.993 1.998 1.979 1.991 1.986 1.988 – 1.953 2.006 – – – 1.989–1.990g

a b c d e f g

Ref. [41]. Ref. [16]. Ref. [14]. Ref. [40]. Ref. [39]. Ref. [37]. Ref. [58–61].

66

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71

Calculations for the interfaces used 480 bands for one and two Cu2O overlayers, 560 bands for three and four Cu2O overlayers, and 640 bands for five Cu2O overlayers. 80, 160, 240, 320, and 400 bands were used for calculations of one, two, three, four, and five trilayers, respectively, of the unsupported Cu2O coating. 320 bands were used for the clean ZnO substrate. A Γ-point-centered k-point mesh of 2 × 2 × 1 was used in all cases (chosen based on scaling the converged k-point grids from earlier bulk unit cell calculations), and all other computational parameters were the same as for bulk ZnO.

side view 1.807Å

1.910 Å

3. Results and discussion

top view 3.1. Bulk and surface properties of ZnO Bulk properties of wurtzite ZnO were calculated with DFT-HSE and PBE + U to evaluate the accuracy of each functional and to determine if PBE + U can be used as a reliable and inexpensive alternative to DFT-HSE. Table 1 shows the lattice parameters, bulk modulus, eigenvalue gap, and the energy of the center of the Zn 3d band calculated using DFT-HSE and PBE + U with varying values of U–J. In comparison to experiment, DFT-HSE overestimates the lattice parameters, agrees well with the experimental bulk modulus, and underestimates the internal coordinate u, the band gap, and the energy of the center of the Zn 3d band. Our calculated lattice parameters using DFT-HSE differ by ~0.01 Å from those previously reported [35], likely due to differences in basis sets, pseudopotentials, and other numerical settings. For PBE + U, the lattice parameters decrease with increasing values of U–J, while the bulk modulus, band gap, and Zn 3d energy all increase in absolute magnitude with increasing U–J. The u parameter remained essentially constant for all values of U–J. The lattice parameters are closest to experiment for a U–J value of 4 eV; however, a value of 8 eV or greater is needed for an accurate Zn 3d band energy and a band gap closer to the experimental value. We chose to use a U–J of 4 eV (denoted PBE + 4) for all further calculations to optimize structural accuracy, as the band gap would still be significantly underestimated even at higher values of U–J. A comparison of PBE + 4 and DFT-HSE shows that PBE + 4 is just as good as DFT-HSE for structural properties, but that HSE better agrees with experiment for the band gap, indicating that HSE is still the best functional for bulk calculations. However, the failure of DFT methods to accurately predict the band gap indicates that accurate analysis of the band structure requires a higher level of theory such as the GW approximation [56,57]. Partial charges have previously been calculated by Uddin and Scuseria using Mulliken population analysis of the real space density matrix, resulting in charges of +0.69, +0.73, +0.77, and +0.88 on the Zn atom with LDA, PBE, TPSS, and HSE functionals, respectively [35]. This relatively low charge separation had been explained as indicative of the partial covalency of ZnO. Because Mulliken populations are dependent on the basis sets used, we use Bader analysis [64] as an unbiased means to calculate the charge separation with PBE + 4 and HSE functionals, resulting in charges of +1.21 and +1.31, respectively, on Zn. Thus the Bader analysis suggests that the Zn\O bonds are more ionic than previously thought, though still partially covalent in character. Having established PBE + 4 as a reliable alternative to DFT-HSE for bulk structural properties, we next compared the performance of both methods in calculating surface properties of ZnOð1010Þ (Table 2). Surface properties were calculated for slabs with six, eight, 10, and 12 layers to test for convergence with respect to slab thickness. The bond distances and tilt angles of middle layer dimers are one metric of convergence with respect to slab thickness, as the middle layer is expected to exhibit bulk properties. As slab thickness increased, DFT-HSE and PBE + 4 structures both showed some convergence of the middle layer toward bulk character. The surface energy and surface dimer bond length did not change significantly with slab thickness, but as

2.388 Å

Fig. 3. Relaxed geometries of the Cu2O(111) surface, showing side and top views of the ideal (1 × 1) surface. Red and pink spheres represent oxygen and copper, respectively. In the top view, all subsurface atoms are grayed, with the darker gray representing oxygen.

