Conference-ACSIN-10-First Principles Study of Oxygen Vacancies Near Nickel / Zirconia Interface

The effect of the nickel/zirconia (111) interface on oxygen vacancy formation energies in zirconia is investigated utilizing first principles simulation. The relationship between vacancy formation energy and the Fermi level is found to be similar to that calculated in the bulk system when the vacancy is located at three oxygen layers away from the interface. Moreover, we find a modulation of about 1 eV in the formation energies when the vacancies are located closer to the interface and relate this to the interface electronic states. [DOI: 10.1380/ejssnt.2010.93]


I. INTRODUCTION
Zirconia (ZrO 2 ) is a technologically important material with various applications.Due to its relatively high permittivity, zirconia is one of the potential replacements for SiO 2 dielectrics in metal-oxide-semiconductor (MOS) transistors.It is also used for thermal barrier coating and anti-wear applications.Furthermore, zirconia can be transformed into an oxygen ion conductor by doping with aliovalent cations (for example Mg 2+ , Ca 2+ , Sr 2+ , and Y 3+ ) and thereby introducing mobile oxygen vacancies.Aliovalent cation doping also results in stabilization of the material in the cubic fluorite phase (non-doped bulk zirconia is monoclinic at room temperature and zero pressure and transforms into tetragonal and cubic phases at higher temperatures), making it ideal for high-temperature electrochemical device applications such as solid oxide fuel cells (SOFCs) which operate at up to 1200 K. Usually, yttria (Y 2 O 3 ) is the dopant of choice because of low cost and chemical stability, and zirconia doped with yttria is commonly referred to as yttria-stabilized zirconia, or YSZ.
The understanding of the phase stability of zirconia, as well as the formation and migration of oxygen vacancies in zirconia is crucial for modeling robust and highperformance devices.As for bulk zirconia, there are many experimental studies on this subject [1][2][3][4][5][6][7], as well as theoretical works that, in many cases, successfully explain the experimental results [8][9][10][11][12][13][14][15][16][17][18][19].On the other hand, recent advances in fabrication and characterization techniques have made possible the experimental observation of ultrathin films (of nm-order thickness) or nanocrystalline powders [20][21][22][23].Several workers have reported that in such nanostructures, tetragonal or cubic phases can be stable at room temperature without any doping and have related this fact to the formation of oxygen vacancies.There is also an increasing interest stemming from the idea of nanoionics [24], which tries to utilize the char- acteristic behavior of ions at surfaces and interfaces (for example, enhancement of ionic conductivity or reactivity compared to bulk) which become dominant in nanostructures.There are several works reporting the conductivity of ultrathin YSZ films [25][26][27], but the results are contradictory.Moreover, theoretical works on the effect of interfaces and surfaces (that is, non-bulk effects) on oxygen vacancy formation and migration are scarce, and a clear atomistic picture is lacking.This is the subject of this contribution.
The specific system that we consider is the Ni/cubic ZrO 2 (c-ZrO 2 ) interface.This system is of particular interest in applications such as thermal barrier coating, Ni/YSZ cermet anodes used in SOFCs, and as a possible gate metal-oxide pair in MOS transistors.Several experimental observations of this system have been reported [28,29], as well as theoretical works focusing on the adhesion of the interface [30][31][32] or the Schottky barrier height [29].In this work, we instead focus on the effect of the interface on the potential energy landscape felt by oxygen vacancies.

