First Principles Investigation of Nickel-Graphene Interfaces

Transcription

1 Research Experience for Undergraduates Report First Principles Investigation of Nickel-Graphene Interfaces by Andrew J. Ross (Saint Anselm College) Advisers: L. Adamska Y. Lin I. I. Oleynik Physics Department University of South Florida August

2 First Principles Investigation of Nickel-Graphene Interfaces Author: Andrew Ross Advisers: L. Adamska Y. Lin I. I. Oleynik Abstract Graphene, an atom-thick layer of carbon, has been shown to possess unique electronic properties which make it an attractive candidate for nanoelectronics applications. Epitaxial growth of graphene on metal substrates is one promising methods of large-scale graphene s wafer production. In the case of graphene s growth on Ni(111) surface, the small lattice mismatch between these two materials is responsible for growth of high quality graphene samples. We present results of first-principles density functional theory (DFT) investigation of the structural, electronic, and magnetic properties of graphene/ni(111) interfaces relevant to experimental studies of graphene growth on nickel substrates. DFT calculations were performed to identify the favored binding sites for different interface geometries. Additional adlayers of Ni and Cu either adsorbed on top of the graphene/metal interface, or placed below the graphene were studied in order to model processes of metal intercalation. It is found that the fcc site is the favored binding site of graphene on the Ni(111) substrate, and the metal adlayers on top of the graphene/ni(111) preferentially bind to the top graphene site. It was also found that the interaction between graphene/ni(111) and the top Cu adlayer is much weaker compared to that for Ni adlayer. The atomic, electronic, and magnetic properties of these interfaces, including induced magnetic moments in graphene/ni(111) and {Cu,Ni}/graphene/Ni(111) systems will also be discussed. 2

3 Contents 1. Introduction 2. Numerical Setup 2.1 DFT parameters 2.2 Relaxed lattice constants 2.3 Systems of interest 2.4 Measured quantities 2.5 Interacting versus non-interacting limits 3. Atomic and Electronic Properties 3.1 Nickel-graphene interface 3.2 Ni-graphene-(Ni, Cu) interfaces 3.3 Discussion: weak versus strong interfacial interaction 4. Magnetic Properties 4.1 Reduction of Ni magnetic moment 4.2 Induced magnetic moment in carbon atoms 4.3 Charge transfer in nickel-graphene systems 5. Conclusions 6. References 3

4 1. Introduction Practical applications of graphene would require large, high quality graphene sheets, but techniques for creating such sheets have yet to be perfected. One method of growing graphene is epitaxial deposition on metal substrates. In order to refine this technique, the interfacial interactions between graphene and metal substrates must be understood. In order to better understand the processes of epitaxial graphene growth on nickel substrates, we applied density functional theory to calculate atomic, electronic, and magnetic properties of graphene in contact with nickel and copper. Nickel is a good example of metal interacting strongly with graphene and perturbing its electronic structure [1], in contrast graphene interacts weakly with copper and preserves its semi-metallic properties [1]. Our goal is to take closer look at this problem. The structure of this report is the following. First we explain in details the systems of interest and physical quantities we want to compute. In next two sections we present our findings. In Conclusions section we summarize the results and give ideas for further studies. 2. Numerical Setup 2.1 DFT parameters Density functional theory (DFT) was employed to perform a first-principles investigation of graphene-metal interfaces on the Ni(111) substrate. DMol code was used here with explicit treatment of all electrons, so no pseudopotentials were used. Because the generalized gradient approximation (GGA) overestimates the interfacial distance between the nickel substrate and graphene layer, the local density approximation (LDA) was used since it agrees well with experiment. Because nickel is ferromagnetic, spin-polarized calculations were employed. We composed the simulation cell in the following way. Nickel substrate was built by cleaving Ni(111) 5-layer surface. In order to avoid artificial effect, we completed the cell with 90 Å of vacuum. Further we fixed 2 Ni layers (later these layers are referred as 1 and 2), and let other 3 layers (3-5) to fully relax. Graphene was deposited on top of 5th nickel layer. 2.2 Relaxed lattice constants In order to have accurate forces in our simulation cell, and a result of forces--accurate geometry, we have to optimize lattice constant using chosen DFT parameters. In order to calculate the lattice 4

5 constant of bulk nickel, we computed binding energy for lattice constants near equilibrium experimental value, 3.36 Å to 3.47 Å in steps of 0.01 Å. Results are plotted in Fig. 1. The data points were fitted by cubic spline interpolation. We found Å to be the lattice constant, which is 2% less than the experimental value of Å.. Figure 1. Energy versus lattice constant curve for bulk nickel relaxation. Cubic spline interpolation was used to fit the curve to the data points, and the equilibrium lattice constant was identified by extracting the minimum energy value from the curve. The equilibrium bulk nickel lattice constant was identified to be 3.45 Å, 2% less than the experimental value. 2.3 Systems of interest Three Ni-graphene configurations were investigated, fcc, hcp, and hollow, as shown in Fig. 2. Fcc was identified as the favored configuration, therefore it was used for further investigation. Next step was to deposit metal on graphene. Metal adlayers were tested only for the favored fcc graphene structure. For these systems, three adsorption sites were investigated, top, top-corner, and hole, see Fig. 3. Each of these sites were tested with two different metal adatoms, either nickel or copper. These atoms were adsorbed either on top of the graphene layer, or placed below it to model intercalation. 5