the number of layers increased, the surface dimer tilt angle, θ, decreased. The change in θ as a function of slab thickness is principally due to changes in z2 (Fig. 1), showing that thicker slabs allow for greater downward displacement of the O atom. Both PBE + 4 and DFT-HSE compare well to the DFT-LDA and DFT-PBE calculations performed with 20-layer slabs [16] and are a distinct improvement over the earlier theoretical models using thinner slabs and DFT-B3LYP [14], TB [39], HF [40], or DFT-LDA [41], validating the importance of using a model with a well-converged geometry. The 20-layer slabs exhibited more complete convergence, with almost no middle layer tilt angle, but we expect that a substrate thickness of eight layers is a sufficient model based on its level of convergence. The surface dimer tilt angles calculated with DFT-HSE and PBE + 4 are within the experimental range, but the predicted dimer bond lengths are slightly lower than experiment. The negligible differences between the predictions of DFT-HSE and PBE + 4 validate that PBE + 4 can be used as an accurate method to Table 4 Bader charges on the individual atoms of the five-layer Cu2O(111) slab from PBE + 6 charge densities. The number in the atom name denotes the layer in which the atoms are located, with 1 representing the surface layer and 3 representing the middle layer. O1-CUS and Cu1-CUS are the coordinatively unsaturated surface atoms. Bader charges from the bulk calculation (denoted O-bulk and Cu-bulk) are reported for comparison. Atom

Bader charge

O1-CUS Cu1-CUS O1 Cu1 O2 Cu2 O3 Cu3 O-bulk Cu-bulk

−0.953 0.368 −1.004 0.535 −0.998 0.497 −0.998 0.496 −1.010 0.505

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71

a

b

oxygen and the coordinatively unsaturated copper lengthens to 1.910 Å. The predicted structure differs from previous DFT-PBE predictions [19,43,44] in its breaking of the bulk-like symmetry of the surface, which we find is essential to find the true lowest energy surface. The PBE + U surface energy for Cu2O(111) is 0.67 J/m2, which is slightly lower than previous DFT-PBE values of 0.71 and 0.76 J/m2 [43,44]. Bader analysis was used to analyze the charge distribution throughout the slab (Table 4). The charges of the coordinatively unsaturated copper and oxygen atoms are slightly reduced in comparison to bulk charges, but overall, ionic charges do not vary significantly between layers, as is typical of nonpolar surfaces. The surface unsaturation of copper causes slightly reduced ionicity, which indicates that the unsaturated copper atom may play an essential role in the surface chemistry of Cu2O(111).

z

Fig. 4. Two orientations for the Cu2O overlayer, where the overlayer orientation in a and b differ by a rotation of 180° about the z-axis.

calculate the surface structural properties of ZnO. For all later calculations of the Cu2O/ZnO interface, we therefore use PBE + U with a U–J value of 4 eV and a substrate thickness of eight layers. Bader analysis was used once again to analyze the partial charges of the atoms in each layer of the eight-layer slab (Table 3). Using Mulliken charges and bond overlap populations, Wander and Harrison had concluded that the surface dimer bond is less ionic (with a difference of 0.079 between the charges on the surface dimer ions and those in the bulk) and is better characterized as a covalent bond [14]. However, our Bader charges indicate that the surface dimer charges differ from the bulk charges only by 0.041 for PBE + 4 and 0.049 for DFT-HSE, indicating that the difference in ionicity is quite minimal. Based on Bader charge analysis, the surface dimer bond is best characterized as a polar covalent bond that is in fact more ionic than covalent.

