Energetics of Mg , B , Cu , and Ti Atoms Adsorbed on the ZnO Polar Surfaces from First Principles

Using the density functional theory we have studied the energetics of the adsorbed atoms, Cu and Ti, on the (0001) zinc and (0001̄) oxygen polar surfaces of zinc oxide (ZnO). We have revisited the energetics of Mg and B atoms on the surfaces (Phys. Rev. B 77 035330 (2008)) and investigated them in connection with those of Cu and Ti. On the Zn polar surface, B and Ti atoms are adsorbed on the hcp site and are strongly bound to the oxygen atoms in the subsurface. Mg atom preferably binds to the three oxygen atoms on the O polar surface in the distances of 2 Å. Cu atom is also adsorbed on the Zn surface. We found an energy barrier 0.17 eV for the Cu migration along the path from the fcc site to the hcp site on the Zn surface. After the structural relaxation, Ti atom on the O surface infiltrated into the subsurface region and fitted into the tetrahedral cage made of the four oxygen atoms. Our results are consistent with the available experimental data and explain their energetics in atomic scale. Determinant factor of their preference of the sites is investigated. [DOI: 10.1380/ejssnt.2011.199]


I. INTRODUCTION
Zinc oxide (ZnO) is a wide band-gap II-VI semiconductor and has been shown to have major potential for use in optical devices in the UV wavelength region, catalysis, and gas-sensors [1][2][3][4][5].The physical and chemical properties of ZnO are usually modified to meet the requirement specific to each application by doping heterogeneous atoms.To understand the energetics of the heterogeneous atoms on the ZnO polar surface is quite important to control the quality of the ZnO based optoelectronic devices.
It has been found that the Ti doping to the ZnO improves its conductivity as well as its transparency in the visible range [6].Ethanol gas-sensing property of the ZnO is also enhanced by the Ti doping [7].Although the detailed mechanism is still unclear, the outstanding capability of the Ti doping is practically important for the manufacturing industries.The ZnO based polar semiconductor heterostructure has also attracted much interest in recent years because of the possibility to realize a two-dimensional electron-gas (2DEG) system.Above all, Zn 1−x Mg x O/ZnO has been considered to be one of the most promising 2DEG systems due to the large polarization of ZnO, the relatively small lattice mismatch, and the large conduction-band offsets at the interface [8,9].Theoretical investigation on the system has revealed that the change in polarization is mostly governed by piezoelectric effects connected with the Mg concentration and the changes of the a and c lattice constants [10].On the other hand, it is also well known that the Cu deposition on the ZnO surface effectively induces the catalysis capability for the methanol synthesis [11].Theoretical investigations indicate that the Cu on the ZnO polar surface exchange their electrons with the ZnO substrate and stabilize the surface state [4,12,13].
In view of these circumstances, we conduct a detailed study on the energetics of the Ti and Cu atoms on the ZnO polar surface.We also revisit the energetics of the Mg and B adsorbed atoms on the ZnO polar surface [14]    * Corresponding author: nisidate@iwate-u.ac.jp to examine the electron redistribution process.For the (0001) Zn polar surface, we find that the Mg and Cu atoms are adsorbed on the hcp site as well as on the fcc hollow site.The Mg adsorbed on the fcc site of the Zn surface induces small local strain in the Zn-O hexagon.The B and Ti atoms prefer the hcp hollow site and form bindings to the oxygen atoms at the subsurface.For the (000 1) O polar surface, the Cu and Mg favor the fcc hollow site.We found an energy barrier 0.17 eV for the adsorbed Cu along the migration path from the fcc site to the hcp site on the Zn surface.After the structural relaxation, Ti atom initially placed on the O surface infiltrated into the subsurface region and fitted into the tetrahedral cage made of the four oxygen atoms.Determinant factor of their preference of the sites is investigated.

