Article pubs.acs.org/JCTC
Novel High-Throughput Screening Approach for Functional Metal/ Oxide Interfaces Ofer Neufeld† and Maytal Caspary Toroker*,‡ †
The Nancy and Stephen Grand Technion Energy Program and ‡Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel S Supporting Information *
ABSTRACT: Metal/oxide interfaces have long been studied for their fundamental importance in material microstructure as well as their broad applicability in electronic devices. However, the challenge involved in characterizing the relation between structure and electron transport of a large number of metal/ oxide combinations inhibits the search for interfaces with improved functionality. Therefore, we develop a novel highthroughput screening approach that combines computational and theoretical techniques. We use a Density Functional Theory + U (DFT+U) quantum mechanical formalism to produce effective Schrödinger equations, which are solved by wave packet propagation to simulate charge transport across the metal/oxide interface. We demonstrate this method on αFe2O3/Mt interfaces, for Mt = Ag, Al, Au, Ir, Pd, or Pt metals. We use this novel method to screen for binary alloys of these metals at the α-Fe2O3/Mt interface and perform a successful validation test of the methodology. Finally, we correlate the interface potential energy and the charge transport permeability through the interface. Counterintuitively, among the interfaces studied, we find that higher mismatch interfaces have better charge transport permeability. We anticipate that this method will be useful as a computationally tractable strategy to perform high-throughput screening for new metal/oxide interfaces.
1. INTRODUCTION The metal/oxide interface is a fundamental element of materials microstructure.1 For example, in the process of corrosion an oxide layer forms on top of a metal in an air or water environment. Therefore, we can usually find the metal/ oxide interface wherever corrosion takes place, such as appliances, ships, and turbine blades.2 Furthermore, metal/ oxide interfaces appear in a wide variety of technological applications, such as memory devices,3,4 sensors,5,6 catalysts,7,8 photovoltaics (PV), 9,10 and photoelectrochemical cells (PEC).11 Accordingly, they have been intensely studied for several decades.9,12−15 Recently, such interfaces have attracted special attention in catalytic and magnetic nanostructures.16−18 Functional metal/oxide interfaces have been much sought after in the long history of several research fields.19−23 In the field of electronics,24−26 oxides usually serve as insulators because many of them have low electronic mobility and a wide band gap.27−29 However, a severe limitation of transistor performance is electron leakage through the metal/oxide contacts.30,31 Recent studies show that the atomic structure at the interface plays a critical role in determining electrical performance.32 Therefore, characterizing material properties that control electronic conductivity through the metal/oxide interface is of significant value.33−35 Another field where the function of metal/oxide interfaces is of critical importance is electrochemistry.26 In electrochemistry, © 2016 American Chemical Society
the type of metal added to an oxide as a cocatalyst or as a supporting underlayer drastically changes the surface reaction efficiency. For example, the Fe2O3/Pt interface was synthesized as nanorod arrays for catalyzing water oxidation and as nanoparticles for catalyzing carbon monoxide oxidation.36 As demonstrated for α-Fe2O3 using transient absorption spectroscopy measurements,37,38 an important factor determining functionality is the ability of electrons to transfer through the interface for participating in surface chemical reactions. An emerging “hot” research area is within the topic of surface plasmons in metallic nanoparticles attached to an oxide substrate.39 This architecture introduces a physical phenomenon that can be exploited for sensors and photovoltaic cells. When the metal is illuminated with photons, the energy could be directly converted to excite high energy electrons. An efficient mechanism to collect such electrons is to form a Schottky barrier between the metal and an oxide semiconductor. For example, recent studies have investigated plasmonic electron generation with Au nanoparticles in contact with TiO2.40 Therefore, understanding the relation between metal/oxide composition and the rate of electron penetration through the interface is the key to designing better performing materials. Received: December 16, 2015 Published: February 26, 2016 1572
DOI: 10.1021/acs.jctc.5b01192 J. Chem. Theory Comput. 2016, 12, 1572−1582
Article