3.2. Surface properties of Cu2O The bulk properties of Cu2O have been fully explored previously [29], and so we limit our discussion here to characterizing the Cu2O(111) surface. In our PBE + U model of the ideal Cu2O(111) surface, we observed significant relaxation from bulk-like termination (Fig. 3), where a surface copper dimer forms with a bond length of 2.388 Å. The surface bond between the linearly coordinated copper and the coordinatively unsaturated oxygen contracts slightly from the bulk length of 1.851 Å to 1.807 Å, while the bond between a subsurface

a

67

3.3. Adhesion of Cu2O(111)/ZnOð1010Þ We first investigate how the interface energy depends on the lateral position of the Cu2O overlayer on the ZnO substrate, seeking to optimize the chemical interaction between the two layers. A single Cu2O trilayer was used as a test case, and total energies were calculated without structural optimization (i.e., both the substrate and overlayer were fixed at bulk-like atomic positions). Two possible orientations exist for the Cu2O overlayer, differing by a rotation of 180° about the z-axis (Fig. 4), so both orientations were tested. Due to the symmetry and periodicity of the overlayer and substrate, lateral shifts only needed to extend to 0.25 and 0.5 of the b1 and b2 directions of the interface lattice vectors. In the b1 direction, three points were sampled at intervals of 0.125 of the interface lattice vector, or 0.813 Å. In the b2 direction, five points were sampled at intervals of 0.1 of the interface lattice vector, or 1.044 Å. Overall, a total of 15 overlayer lateral positions were sampled for each orientation, and the distribution of total energies is shown in Fig. 5. The optimal alignments for orientations a and b are identified as the (0, 0) and (0, 0.1) positions, respectively. The structures of these two configurations were subsequently optimized, resulting in a total energy for orientation b that is 0.325 eV lower than orientation a, indicating that the relaxed structure from orientation b is the lowest energy structure. Fig. 6 shows the optimal overlayer structure from orientation b (the overall lowest energy structure), illustrating the alignment of the surfaces to allow for interfacial bonding between the O atoms of Cu2O overlayer and the Zn atoms of the substrate as well as interactions between the Cu atoms of the overlayer and the O atoms of the substrate. These interfacial bonds allow the ZnO surface atoms (Zn1, Zn2, O3, and

b

Fig. 5. PBE + U total energy (eV) of the unrelaxed interface as a function of lateral alignment for the two orientations a and b shown in Fig. 4. The x and y axes represent fractional shifts along the b1 and b2 directions, respectively. The lowest-energy alignments for orientations a and b are identified as the (0, 0) and (0, 0.1) shifts, respectively.

68

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71 Zn2

O3

O4

Cu3

a

b

O2

Cu4 O1

b2 Cu1

Zn1

Cu2

b1

b1

b2

Fig. 6. The optimal configuration for a single Cu2O overlayer on the ZnO surface, showing a top view (left) of only the ZnO surface dimers and the first Cu2O overlayer, and an additional side view (right) of the interface. All unique atoms are labeled in the top view. Red, gray, and pink spheres represent O, Zn, and Cu atoms, respectively.

O4) and the coordinatively unsaturated atoms of the Cu2O surface (O1 and Cu3) to regain their bulk coordination, contributing to the adhesive strength of the interface. It turns out that the single Cu2O overlayer does not undergo significant reorganization from the bulk structure, and so the interfacial bonds identified here also characterize the interactions occurring in interfaces with thicker coatings. Orientation b with a (0, 0.1) shift was used for the base layer when constructing coatings of increasing thickness. The number of Cu2O overlayers was varied from one to five trilayers, and the structure of each interface was fully optimized. Structural optimization did not result in any significant rearrangement of atoms from their bulk positions at the interface. Wsep, Eadh, EZnO,relax, ECu2 O;relax, and ECu2 O=ZnO;inter were calculated for each coating thickness (Table 5). Eadh is 0.85 ± 0.07 J/m2, and is found to vary only slightly as a function of coating thickness. This adhesion energy is less than the cleavage energies (i.e., twice the surface energies) of Cu2O (1.33 J/m2) and ZnO (1.80 J/m2), indicating that the Cu2O(111)/ZnOð1010Þ interface is only weakly stable. ECu2 O=ZnO;inter for all interfaces are all within 0.05 J/m2, indicating that interfacial bonding is largely localized, with little long-range contribution to adhesion. This also validates the use of a single Cu2O overlayer in the earlier optimization of the interface alignment. The variation in Eadh is therefore predominantly due to differences in EZnO,relax and ECu2 O;relax . The most stable interface has a three-layer Cu2O coating whose increased stability is due to its lower energy cost of reorganization. Wsep also has a small variation in energies, excluding an anomalous drop in the energy for the two-layer coating. The difference between Wsep and Eadh is solely due to the strain on the Cu2O coating and is below 0.27 J/m2 for most thicknesses. The atypical decrease from Eadh to Wsep for the two-layer coating results from a reorganization of the unsupported Cu2O slab at ZnO lattice parameters to a crystal structure different than the cuprite structure of Cu2O (Fig. 7), which reduces its energy despite the additional strain.