6 Figure 2. Trial geometries of the three different nickel-graphene systems investigated, fcc, hcp, and hollow, differentiated by the binding sites of the carbon atoms to the five-layer nickel substrate (although for simplicity only 3 layers are shown here). Fcc is characterized by carbon atoms situated above the top layer nickel atoms and over the third adjacent nickel layer. Hcp binding sites are above the top and second adjacent layer nickel atoms. Hollow binding sites are over second and third layer nickel atoms, counted from the top. Figure 3 Trial geometries for binding sites of metal adatoms to the fcc graphene-nickel interface. The top configuration sees the metal adatom situated on top of the carbon atom that is placed above the third layer nickel atom. Top-corner is so-called because its metal adatoms are placed above the carbon atoms on the corners of the primitive cell, above first the first layer nickel atoms. Hole adatoms are placed such that they are above no carbon atom, rather they are directly over the second layer nickel atom. 6

7 2.4 Measured quantities For the nickel-graphene systems described above (see Fig. 2), the work of adhesion W is defined to be the energy necessary to separate the graphene layer from the nickel substrate, divided by the unit cell area A. To find this value, we first had to calculate the energy of the total system (E tot). We then lifted the graphene layer 45 Å above the nickel substrate (to the middle of the cell) and calculated the total energy of the separated system (Esep). The work of adhesion is then defined as W = (Esep Etot)/A. For metal-graphene-metal systems there are two interfaces of interest, each with a corresponding work of adhesion, W1 and W2, calculated similarly to the way we calculate work of adhesion for the Nigraphene systems above (see Fig. 4). W1 corresponds to the case where the top layer is separated from the total system. W2 corresponds to the case where top two layers are separated from the total system. As it displayed the highest work of adhesion for all systems, the top configuration was identified as the favored adsorption configuration. Figure 4. Schematic for calculation of work of adhesion. W1 is the work of adhesion calculated by separating the top layer of material from the system. W2 is the work of adhesion calculated by separating the top two layers of material from the system. D1 corresponds to the distance between the top layer and second layer. D2 corresponds to the distance between the second and third layers. 2.5 Interacting versus non-interacting limits For study of magnetic effects, it is very important to know the features of non-interacting systems to be able to interpret the results. Carbon is known to be non-magnetic material, free graphene is also nonmagnetic. Bulk nickel is ferromagnetic, with slightly larger magnetic moment on the surface, which is a common feature of magnetic materials. How will it be in combined nickel-graphene system? We performed a calculation of the magnetic moments of the atoms in each Ni-graphene structure (fcc, hcp, hollow) as a function of interface distance. The algorithm for this calculation was the following: 7

8 Graphene sheet was initially placed 4 Å above the substrate and geometry optimized. One of carbon atoms was moved downwards in steps of 0.1 Å. At each step, the total system was relaxed. The z-coordinate of this carbon atom was fixed during relaxation (for fcc and hcp cases, Ni-top carbon was fixed, and for the hollow configuration, the Ni-hcp carbon atom was fixed). The binding energy of the systems and magnetic moments on each atom were calculated at each interface distance. Binding energy curves for fcc, hcp, and hollow graphene stacking are plotted on Fig. 5. Results will be discussed in Magnetic Properties section. Figure 5. Binding energy curves for fcc, hcp, and hollow stacking. Fcc has a slightly lower energy than hcp structure. In addition, hollow stacking does not exist at interface distances of less than 2.8 Å. Hollow graphene changes stacking and becomes hcp graphene at very small interface distances (less than 1.3 Å). Original hcp and hollow/hcp binding energies differ slightly because different carbon atoms are fixed in these two structures. 3. Atomic and electronic properties 3.1 Nickel/graphene interface The favorability of each particular interface, depicted in Fig. 2, is judged from work of adhesion calculation. Results are summarized in Table 1. Work of adhesion calculations show that fcc is the favored configuration for the nickel-graphene interface. As well as having the highest work of adhesion, fcc also has the smallest interface distance. Hcp, however, has only a slightly lower work of adhesion (4.9%), and a slightly higher interface distance (0.5%). This suggests that while fcc is favored, hcp may also be a natural configuration of the nickel-graphene system. This agrees with experiment [4], where both fcc and hcp graphene stackings were observed. 8