A. Modeling ZnO surface
Electronic structures were investigated on the basis of the density functional theory (DFT) implemented in the Vienna ab initio simulation package (VASP) code [15].Total energy was calculated in the framework of the projector augmented-wave (PAW) method [16,17].Exchange-correlation energy functional was treated in the generalized-gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE) [18,19].Crystal structure was optimized using the cut-off energy of 500 eV and the 20 × 20 × 20 Monkhorst-Pack k-point mesh [20] for the reciprocal space sampling.The optimized structural parameters, a = 3.295 Å, c = 5.282 Å, and u = 0.3817, are in good agreement with the experimental values (a = 3.250 Å, c = 5.207 Å, and u = 0.3819) [21].
We model the ZnO polar surface as a slab which is constructed of 4×4×2 ZnO unit cells with the optimized structural parameters.Very large vacuum domain with the height of 20 Å is set over the surface.In this supercell geometry, the distance between the adsorbed atom and its image atom in the lateral direction is larger than 13 Å and the minimum concentration of adsorbed atom on the slab is θ = 1/16 ML.To accelerate the convergence of total energy calculations with respect to slab thickness, the oxygen (zinc) dangling bonds on the back side of the (0001) Zn surface ((000 1) O surface) are terminated by the hydrogen like pseudo-atoms with the valency of 0.5|e| (1.5|e|) [22].The total number of atoms including the pseudo-atoms amounts to 112.We use the lower cut-off energy of 350 eV and the reduced k-point mesh of 2×2×1 to suppress the huge computational cost in the slab computations.Spin polarization effect is included and the dipole correction is applied.Three symmetric sites for the adsorptions are considered.The top site, just above a surface atom, the hcp hollow site, above a subsurface atom, and fcc hollow site with no atom beneath [14].Initially, we place an atom 3 Å above the selected adsorption site, and then, all the atoms except those in the two bottom layers are relaxed under the condition that the residual force acting on each atom becomes smaller than 0.01 eV/ Å.
To verify the electronic nature of the polar surfaces, we calculate the surface band structures.For this purpose, we use the smaller slab constructed of 1×1×3 ZnO unit cells in which six Zn-O double layers are stacked along the c axis.The calculated surface band structures of the (0001) Zn and the (000 1) O polar surfaces are shown in Figs.1(a) and (b), respectively.Recently, electronic state of the pristine polar surfaces of ZnO has been investigated by means of the DFT computations to elucidate their stability [23,24].Freeman et al. have shown that the ZnO ultra thin film thermodynamically prefers a graphitic structure to a wurtzite structure.On the other hand, wurtzite ZnO consisting of more than six Zn-O double layers becomes to be stable via metallization of the polar surfaces [23].Song et al. have also examined the stabilization mechanism of the wurtzite ZnO by means of the all-electron full-potential linearized augmented planewave (FLAPW) method [24].They have used the ZnO slab passivating the backside dangling bonds to prevent the charge transfer between the front side surface and the backside surface, and have shown that the localized surface metallic state arises purely from the non-bonding character of the polar surfaces.In the present study, the charge transfer between the front side surface and the backside surface is prohibited due to the passivation of the backside dangling bonds.Therefore the surface states of the (0001) Zn and the (000 1) O surfaces originate purely from the Zn 4s and O 2p dangling bonds, respectively.These states are well localized at the each polar surface, consisting with the FLAPW investigation [24].Recently, the valence-band structure of the polar ZnO surfaces has been studied by means of the angle-resolved photoelectron spectroscopy experiment [25] and the electronic states of the hydrogen free (000 1) O polar surface have been observed in the upper portion of the valence band region.The origin of the state has been identified as the O 2p dangling bonds.Our calculated surface band structure qualitatively consists with the experimental result.However, they have observed only a bulk like characteristics for the (0001) Zn surface.It has been known that the Zn polar surface has many triangular shaped pits and island.At their step edges, O atoms corresponding to θ = 1/4 ML are exposed, stabilizing the Zn polar surface [22,26].Therefore, it has been considered that the exposed O atoms at the step edges cover up the electronic state of Zn surface from the experimental observation [26].Meanwhile, we employ the slab model constructed here to gain an insight into the properties of the pristine polar surfaces.