Table 5 PBE + U ideal work of separation (Wsep), adhesion energy (Eadh), relaxation energies (EZnO,relax, and ECu2 O;relax ), and interaction energies (ECu2 O=ZnO;inter ) for different coating 2

thicknesses of the Cu2O(111)/ZnOð1010Þ interface (J/m ).

Fig. 7. Top view of the equilibrium structure of the two-layer Cu2O slab relaxed at (a) Cu2O lattice parameters and (b) ZnO lattice parameters, illustrating the unique reorganized structure at ZnO lattice parameters.

The bond lengths between interacting atoms at the interface are shown in Table 6. One of each of the Zn\O and O\Cu interfacial bond lengths are close to the PBE + U bond lengths in bulk ZnO (1.978 and 1.989 Å) and Cu2O (1.851 Å), indicating that strong bonding may occur through these interactions. This is verified by a plot of the electron density difference between the interface and the separated slabs frozen at the corresponding interfacial geometry (Fig. 8), which shows an accumulation of charge along these interfacial bonds. There is no change in the charge above or below the first layers of the coating and substrate, again illustrating that interfacial bonding is predominantly localized. Bader analysis was also used to calculate the charges of atoms in the interface and in the separated slabs frozen at the interfacial geometry (Table 7). The charges of the atoms at the interface do not change significantly from the separated slabs, indicating that interfacial bonding is not accompanied by substantial charge transfer. Additionally, the consistency of Bader charges through varying coating thickness shows that the character of interfacial bonding remains relatively constant for more than one overlayer. Only charges of atoms at the interface changed upon interface formation, consistent with the localized nature of interfacial interactions, although there was also a slight increase in negative charge on a single O atom in the second trilayer (denoted O1b, as it occupies the same position as O1, albeit in the second layer). The minimal impact on the charges in the Cu2O coating indicates that ZnO potentially stabilizes the Cu+ ions without changing their oxidation states. Finally, to analyze the impact of the ZnO substrate on the electronic structure of the Cu2O coating, the site-projected local densities of states (LDOS) were plotted for each Cu2O layer in each interface (Fig. 9). The LDOS of the unsupported five-layer Cu2O slab are shown for comparison, where the middle layer (layer 3) may be considered bulk-like, while the surface layer (layer 1) represents the ideal electronic structure of the Cu2O surface. One impact of the ZnO substrate on the Cu2O electronic structure is the appearance of states between −8.0 and −7.0 eV in the first layer of most coatings. These states are due to mixing with Zn 3d states at these energies. Such states do not persist beyond the first layer of each coating, once again indicating that interfacial bonding is highly localized. Another impact of the ZnO substrate on the Cu2O Table 6 PBE + U distances (Å) between interacting atoms at the interface, as labeled in Fig. 6, as a function of Cu2O overlayer thickness.

# Cu2O layers

Wsep

Eadh

ECu2 O;relax A

EZnO;relax A

ECu2 O=ZnO;inter A

# Cu2O layers

Zn1–O1

Zn2–O2

O3–Cu3

O4–Cu4

1 2 3 4 5

1.009 0.245 1.148 1.003 1.095

0.908 0.783 0.911 0.823 0.825

0.306 0.539 0.424 0.460 0.478

0.284 0.200 0.189 0.192 0.190

−1.498 −1.523 −1.524 −1.475 −1.494

1 2 3 4 5

2.029 1.954 1.960 1.971 1.964

2.733 2.880 3.042 2.825 2.924

1.912 1.928 1.893 1.899 1.899

2.199 2.129 2.263 2.237 2.245

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71

69

e d c b a

Fig. 8. Isosurfaces of the PBE + U electron density difference between each interface and its separated slabs frozen at the interfacial geometry. The isosurface level is set to 0.005 e− Å−3, and yellow and blue represent an increase and decrease in charge density, respectively. Interfaces increase in thickness from one overlayer in (a) to five layers in (e).