II. MODEL AND METHOD
We employ SIESTA [33], a first principles simulation package based on density functional theory.In SIESTA, the wavefunctions are expanded using atom-localized pseudoatomic orbitals, allowing for faster calculation with moderate accuracy compared to planewave codes.The GGA-PBE functional [34] is adopted throughout our calculations.We use pseudopotentials of Troullier-Martins [35] type to represent the effect of the core electrons.The basis set is generated according to the recipe outlined in [36].We choose a pressure parameter of 0.1 GPa, and we control the radius of the second zeta orbitals by optimizing the split-norm parameter (the optimized value is 0.135).For Ni, a single zeta basis set with polarization orbitals (SZP) is used, while a double zeta basis set with polarization orbitals (DZP) is used for Zr and O.For Zr, the semi-core 4s and 4p orbitals are included in the valence for higher precision.The range of the 5s and 5p orbitals of Zr are controlled by an energy shift parameter of 0.15 eV.
We study three systems in this work: (1) c-ZrO 2 bulk, (2) Ni/c-ZrO 2 O terminated interface, and (3) Ni/c-ZrO 2 Zr terminated interface.We do not consider dopant cations such as Y in this work because we want to focus on the effect of the interface and dopants would make analysis difficult.The bulk is represented by a cubic supercell consisting of 32 ZrO 2 units (Fig. 1(a)).A k-point mesh of 2 ×2 ×2 is used, and a real space mesh cutoff parameter of 400 Ryd is employed.We also perform cal-TABLE I: Formation energies of doubly positive and neutral vacancies in various phases of zirconia with potential alignment and image charge corrections (except for tetragonal phase from ref. [9], which did not take potential alignment into account).The values are calculated for µO = µO 2 (oxidation limit) and F = 0.  culations on a smaller hexagonal supercell with 12 ZrO 2 units (Fig. 1(b)).A k-point mesh of 4 ×4 ×4 is used in this case.
As for the interface models, we employ a slab geometry, which is often used to study interfaces under the periodic boundary condition.The specific orientation relationship that we consider is the cube on cube relationship of (111) Ni (111) ZrO2 and [1 10] Ni [1 10] ZrO2 .The same interface was examined by Matsunaga et al. [32], although they did not consider the effect of vacancies.The side view and interface projection of our interface models are shown in Fig. 2. The numbers alongside the figure will be used to refer to each of the layers in the rest of this paper.The O terminated model is stoichiometric, while the Zr terminated model is O deficient.There are 2 ×2 units of ZrO 2 and 3 ×3 units of Ni at the interface.The Ni lattice parameter was shrunk by 3% to compensate for the misfit between c-ZrO 2 and Ni (the calculated lattice parameter values are 5.14 Å for ZrO 2 and 3.53 Å for Ni).A 4 ×4 k-point mesh was employed in the directions parallel to the interface, and a single k-point is considered in the perpendicular direction.A real space mesh cutoff of 800 Ryd is used.http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology

A. Vacancy formation energies
First, we calculate the formation energies of oxygen vacancies in each model.The formalism for calculating formation energies of point defects is well established [37][38][39], and in our case, the formation energy of an oxygen vacancy with charge q is calculated as O ] is the total energy of the supercell with one vacancy, E[perfect] is that without any vacancy, and µ O is the oxygen chemical potential.The last term on the right hand side is relevant when calculating the formation energy of charged defects using a charged supercell; q is the total charge in the supercell, E V is the valence band maximum (VBM), and F is the Fermi level relative to the VBM.Also, there is a constraint on the oxygen chemical potential from consideration of the equilibrium conditions in the reduction and oxidation limits of ZrO 2 : µ ZrO2 , µ Zr and µ O2 are taken from total energy calculations of c-ZrO 2 , hcp Zr metal, and the oxygen molecule.
When working with charged supercells, a neutralizing jellium background is introduced to keep the Coulomb energy from diverging.This in turn causes spurious interactions between the defect charge, their image charges in adjacent unit cells, and the background jellium.In order to correct for this, we employ the widely used first-order correction proposed by Makov and Payne [40]: where α is the lattice dependent Madelung constant, is the dielectric constant of the material, and L is the characteristic supercell length.This value is added to the calculated total energy.For the value of the dielectric constant, we use the theoretical value of = 35.5 obtained from density functional perturbation theory [41].
The correction for the doubly positive charge state in the supercell of Fig. 1(a) is 0.224 eV, while that of Fig. 1(b) is 0.305 eV.
There is also the problem that the reference point of the energy eigenvalues may shift due to change in the electrostatic potential.This can be corrected for by taking the difference of the electrostatic potential in regions far away from the defect in charged and neutral supercells [39].We find that the correction to the formation energy by potential alignment is 0.08 eV for the supercell of Fig. 1 (a),  while that for the supercell of Fig. 1 (b) is 0.21 eV.The calculated formation energies for oxygen vacancies in c-ZrO 2 bulk system are tabulated in Table I along with values for tetragonal and monoclinic phases from the literature.We do not consider singly positive vacancies in this work since previous works have shown that two singly positive vacancies are unstable with respect to disproportionation into neutral and doubly positive vacancies.The formation energy of V 2+ O is the lowest in the cubic phase, and this is consistent with the observed presence of a large number of oxygen vacancies in c-ZrO 2 thin films or nanocrystals.The Fermi level-dependence of formation energies of neutral and doubly positive oxygen vacancies in the oxidation and reduction limits are shown in Fig. 3.It shows that even in the oxidation limit, doubly positive oxygen vacancies may form without aliovalent cation doping when the Fermi level is low, e.g., in contact with highwork function metals.Vacancy formation due to doping can also be understood on a similar footing: replacing 2 Zr atoms by Y reduces the number of valence electrons by 2, shifting the Fermi level to the VBM.A doubly positive oxygen vacancy is then formed as indicated by the low formation energy, and the Fermi level is shifted back to the middle of the band gap.We also note that the transition point between doubly positive and neutral vacancies (the crossing of the lines indicating the two charge states) is located at F = 3.We use a relatively small supercell for the Ni/c-ZrO 2 interface model in the interface-parallel directions in order to complete the simulation in a feasible amount of time.Therefore, we check the effect of using a small supercell on the calculated values by calculating vacancy formation energies using the supercell shown in Fig. 1(b).The formation energy for the neutral vacancy decreased by 0.50 eV, while that for the doubly positive vacancy increased by 0.85 eV.This probably reflects vacancy-vacancy interactions (or in other words, the dependence of formation energy on concentration).The charge state transition point is located at F = 2.67 eV.From the above, we find that the small supercell has a not-so-small effect on the calculated values.We keep this in mind when doing further analysis (that is, there is some uncertainty in the exact values of the formation energies when comparing different systems because of the various supercell sizes).
Finally, we turn to the Ni/c-ZrO 2 interface systems.We only consider neutral supercells.The vacancy formation energies for three oxygen layers closest to the interface are shown in Fig. 4. For the O terminated case (Fig. 4(a)), we calculated vacancy formation energies for two inequivalent sites (on-top and bridge) in layer 4 (the layer facing Ni).The vacancy formation energy of the on-top site was 0.1 eV lower than the bridge site, but this difference is minute compared to the dependence on the distance from the interface.The interface clearly modifies the vacancy formation energies, or in other words, the potential energy landscape felt by oxygen vacancies; the low-formation energy layers may act as trapping sites for migrating oxygen ions.Furthermore, the range of the formation energies for the Zr terminated system is about 2 eV higher than that of the O terminated system.The reason for this will be analyzed later in this paper.