B. Atomic chemical potential and charge density
The adsorption energy of an atomic species X (=Mg, B, Cu, or Ti) adsorbed on the site (=fcc, hcp, or top) on the ZnO surface is defined as where E tot slab+Xsite and E tot slab are the total energies of the slab with and without an adsorbed atom X on the site, respectively, and µ X is the atomic chemical potential of the atomic species X and is defined as the energy per atom in its reference state.The structural parameters of the reference states optimized by the DFT calculations are summarized in Table I.In this definition of µ X , the adsorption energy is the energy gain in the adsorption and its negative (positive) value indicates that the adsorption proceeds favorably (unfavorably) with respect to the atomic reservoir in which µ X is evaluated.
The electron redistribution profile due to adsorption can be visualized using the difference of the spatial distribution of the charge densities defined by where ρ[slab + X site ] and ρ[slab] are the spatial charge density profiles of the slab with and without the atom X, respectively, and ρ[X] is the spatial charge density profile of the atom X.In this definition, electrons are redistributed from the negative ∆ρ to the positive ∆ρ in the adsorption.All the atomic positions are fixed in their optimized geometries in the evaluations of ∆ρ.

III. RESULTS AND DISCUSSION
The adsorption energies ∆E  top) of the (0001) Zn and of the (000 1) O surfaces are given in Tables II and III, respectively.In the following, we review the energetics of the adsorbed atoms.

A. B atom adsorption
On the (0001) Zn surface, the B atom has the large adsorption energies on the fcc (2.06 eV) and the top (4.05 eV) sites while it has the lowest one (0.95 eV) on the hcp site, suggesting that the B is preferably adsorbed on the hcp site of the Zn surface.The present results for the adsorption energies are slightly different from the values obtained in the previous work [14].The origin of this differences is due to the difference in the atomic relaxations: we fixed the atomic positions of the two bottom layers during the structural relaxation while all the atoms were allowed to relax in the previous work.
The local atomic structure around the B atom on the hcp site of the Zn surface is depicted in Figs.II), and as a result of this strong bonding, the three neighboring Zn atoms are displaced from the surface forming a small crater.The total number of the redistributed electrons in the adsorption amounts to 1.37.On the (000 1) O surface, the B atom has the remarkably low adsorption energies on the fcc site (−5.82 eV) as well as on the hcp site (−5.47 eV).In both of which the adsorbed B is surrounded by three neighboring oxygen atoms at the equal distance of 1.4 Å.The local atomic structure around the B atom adsorbed on the fcc site of the O surface is depicted in Figs.2(c) (top view) and (d) (slant view), where the formation of the sp 2 bonding configuration is clearly seen.The number of electrons redistributed in the adsorption is 0.93.In the meantime boron has been used as a deoxidant in the production of oxygen-free copper [30].Our result indicates that the B will act as a deoxidant on the ZnO surface leading to the reduction of the number of chemically active oxygen sites on the surface.

B. Mg atom adsorption
The adsorption energies are low for the Mg adsorptions on the fcc (0.48 eV) and the hcp (0.47 eV) sites of the Zn surface (Table II).The local atomic structure around the Mg atom adsorbed on the hcp site is shown in the Figs.3(a  are donated to the Mg-Zn interface regions.The number of electrons donated from the Mg is 0.68.On the (000 1) O surface, Mg has the lowest adsorption energy of −4.71 eV on the fcc site.The local atomic structure around the Mg adsorbed on the fcc site is shown in the Figs.3(c) and (d).The Mg-O bond lengths ∼1.97 Å (Table III) are slightly shorter than the equilibrium Zn-O bond length of 2.0 Å and hence a local strain is induced there.The number of electrons redistributed in the adsorption is 1.16.