Table 7 PBE + U Bader charges of atoms at the interface, with differences from the individual slabs (frozen at the interfacial geometry) shown in parentheses. The unique atoms presented are defined in Fig. 6; here, O1b is an oxygen occupying the same position as O1, albeit in the second trilayer. # of Cu2O O1 overlayers 1 2 3 4 5

−1.06 (−0.05) −1.04 (−0.06) −1.04 (−0.06) −1.05 (−0.06) −1.05 (−0.06)

O2

O1b

Cu1

Cu2

Cu3

Cu4

Zn1

Zn2

O3

O4

−0.97 (0.00) −1.01 (0.00) −0.99 (0.00) −1.01 (0.00) −1.02 (0.01)

N/A −1.01 (−0.01) −1.00 (−0.02) −1.00 (−0.02) −1.00 (−0.02)

0.54 (−0.04) 0.48 (−0.03) 0.49 (−0.02) 0.49 (−0.02) 0.49 (−0.02)

0.54 (−0.04) 0.48 (−0.03) 0.49 (−0.02) 0.49 (−0.02) 0.49 (−0.02)

0.35 (0.05) 0.50 (0.04) 0.50 (0.03) 0.50 (0.04) 0.50 (0.04)

0.61 (0.07) 0.57 (0.07) 0.57 (0.07) 0.57 (0.06) 0.58 (0.06)

1.21 (0.06) 1.21 (0.05) 1.21 (0.05) 1.22 (0.05) 1.20 (0.06)

1.09 (−0.06) 1.14 (−0.03) 1.12 (−0.04) 1.15 (−0.02) 1.13 (−0.03)

−1.17 (0.00) −1.19 (0.00) −1.17 (0.01) −1.18 (0.00) −1.17 (0.00)

−1.15 (0.02) −1.17 (0.00) −1.16 (0.01) −1.17 (0.01) −1.16 (0.00)

coating is the creation of small gaps immediately below the Fermi level. This effect is most evident in the layer at the interface (layer 1), although by a coating thickness of four layers, this effect on the layer at the interface is diminished. In the thinner layers (one through three layers), this gap-like electronic structure below the Fermi level persists even until the surface layer, and it is only by a thickness of four layers that the surface layer (layer 4) reproduces the electronic structure of the unsupported surface layer (layer 1). This indicates that the effect of the ZnO substrate on the electronic structure of the coating is somewhat diminished at a thickness of greater than three layers. Regardless, there is still a lasting effect on the density of states, which is evident in the impact on the band gap (Table 8). Even in the thickest coating, the ZnO substrate lowers the PBE + U Cu2O band gap from 0.86 eV to 0.31 eV. A comparison between the band gaps of unsupported Cu2O with its native lattice vectors and the band gaps of unsupported Cu2O under strain of the ZnO lattice vectors shows that the impact of the strain on the Cu2O band gap is minimal, and it is predominantly the influence of the substrate that decreases the band gap. (Note that the band gap of the two-layered Cu2O at ZnO lattice vectors increases significantly because of the significant structural reorganization under strain discussed earlier.) However, because PBE + U underestimates the fundamental gap of Cu2O, we can only derive a qualitative conclusion regarding the reduction of the band gap by the ZnO substrate. The reduction of the Cu2O band gap by the ZnO substrate may be beneficial in solar energy applications by increasing absorption of the solar spectrum, as long as the band edges bridge the reaction redox potentials to preserve the thermodynamic feasibility of photocatalysis. However, the effect of the ZnO substrate on the stability of the Cu2O overlayer against photodecomposition is inconclusive, as it cannot be analyzed from a purely thermodynamic perspective. The cathodic and

anodic decomposition potentials of Cu2O lie very close together and well within the gap, and it is impossible to absolutely protect the material from photodecomposition by reducing the band gap, especially without destroying its ability to photocatalyze CO2 reduction [65]. Therefore, modification of the band edge potentials will not signify greater catalytic stability. Rather, any improvement to photocatalytic stability by using a ZnO support will likely be due to changes in reaction kinetics, which requires further study. For instance, a similar argument based on competing reaction kinetics was used to explain the absence of catalyst photodecomposition in the photoreduction of CO2 on hybrid CuO–Cu2O nanorods [11].