Journal of Chemical Theory and Computation Unfortunately, there is a large number of metal and oxide combinations, relative orientation relationships, terminations, atomic ordering, etc. Hence, an efficient and reliable algorithm is required to guide in scanning for new material interfaces.41−45 In this paper, we develop a high-throughput screening method for metal/oxide interfaces. The method enables simulating charge transport in realistic materials by combining first principle calculations with wave packet propagation. According to this method, an effective model Hamiltonian for the metal/oxide interface is built with the Kohn−Sham potential energy. This is a computational tractable model Hamiltonian that can be used for performing charge transport calculations through the interface. Building an effective model Hamiltonian based on the Kohn−Sham potential is a novel approach that combines computational and theoretical methods. A somewhat similar approach can be identified in tight-binding models that map an ab initio model to an effective tridiagonal matrix Hamiltonian.46 The corresponding software required for carrying out this combined approach should allow extracting the ab initio data in a convenient format for further processing. This is achievable with any Density Functional Theory code that provides the Kohn−Sham potential. We demonstrate the method on the α-Fe2O3/Mt interfaces with Mt = Ag, Al, Au, Ir, Pd, and Pt. This interface system is chosen since α-Fe2O3 (also known as hematite, α dropped from this point on) is used as a benchmark for electronic structure studies of metal oxides.47,48 In addition, Fe2O3 is a known safe and abundant catalyst with an appropriate band gap and band edge positions for water splitting that has a high theoretical water splitting efficiency.49 Moreover, metal deposition on top50,51 or bottom11 of Fe2O3 was seen to increase photocurrents.49,52−55 Using this model system, we scan for binary alloys of the metal at the Fe2O3/Mt interface and perform a successful validation test for the method. Correlating charge transport through the interface with interface potential energy reveals that the interface mismatch plays a key role in determining charge transport penetration through the interface. We anticipate that our high-throughput scheme will be used for an instructive understanding of how to select and design functional interfaces. The manuscript is organized in the following way. In section 2, we present the new method for screening metal/oxide interfaces. In sections 3 and 4, we describe the computational and numerical details involved in executing the method. Next, in section 5, we present a validation test of the model. In section 6, the novel effective potential energy of the metal/ oxide interface as implemented in the Fe2O3(0001)/Mt(111) system is described. In section 7, we show correlation between the charge transmission coefficient and the shape of the potential energy function. Finally, in section 8, the potential energy function is correlated with interface mismatch, which allows prediction of possible junctions to be used in specific applications.
Figure 1. Scheme of the novel high-throughput screening approach for metal/oxide interfaces.
oxide interfaces and perform an analytic continuation of the potential energy (step 1 in Figure 1). The potential is incorporated into an effective Schrödinger equation for the interfaces. The equation is solved with wave packet propagation (step 2), and the transmission coefficient is extracted. The process is repeated for selected interfaces (more metals or oxides), forming a library of data containing potential energy functions and transmission coefficients for several representative interfaces (step 3). Based on the potential energies calculated from DFT for a few prototype interfaces, and their corresponding transmission coefficients, the potential energies of better novel interfaces can be deduced (step 4). For example, the optimal potential energy for enhancing electronic flux may fall between the values of two known interfaces (e.g., Al2O3/Pt and Fe2O3/Pt), if for instance the inclusion of one material lowers the barriers in the second material, leading us to design a novel alloy at the metal/oxide interface (e.g., Fe2‑xAlxO3/Pt). In the results of section 5, we show that in the Fe2O3/Mt system the potential energy of the interface with a metallic alloy is well approximated by a weighted average of the potential energies of two parent materials. As another example, the optimal system can be found by extrapolating properties of two known interfaces: e.g., Fe2O3/ metal#1 and Fe2O3/metal#2 interfaces, where Fe2O3/metal#3 has an even larger transmission coefficient. We anticipate that in this case the potential energy of the third interface will be an extrapolation of the interface potential energies of the two known interfaces. In the examples above, the potential energy of a third novel interface is not calculated from DFT but is inferred according to the DFT-calculated potential energies of two other interfaces. The ability to take an average of potential energies or to extrapolate the potential energy by analytically changing the height and length of barriers is efficient; this approach does not require a heavy DFT calculation and is well suited for highthroughput screening.