B. Analysis of the electronic structure near the interface
In order to clarify the effect of the interface on vacancy formation energies, we first examine the charge transfer due to interface formation.To this end, we employ Mulliken charge analysis to identify how many electrons belong to each atom.It should be noted that Mulliken charges are highly dependent on the basis set, and thus we use Mulliken charges only to identify trends in the charge transfer.
The differences of Mulliken charges in the interface systems and that of bulk c-ZrO FIG.9: (a) The electron accumulation or depletion in each layer in the O terminated system due to vacancy formation in layers 7, 6, and 4 (on-top site and bridge site).(b) The electron accumulation or depletion in each layer in the Zr terminated system due to vacancy formation in layers 8, 6, and 5.The values are obtained by taking the difference between Mulliken charges in the interface system with and without a vacancy.Positive values indicate electron accumulation, i.e., more electrons are assigned to the layer after vacancy formation.The vacancy is assigned the same amount of Mulliken charge as a neutral oxygen atom, that is, 6.
system, a pronounced depletion is seen in the interface Ni layers (layer 3 and 16) and O layers (layer 4 and 15), while accumulation is observed in the first Zr layers (layer 5 and 14).In the Zr terminated system, there is large electron accumulation at the interface on both Zr and Ni (layers 2, 3, 4, 13, 14, and 15) because of the nonstoichiometry of the ZrO 2 system: the oxygen deficiency causes an excess number of electrons to be left at the interface, some of which is transferred to Ni.We also note that the middle layers in the Ni and ZrO 2 slabs exhibit charges almost identical to that of bulk.The variation in the local electrostatic potential caused by interface formation is likely to be a factor in the variation of formation energies shown in Fig. 4, although no clear relation can be found between Figs. 4 and 5.
Next, we turn to PDOS analysis for explanation of the results presented in Fig. 4. Figure 6 shows the sum of PDOS of atoms in each layer in the interface systems (without vacancies).In both O terminated and Zr terminated systems, the PDOS of layers closer to the interface clearly show formation of metal induced gap states (MIGS) due to interaction with Ni.On the other hand, a clear band gap is observed in the layers 7 to 9 in the O terminated system and layers 6 to 8 in the Zr terminated system, indicating that the middle of the c-ZrO 2 slab is bulk-like.This is consistent with the charge analysis performed earlier.However, when comparing the two terminations, there is one important difference: the Fermi level with respect to the VBM of the bulk-like layers (i.e., the Schottky barrier height) in the Zr terminated slab is about 1 eV higher than that of the O terminated slab.This is due to the difference in the interface dipoles of the two systems.Comparing Figs.5(a) and (b), we see that the charge transfer in the O terminated system induces a dipole that pushes the average potential energy of the Ni slab lower with respect to the ZrO 2 slab.This shows the same trend as that reported by Dong et al. [29], where they reported a higher p-type Schottky barrier for the Zr terminated (001) Ni (001) ZrO2 ; [100] Ni [110] ZrO2 interface compared to the O terminated one.In the O terminated system, F 2 eV, so according to Fig. 3 obtained from bulk calculations, the formation energy in the oxidation limit should be around 3.5 eV with the vacancy in the doubly positive state.In the Zr terminated system, F 3 eV, so the formation energy is predicted to be about 5.5 eV, although it is difficult to judge the charge state because of the closeness to the charge transition level and the uncertainty due to different supercell sizes mentioned earlier.These formation energy values compare very well with the values calculated near the center of the O and Zr terminated slabs (layer 7 in Fig. 4(a) and layer 8 in Fig. 4(b)), and explains the difference in the range of formation energies between the two terminations.Whether the vacancy is doubly positive or neutral as predicted can be judged from the PDOS of Zr atoms nearest neighbor (NN) to the vacancy: a vacancy localized gap state is seen below the Fermi level in the neutral vacancy, while no such state is found in the doubly positive vacancy (Fig. 7).The PDOS of Zr atoms NN to the layer 7 vacancy in the O terminated system (Fig. 8 (a)) confirms that this vacancy is doubly positive, while that of layer 8 in the Zr terminated system (Fig. 8(b)) shows that the vacancy is neutral.The doubly positive vacancy does not imply a charged supercell: electrons originally assigned to the oxygen vacancy site are transferred to the states at the Fermi level, i.e., metallic states near the interface.This is clearly seen in the change of Mulliken charges due to vacancy formation (Fig. 9).In the O terminated system, the Mulliken charge originally assigned to the vacancy site is redistributed to layers 3 (Ni) and 5 (Zr).On the other hand, the vacancy charge in the Zr terminated system is mostly redistributed to the nearest Zr layers and no significant increase is seen in the Mulliken charge of the interface Ni layers.
We now turn to the dependence of the vacancy formation energies on the distance from the interface, which can be understood as perturbations by the local chemical environment from the "bulk" value discussed above.In the O terminated system, vacancy formation energies in layer 4 are 2.4-2.5 eV, which is about 0.8 eV lower than layer 7.This can be explained by the fact that Ni-O bonds at the interface are weak compared to Zr-O bonds in bulk c-ZrO 2 .The PDOS of Ni in layer 3 is very similar to that of layer 1 (which can be considered as bulk Ni), indicating a relatively weak interaction with O orbitals of layer 4 (especially when compared to the Zr terminated case shown in Fig. 6 As for the Zr terminated system, the fact that the vacancy formation energy at layer 6 is 1 eV lower than layer 8 is surprising when considering the relative similarity of the PDOSs in Fig. 6(b).However, there is a significant difference in the PDOS after vacancy formation (Fig. 8): the sharp PDOS peak in the band gap in layer 8 corresponding to the vacancy state has almost disappeared in layer 6, indicating some interaction with MIGS and the broadening of the vacancy level.The same can be said of the layer 5 vacancy.The difference in the formation energies of layers 5 and 6 can be explained by the difference in the O PDOS before vacancy formation: in the PDOS of layer 5, the highest peak is shifted to lower energy indicating that the oxygen atom is more stable than in layer 6.This in turn means that the oxygen vacancy is less stable.