4. Conclusions PBE + U has been established as an alternative for HSE in accurate structural predictions of bulk wurtzite ZnO, where a U–J value of 4 eV best reproduces experimental structures. Bader analysis revealed the significant ionic character of ZnO. Both PBE + U and DFT-HSE perform well in calculating properties of the ZnOð1010Þ surface, in agreement with some earlier DFT-LDA and DFT-PBE calculations, showing that slab thickness and geometry convergence have a greater impact on surface properties than the DFT method used. The PBE + U surface energy is 0.90 J/m2. Bader analysis of the electron density indicates that charge separation in the surface dimer differs only slightly from bulk ionicity. The Cu2O(111) surface was examined with PBE + U (U–J = 6 eV), which showed that the surface relaxes from bulk-like termination to form copper dimers and some bond lengths change to make the surface slightly more compact. The surface is quite stable with an energy of 0.67 J/m2. Bader analysis of the electron density shows that the

70

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71

1 Cu2O layer

6

Cu 3d Cu 4s O 2p Zn 3d

(1)

3 Cu2O layers

(1)

Cu 3d Cu 4s O 2p Zn 3d

4

6

(1)

Cu 3d Cu 4s O 2p Zn 3d

4

DOS

4

2 Cu2 O layers

6

2

0 -8

-6

-4

-2

0

2

4

2

2

0

0

6

Energy (eV) 6

6

(1)

Cu 3d Cu 4s O 2p Zn 3d

4

6

(2)

5 Cu2O layers 4

4

2

2

(2)

2 0

0 -8

-6

-4

-2

0

2

4

6

Energy (eV)

0

6 6

(2)

4

(3)

4Cu2O layers

6

(1)

Cu 3d Cu 4s O 2p Zn 3d

4

4

2 2

2 0 -8

0

6

DOS

-6

-4

6

(3)

4

4

2

2

2

0

0

0

6

6

4

4

4

2

2

2

0

0

0

6

(5) 4

4

4

2

2

2

-8

-6

-4

-2

0

Energy (eV)

2

4

6

4

6

0 -8

Cu 3d Cu 4s O 2p

(2)

6

(4)

0

2

(1)

6

(3)

6

0

Unsupported 5-layer Cu2O slab

6

(2)

4

(4)

-2

Energy (eV)

0

(3)

0 -6

-4

-2

0

Energy (eV)

2

4

6

-8

-6

-4

-2

0

Energy (eV)

2

4

6

L.I. Bendavid, E.A. Carter / Surface Science 618 (2013) 62–71 Table 8 PBE + U band gaps (eV) of unsupported Cu2O relaxed at Cu2O lattice vectors, unsupported Cu2O relaxed at ZnO lattice vectors, and ZnO-supported Cu2O as a function of coating thickness. Coating thickness (# layers)