2. GENERAL SCHEME OF THE SCREENING METHOD Our suggested algorithm on metal/oxide systems combines several quantum mechanical methods as described in Figure 1. First, we perform the Density Functional Theory (DFT) calculation on the metal/oxide interfaces with a pure metal. Then we extract the Kohn−Sham (KS) potentials of the metal/ 1573
DOI: 10.1021/acs.jctc.5b01192 J. Chem. Theory Comput. 2016, 12, 1572−1582
Article
Journal of Chemical Theory and Computation
Figure 2. (a) Fe2O3 (0001) oxygen-terminated slab. (b) FCC metal (111) slab. Blue shading represents the unit cell of the metal and Fe2O3 which creates the interfaces. (c)-(h) Relaxed Fe2O3/Mt interfaces for Mt = Ag, Al, Au, Ir, Pd, and Pt, respectively. Created using VESTA.90
[Kr], and [Xe]4f14, inner shell electrons, respectively, since these show good agreement with experiments (Table S.1 in the Supporting Information), and previously converged the geometry and electronic structure in Fe2O3.47,60 The KS equations were solved with a plane-wave basis set to self-consistency under three-dimensional periodic boundary conditions. Symmetry was not imposed for a better description of the interface geometry. k-space integration was performed with the tetrahedron method with Blöchl corrections.73,75 A Γcentered k-grid converged all cells to a total energy within 1 meV/atom. Geometrical relaxations took place with a conjugate gradient algorithm, and forces were converged to a tolerance of 0.03 eV/Å. All slabs were separated from their periodic image by a 10 Å vacuum layer which converged the total energy up to 0.1 meV/atom. Pure Fe2O3 was described with a 30-atom hexagonal unit cell with long-range antiferromagnetic order.76,77 The Fe2O3 bulk was then cleaved in the (0001) plane with an oxygen atom termination since this termination was found to be most strongly bonded to metals in several studies (seen in Figure 2a).78,79 With regards to the metal, the bulk metal is relaxed, and a pure metallic lattice parameter is obtained. The metal is then transformed such that the (111) planes are in the z direction and the xy plane is described with hexagonal lattice
3. COMPUTATIONAL DETAILS FOR DENSITY FUNCTIONAL THEORY CALCULATIONS (STEP 1) Spin-polarized DFT calculations were performed with the Vienna Ab Initio Simulation Package (VASP).56−58 We use the Perdew−Burke−Ernzerhof (PBE)59 of the general gradient approximation (GGA) exchange-correlation (XC) functional in all computations. This functional describes well systems of Fe2O3 (with an added U value)47,60 and all the chosen metal systems.55,61−63 This is further verified in Table S.1 provided in the Supporting Information. We used a spin polarized DFT+U formalism of Dudarev et al.64 to account for electronic interactions in Fe2O3 which are ill-described by regular DFT XC approximations.65−67 A U value of 4.3 eV which was derived ab initio47 was used for the Fe atoms to correctly describe the Fe2O3 electronic ground state.68,69 No orbital corrections were given to other metal atoms (that is, U = 0) since metal bonding means no half-filled orbitals or highly correlated electrons as in Fe2O3 and knowing that Ag,61 Al,62 Au,55,61 Ir,63 Pd,55 and Pt60,70−72 are well described by regular DFT approximations. Projected augmented wave (PAW) potentials73,74 represented all frozen core electrons and nuclei for each atom. For Fe, O, Ag, Al, Au, Ir, Pd, and Pt atoms the appropriate PAW potentials replaced [Ar], [He], [Kr], [Ne], [Xe]4f14, [Xe]4f14, 1574
DOI: 10.1021/acs.jctc.5b01192 J. Chem. Theory Comput. 2016, 12, 1572−1582
Article
Journal of Chemical Theory and Computation
Figure 3. Potential energy functions: (a) Pt/Fe2O3/Pt interface potential energy averaged over the xy plane as outputted by a DFT calculation, (b) pure bulk Fe2O3 potential energy averaged over the xy plane as outputted by DFT calculation, and (c) analytically continued Fe2O3/Pt interface potential energy. In (a) and (c) the energy scale is referenced to vacuum. In (c) the interface potential energy barrier maxima is positioned at z = 0.
we explicitly set the initial conditions, which are chosen through the DFT+U calculation as specified in the Supporting Information. This way the + U contribution is indirectly accounted for, and changes in the dynamics are expected to be insignificant (which can be verified in a future model extension). The potential is referenced to the energy in the vacuum of the slab and averaged over the xy plane, thus producing an average one-dimensional potential function for the interface (Figure 3a). There are several reasons for modifying this potential energy obtained from DFT. First, the potential is usually calculated for a slab with a metal/oxide/metal junction in order to cancel errors arising from the dipole across the slab (Figure 3a), while we are interested in a single metal/oxide interface. Second, the slab includes only a few layers of oxide and metal. In order to extend the potential energy of a single metal/oxide interface to more layers, we used analytical continuation of the potential with the potential energy from bulk unit cell calculations (Figure 3b and c). Analytic continuation is achieved by dividing the KS potential energy outputted from the DFT calculation to three regions: a bulk Fe2O3 region, an interface region, and a bulk metallic region. The interface region is unchanged, and its functional form is given by a cubic spline interpolation. The metallic bulk region is easily fitted via least-squares to a cosine function with a wavelength identical to the metallic (111) dspacing and amplitude which is extracted from the DFT potential energy. The bulk Fe2O3 region is analytically continued with the self-consistent KS potential energy from a DFT bulk Fe2O3 calculation (Figure 3b). The areas are “patched” together at the minimas such that the potential is continuous and has a continuous derivative. The large potential energy barrier at the interface is set to z = 0.
vectors similar to the Fe2O3 system (see Figure 2b). We choose the (0001) and (111) facets since they are stable for Fe2O380−82 and for face-centered cubic (FCC) metals,83 respectively. Only thermodynamically stable FCC metals with structures that can be described with hexagonal symmetry and low lattice mismatch to Fe2O3 (