IV. CONCLUSION
We have investigated the effect of the Ni/zirconia interface on the formation energy of oxygen vacancies in zirconia.We find that the alignment of the Fermi level depends on the interface termination, which in turn decides the formation energy in bulk-like regions relatively far away from the interface.The formation energies in the immediately adjacent layers to the interface (2 or 3 oxygen layers) are modified from this bulk value by up to 1 eV due to the different chemical environments.This is likely to have a large impact on the migration of oxygen ions near the interface, although further studies are needed to clarify how much the ionic conductivity is modified at the interface.

FIG. 1 :
FIG. 1: The bulk zirconia supercells used in this work.The red spheres are O atoms, and the green spheres are Zr atoms.

FIG. 2 :
FIG. 2: The atomic arrangements of the (a) O terminated and (b) Zr terminated interface supercells and those projected on the interface plane.The interface Ni layer and two layers of ZrO2 are shown in the interface projection.

FIG. 3 :
FIG.3:The Fermi level-dependence of vacancy formation energies in the bulk system.Blue lines represent neutral vacancies, while red lines represent doubly positive vacancies.The solid lines indicate formation energies in the oxidation limit, while dashed lines represent those in the reduction limit.

FIG. 4 :
FIG. 4: Vacancy formation energies for the first three oxygen layers in (a) O terminated and (b) Zr terminated Ni/c-ZrO2 systems.Layer 4 is the layer closest to the interface.The oxygen chemical potential is fixed at the oxidation limit.

FIG. 5 :
FIG. 5: The electron accumulation or depletion (sum of 4 atoms in ZrO2 layers and 9 atoms in Ni layers) in each layer due to interface formation in (a) O terminated and (b) Zr terminated interface systems.The values are obtained by taking the difference between Mulliken charges in the interface system and that of bulk Ni and c-ZrO2.Positive values indicate electron accumulation, i.e., more electrons are assigned to the layer in the interface system compared to bulk.

FIG. 6 :
FIG. 6: The PDOS of (a) layers 1 to 9 in the O terminated system and (b) layers 1 to 8 in the Zr terminated system.The sums of the PDOS of atoms in each layer are presented.For Ni, the upspin states are indicated by positive values and downspin states by negative ones.Only the upspin states are shown for Zr and O layers because there is very little spin polarization in those layers.The Fermi level is indicated by the dashed vertical lines.The gray hatching indicates the bandgap of c-ZrO2 in the middle of the slab.

FIG. 7 :
FIG. 7: The PDOS of the Zr atom NN to the neutral vacancy (top) and the doubly positive vacancy (bottom) calculated in the bulk supercell.The dashed vertical lines indicate the Fermi level.

FIG. 8 :
FIG. 8: (a)The PDOS of atoms NN to the vacancy in the O terminated system when the vacancy is in layers 7, 6, 4 (on-top site), and layer 4 (hollow site).(b) The PDOS of atoms NN to the vacancy in the Zr terminated system when the vacancy is in layers 8, 6, and 5.The PDOSs for one atom from each of the layers adjacent to the vacancy are plotted.The dashed vertical lines represent the Fermi level.
2 and Ni are shown in Fig. 5. Here, positive values indicate electron accumulation upon interface formation with respect to bulk, while negative values indicate electron depletion.In the O terminated Volume 8 (2010) Kasamatsu, et al.
(b)).Moreover, first principles tensile tests performed by Matsunaga et al. resulted in fracture at the Ni-O interface, indicating the relative weakness of the Ni-O bonding.The bulk-like character of the PDOSs of layers 6 to 8 along with similar formation energies of vacancies in layers 6 and 7 indicate that the effect of the interface is limited mostly to the first oxygen layer.