Unsupported Cu2O, Cu2O lattice vectors

Unsupported Cu2O, ZnO lattice vectors

ZnO-supported Cu2O

1 2 3 4 5

1.21 1.06 1.00 0.98 0.86

0.69 1.52 0.88 0.78 0.76

0.44 0.31 0.36 0.36 0.31

coordinatively unsaturated atoms at the surface have reduced charges, but overall the charge distribution does not exhibit a large variation across layers. The Cu2O(111)/ZnOð1010Þ interface has been identified as a weakly stable interface, with an adhesion energy of 0.85 ± 0.07 J/m2. The interface is stabilized by localized chemical interactions between Zn ions of the ZnO surface and O ions of the Cu2O surface, as well as O ions of the ZnO surface and Cu ions of the Cu2O surface. A slight accumulation of charge is observed along these interfacial bonds. The most stable Cu2O coating contained three trilayers, which is also the maximum thickness for which the ZnO substrate will have a significant impact on the Cu2O electronic structure. Regardless, the ZnO substrate reduces the Cu2O band gap for all coating thicknesses. While this study helps to elucidate the stability, chemical interactions, and electronic structure of the Cu2O(111)/ZnOð1010Þ interface, further work must be done to examine the impact of the ZnO substrate on chemical reactions occurring on the Cu2O(111) surface. Specifically, reaction kinetics are crucial in evaluating catalyst stability against photodecomposition. Acknowledgments E.A.C. acknowledges the support of the Air Force Office of Scientific Research and the Department of Energy, Basic Energy Sciences for funding and the DoD High Performance Computing Modernization Program at the NAVY, AFRL, and ERDC DSRC for supercomputer resources. L.I.B. acknowledges support as a National Science Foundation Graduate Fellow. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.susc.2013.07.027. References [1] S.L. Meisel, J.P. McCullough, C.H. Lechthaler, P.B. Weisz, Chemtech 2 (1976) 86. [2] C.D. Chang, C.D. Chang, Production of Gasoline Hydrocarbons, U.S. Patent 3928483, 1975. [3] F.G. Dwyer, F.V. Hanson, A.B. Schwartz, Conversion of Methanol to Gasoline Product, U.S. Patent 4035430, 1977. [4] K. Klier, Adv. Catal. 31 (1982) 243. [5] J.B. Bulko, R.G. Herman, K. Klier, G.W. Simmons, J. Phys. Chem. 83 (1979) 3118. [6] Y. Kanai, T. Watanabe, T. Fujitani, T. Uchijima, J. Nakamura, Catal. Lett. 38 (1996) 157. [7] E.I. Solomon, P.M. Jones, J.A. May, Chem. Rev. 93 (1993) 2623. [8] J. Frese, J. Electrochem. Soc. 138 (1991) 3338.