C. Cu atom adsorption
For the Zn surface, the Cu on the fcc site attracts three neighbouring Zn atoms in the distances of 2.51 Å and has the lowest adsorption energy (Table II).The local atomic configuration is shown in Figs. 4 (a   a The Mg initially placed on the top site immediately moved to the fcc site and adsorbed there in consequence of the relaxation and exhibited the same energetics and atomic configuration as those of the fcc case, and the values of the adsorption energy as well as the neighbor atoms are omitted from the table. b The Ti initially placed on the top site immediately infiltrated into the subsurface region and fitted into a cage made of four oxygen atoms in consequence of the relaxation.transfer from Cu to the Zn [31].The Cu atom on the hcp site shows similar bonding nature with the slightly higher adsorption energy.To explore the energy profiles for the diffusion process on the adsorbed Cu on the (0001) Zn surface, we use the climbing nudged-elastic-band (C-NEB) technique [32,33].The estimated energy cost for the Cu migration along the fcc →hcp route amounts to ∼ 0.17 eV (Fig. 5).The high energy cost indicates that the Cu migration on the Zn polar surface is only possible in the high-temperature circumstance.We also tried to estimate the energy cost for the Cu migration on the (000 1) O surface but could not obtain any converged result probably due to the strong binding tendency to the O atoms.
The Cu atom on the fcc site of the (000 1) O surface makes bindings with the three neighboring atoms (Figs. 4  (c) and (d)) with the lowest adsorption energy (−0.35 eV).Total number of electrons redistributed from the Cu to the p orbitals of the neighboring oxygen atoms is 1.16.The adsorption energies are somewhat different from those evaluated by Meyer [13].This difference probably comes from the difference of of the reference states used to evaluate the atomic chemical potentials and has no relevance to the adsorption characteristics.

D. Ti atom adsorption
The Ti atom has the lowest adsorption energy on the hcp site of the Zn surface.It strongly interacts with three neighboring Zn atoms at the distance of 2.6 Å and makes a bond with one oxygen atom in the distance of 1.74 Å.The local atomic configuration is shown in Fig. 6(a) and (b).Total amount of electrons redistributed from the Ti to the surrounding three Zn atom as well as to the O atom just beneath the Ti is 1.48.The attractive interaction between the Ti and O atom results in the subduction of the Ti and the upward shift of the neighboring Zn atoms forming a small bulge on the surface.On the O surface, the Ti on the top site has the lowest adsorption energy.The local atomic configuration is shown in Fig. 6(c) and (d).After the structural relaxation, however, the Ti infiltrated into the subsurface region and slightly pushed aside the Zn from there.Recently, the Ti doped Zn polar surface of ZnO has been investigated using the Rutherford back-scattering spectrometry (RBS) [34], which indicated that the considerable amount of Ti atoms were present in the subsurface region.Our result is not only consistent with this experiment but also indicates that the external http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) invasive force resulting from such as the collision of the adsorbed atom and the surface is not necessary to bring about the infiltration.Recent first-principles calculation on the Ti doped ZnO (Ti 0.0625 Zn 0.9375 O) has indicated the occurrence of the strong hybridization of the Ti 3d level with the 2p states of the O neighbors of Ti.We can also confirm the tendency by visualizing the spatial distribution of the electrons.We see that the Ti 3d electrons are donated to the surrounding O atoms forming the 2p orbitals (Figs.6(c) and (d)) resulted from the hybridization of the states.Total number of electrons redistributed from the Ti atom to the neighboring O atoms is 1.58.