71

[9] M. Le, M. Ren, Z. Zhang, P.T. Sprunger, R.L. Kurtz, J.C. Flake, J. Electrochem. Soc. 158 (2011) E45. [10] M. Hara, T. Kondo, M. Komoda, S. Ikeda, J.N. Kondo, K. Domen, M. Hara, K. Shinohara, A. Tanaka, Chem. Commun. (1998) 357. [11] G. Ghadimkhani, N.R. de Tacconi, W. Chanmanee, C. Janaky, K. Rajeshwar, Chem. Commun. 49 (2013) 1297. [12] M.F. Chung, H.E. Farnsworth, Surf. Sci. 22 (1970) 93. [13] A. Wander, N.M. Harrison, Surf. Sci. 468 (2000) L851. [14] A. Wander, N.M. Harrison, Surf. Sci. 457 (2000) L342. [15] A. Wander, F. Schedin, P. Steadman, A. Norris, R. McGrath, T.S. Turner, G. Thornton, N.M. Harrison, Phys. Rev. Lett. 86 (2001) 3811. [16] B. Meyer, D. Marx, Phys. Rev. B 67 (2003) 035403. [17] V.E. Henrich, P.A. Cox, The Surface Science of Metal Oxides, Cambridge University Press, 1996. [18] L.I. Bendavid, E.A. Carter, (2013) (submitted for publication). [19] A. Soon, M. Todorova, B. Delley, C. Stampfl, Phys. Rev. B 75 (2007) 125420. [20] A. Soon, M. Todorova, B. Delley, C. Stampfl, Phys. Rev. B 76 (2007) 129902. [21] A. Önsten, M. Göthelid, U.O. Karlsson, Surf. Sci. 603 (2009) 257. [22] J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118 (2003) 8207. [23] J. Heyd, G.E. Scuseria, J. Chem. Phys. 120 (2004) 7274. [24] J. Heyd, G.E. Scuseria, J. Chem. Phys. 121 (2004) 1187. [25] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [26] S.L. Dudarev, A.I. Liechtenstein, M.R. Castell, G.A.D. Briggs, A.P. Sutton, Phys. Rev. B 56 (1997) 4900. [27] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [28] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 78 (1997) 1396. [29] L.Y. Isseroff, E.A. Carter, Phys. Rev. B 85 (2012) 235142. [30] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. [31] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [32] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [33] J. Tao, J.P. Perdew, V.N. Staroverov, G.E. Scuseria, Phys. Rev. Lett. 91 (2003) 146401. [34] V.N. Staroverov, G.E. Scuseria, J. Tao, J.P. Perdew, Phys. Rev. B 69 (2004) 075102. [35] J. Uddin, G.E. Scuseria, Phys. Rev. B 74 (2006) 245115. [36] C.A. Swarts, W.A. Goddard, T.C. McGill, J. Vac. Sci. Technol. 17 (1980) 982. [37] C.B. Duke, R.J. Meyer, A. Paton, P. Mark, Phys. Rev. B 18 (1978) 4225. [38] H. Morkoç, Ü. Özgür, Zinc Oxide: Fundamentals, Materials and Device Technology, Wiley-VCH, 2009. [39] Y.R. Wang, C.B. Duke, Surf. Sci. 192 (1987) 309. [40] J.E. Jaffe, N.M. Harrison, A.C. Hess, Phys. Rev. B 49 (1994) 11153. [41] P. Schröer, P. Krüger, J. Pollmann, Phys. Rev. B 49 (1994) 17092. [42] K.H. Schulz, D.F. Cox, Phys. Rev. B 43 (1991) 1610. [43] M.M. Islam, B. Diawara, V. Maurice, P. Marcus, J. Mol. Struct. (THEOCHEM) 903 (2009) 41. [44] A. Soon, T. Sohnel, H. Idriss, Surf. Sci. 579 (2005) 131. [45] H. Wilmer, M. Kurtz, K.V. Klementiev, O.P. Tkachenko, W. Grünert, O. Hinrichsen, A. Birkner, S. Rabe, K. Merz, M. Driess, C. Wöll, M. Muhler, Phys. Chem. Chem. Phys. 5 (2003) 4736. [46] K. Ozawa, Y. Oba, K. Edamoto, Surf. Sci. 603 (2009) 2163. [47] O. Dulub, M. Batzill, U. Diebold, Top. Catal. 36 (2005) 65. [48] O. Warschkow, K. Chuasiripattana, M.J. Lyle, B. Delley, C. Stampfl, Phys. Rev. B 84 (2011) 125311. [49] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [50] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [51] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Phys. Rev. B 57 (1998) 1505. [52] A.V. Krukau, O.A. Vydrov, A.F. Izmaylov, G.E. Scuseria, J. Chem. Phys. 125 (2006) 224106. [53] P.E. Blöchl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (1994) 16223. [54] F.D. Murnaghan, Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244. [55] B.C. Bolding, E.A. Carter, Mol. Simul. 9 (1992) 269. [56] H. Dixit, R. Saniz, D. Lamoen, B. Partoens, Comput. Phys. Commun. 182 (2011) 2029. [57] C. Friedrich, M.C. Müller, S. Blügel, arXiv:1102.3255 (2011). [58] H. Liu, Y. Ding, M. Somayazulu, J. Qian, J. Shu, D. Häusermann, H. Mao, Phys. Rev. B 71 (2005) 212103. [59] E.H. Kisi, M.M. Elcombe, Acta Crystallogr. C 45 (1989) 1867. [60] L. Gerward, J.S. Olsen, J. Synchrotron Radiat. 2 (1995) 233. [61] S. Desgreniers, Phys. Rev. B 58 (1998) 14102. [62] V. Srikant, D.R. Clarke, J. Appl. Phys. 83 (1998) 5447. [63] R.A. Powell, W.E. Spicer, J.C. McMenamin, Phys. Rev. Lett. 27 (1971) 97. [64] W. Tang, E. Sanville, G. Henkelman, J. Phys. Condens. Matter 21 (2009) 084204. [65] H. Gerischer, J. Electroanal. Chem. Interfacial Electrochem. 82 (1977) 133.

Fig. 9. Site-projected local densities of states (LDOS) plotted for each layer of the ZnO-supported Cu2O coating at coating thicknesses of one to five layers. The coating thickness is labeled at the top of each column, and each plot is labeled with its layer number in parentheses, where layer 1 is the layer at the interface. LDOS of the unsupported five-layer Cu2O slab are shown for comparison. In the unsupported Cu2O slab, layer 1 is the surface layer and layer 3 is the middle layer. The dashed line in each plot delineates the Fermi level.