IV. CONCLUSIONS
First-principles DFT calculations were performed to investigate the energetics of the adsorbed atoms, Cu and Ti, on the ZnO polar surfaces.We have also revisited the energetics of Mg and B atoms on the surfaces and investigated them in connection with those of Cu and Ti.On the Zn polar surface, the B atom is adsorbed on the hcp site and makes a strong bonding with an oxygen atom on the subsurface.The Mg and Cu atoms have low adsorption energies for the adsorptions on the fcc as well as on the hcp sites.Both atoms make bonding with three neighboring Zn atoms with the similar local atomic configurations.The Ti atom is preferably adsorbed on the hcp site and makes a strong bonding with an oxygen atom at subsurface.Because an atom adsorbed on the hcp site of the Zn polar surface encounters neighboring O atom beneath the site, it is easy for the adsorbed atom to react with the O. Hence all four elements favor the hcp site through the covalent manner or the ionic interaction with the O atom at subsurface.Therefore, we expect that an adsorbed atom which can make a covalent or ionic bond with O prefers the hcp site of the Zn polar surface.The Cu and Mg also favor the fcc site of the Zn polar surface.These elements are known to form alloys with Zn.Because of the metal-lic affinities to the Zn atom, the elements favor the fcc site where no neighbor O atom present while maintaining the coordination number to the Zn atoms.In general, we expect that an adsorbed atom which can form an alloy with Zn prefers the fcc site of the Zn polar surface.On the O polar surface, the B is adsorbed on the fcc site as well as on the hcp site and the sp 2 bonding configuration with the oxygen atoms is formed.When the Mg atom is adsorbed on the O surface, some of its electrons are donated to the p orbitals of the three oxygen atoms, thereby strong ionic bindings are formed.On the O polar surface, the hcp site is less favored.Contrary to the Zn surface, there is a Zn atom just beneath the hcp site which causes the decreased coordination number of the adsorbed atom to the neighbouring O atoms.We expect that an adsorbed atom which prefers O to Zn does not prefer the hcp site.We found relatively high energy barrier 0.17 eV along the migration path of Cu from the fcc to the hcp adsorption sites of the Zn surface.Therefore, we expect that the Cu migration along the fcc →hcp path is only possible when the system is in the high-temperature circumstance.On the top site of the oxygen surface, the Ti initially placed on the top site infiltrated into the subsurface region and pushed aside the Zn atom and fitted into the tetrahedral cage made of the four oxygen atoms in consequence of the structural relaxation.Our result is not only consistent with the experiment but also indicates the unnecessity for external invasive force to induce the infiltration.

FIG. 1 :
FIG. 1: Surface band structures of the (a) (0001) Zn and (b) (000 1) O polar surfaces (blue thin lines).The localized surface states are shown in the blue thick lines.Red thin lines are the bulk band structures projected to the surface.
2(a) (top view) and (b) (slant view), in which equi-density surfaces of ∆ρ are shown.We see that the electrons donated by the B 2p orbital are redistributed not only to the three neighbouring regions but also to the O 2p orbital beneath it.The σ type B-O bond length is 1.31 Å (Table ) and (b), where the electrons of the Mg atom

FIG. 2 :
FIG. 2: Local atomic geometries of the Zn and O polar surfaces with an adsorbed B atom.Gray (red) colored large (small) spheres are the Zn (O) atoms.The adsorbed B atom is the medium sized green sphere.Energetically favorable adsorption configurations are shown, in which the B atom is adsorbed on the hcp hollow site of the Zn surface ((a) top and (b) slant views), and on the fcc hollow site of the O surface ((c) top and (d) slant views).The regions of positive (negative) ∆ρ are depicted as the yellow (blue) equi-density surfaces.
) and (b).We see that the 3d electrons of Cu are donated to the neighbouring Zn 3p orbitals.Total number of the electrons redistributed in the adsorption is 0.56.Recent experimental study indeed suggests that the adsorption of Cu atom on the Zn surface causes the surface band bending due to the charge http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/)

FIG. 3 :
FIG. 3: Local atomic configurations of the Zn and O polar surfaces.The Mg atom is adsorbed on the hcp hollow site of the Zn surface ((a) and (b)), and is adsorbed on the fcc hollow site of the O surface ((c) and (d)).FIG.4: Local atomic configurations of the Zn and O polar surfaces with the adsorbed Cu atom.Cu atom is adsorbed on the fcc hollow site of the Zn surface ((a) and (b)), and is adsorbed on the fcc hollow site of the O surface ((c) and (d)).

FIG. 5 :FIG. 6 :
FIG.5: Energy profile for the Cu diffusion along the fcc →hcp→top→fcc path on the (0001) Zn surface.The circles are the calculated points and the curve is a guide to the eye.Inset shows the slant view of the migrating Cu atom along the energetically favorable path determined by the C-NEB method and is represented as a triangle chain of small spheres.

TABLE I :
Optimized and experimental structural parameters.

TABLE II :
The adsorption energies ∆E X site ads , the number of electrons redistributed ∆ρ, and the neighbor atoms of the atom X on the site (=fcc, hcp, or top) of the (0001) Zn surface.The values ∆ρ are shown only for the preferable adsorptions.

TABLE III :
Adsorption energies of the atom X on the (000 1) O surface.Other prescriptions are the same as those in TableII.