9 3.2 Ni/graphene/{Ni, Cu} interfaces In this subsection we discuss results for nickel and copper monolayer adsorption on graphene sheet. Trial geometries were shown on Fig. 3. We found that top configuration (Fig. 3(a)) is favored both for Ni and Cu, so only these results are shown in Table 2. We can see that the adsorption of a metal atom on top of graphene significantly increases the work of adhesion between graphene and the nickel substrate. The nickel adlayer has the most pronounced effect, with a work of adhesion between graphene and nickel W2 = 3.65 J/m2, 4.0 times larger than the fcc value in Table 1, W = 0.81 J/m2, where no adlayer is present. The nickel adlayer also causes significant corrugation of the nickel substrate, Δd C = 0.3 Å, an order of magnitude higher than the value for all other systems. The copper adlayer increases the work of adhesion, W2 = 1.40 J/m2, 1.7 times greater in comparison with fcc graphene overlayer. We see in the Ni(s)/Cu/gr system that there is very weak binding between graphene and an intercalated copper layer: W1 = 0.34 J/m2. However, copper makes a good surface alloy with nickel, with a work of adhesion between W2 = 2.04 J/m2. Interface W, J/m2 d, Å fcc hcp hollow Table 1. Properties of nickel/graphene interfaces shown in Fig. 2. Quantities are described in section 2.4. Interface W1, J/m2 d1, Å W2, J/m2 d2, Å ΔdC, Å Ni(s)/gr/Ni Ni(s)/gr/Cu Ni(s)/Ni/gr Ni(s)/Cu/gr Table 2. Properties of Ni/graphene/{Ni, Cu} interfaces. 9

10 3.3 Discussion: weak versus strong interfacial interaction Why nickel and copper monolayers adsorbed on graphene behave so differently? In experiment by J. Lahiri et al. [4], copper, deposited on graphene (which resided on Ni(111) substrate), after some time intercalated through graphene and made surface alloy with nickel. But Nickel (in certain temperature regime) made stable surface carbide, and only upon heating graphene sheet was reformed on Ni(111) substrate. Nickel is known to have very high carbon solubility, whereas copper doesn t. Therefore, nickel is prone to stronger interaction with carbon. From our calculation we can observe this difference between two metals (see Table 2). Graphenenickel distance is ~2 Angstroms, graphene-copper distance is ~3 Angstroms. Also, graphene has very small vertical corrugation and 3 times smaller work of adhesion when it sits on intercalated copper, in contrast with pure nickel substrate. With DFT we cannot examine temperature dependence of such interactions, but even at zero temperature we see strong vertical corrugation of graphene and large adhesion work in Ni/graphene/Ni system. 4. Magnetic Properties 4.1 Reduction of Ni magnetic moment Reduction of magnetic moment in nickel layers close to the surface, when nickel is in contact with graphene, was first observed in Ref. [2]. Our results qualitatively agree with their work. The values of magnetic moment of the nickel substrate (fcc configuration) as a function of nickel-graphene interface distance are plotted in Fig. 5. The graphene-substrate interaction reduces the magnetic moment of the top layers of the nickel substrate. The effect is most pronounced for the top interfacial layer of nickel, where the magnetic moment µ = 0.33 µb at the equilibrium distance of 2.1 Å (in contrast, for free Ni(111) surface we computed µ = 0.64 µb). Subsurface layers also have a reduced magnetic moment, the value of which is lesser for layers closer to the surface. For large interface distances (3 Å 4 Å), all layers behave as a clean nickel surface, with layers 1 and 5 approaching surface nickel magnetic moment value of µ = 0.64 µb, and layer 2, 3, and 4 approaching bulk the bulk value of µ = 0.56 µb. For smaller interface distances, the interaction with graphene causes a reduced magnetic moment in the nickel layers. At the equilibrium distance 2.16 Å, 10

11 layer 5 has a magnetic moment of µ = 0.33 µb, and the value for layers 2, 3, and 4 increase with depth into the bulk. 4.2 Induced magnetic moment in carbon atoms Weser et al. [3] measured large induced magnetic moment in carbon atoms ( µb) for graphene adsorbed on Ni(111) surface. We also find induced magnetic moment in carbon atoms, not as large as in [3], but same order of magnitude. The magnetic moments of the carbon atoms in the graphene layer for the same fcc structure are plotted as a function of interface distance in Fig. 5. Each atom has an induced magnetic moment. The moment of the carbon atom occupying the top binding site is µ = µ B at an equilibrium distance of 2.1 Å, and the magnetic moment of the carbon atom at the hollow site is µ = 0.04 µb at equilibrium, both of which are consistent with experiment [3]. Figure 6. (A) Induced magnetic moments of the carbon atoms of the fcc graphene-nickel system as a function of interface distance. At the equilibrium distance of 2.16 Å, the carbon atom situated at the top site has an induced magnetic moment µ = µb, while the carbon atom occupying a hollow site has a value of µ = 0.04 µb. (B) Magnetic moments of the substrate nickel atoms in the fcc graphene-nickel structure as a function of interface distance. Dashed line marks equilibrium interface distance. 4.3 Charge transfer in nickel-graphene systems Mulliken charges indicate charge transfer between neighboring atoms. Sum of Mulliken charges of all atoms in the systems is zero in charge neutral system. For instance, in free graphene Mulliken charge on each carbon atom is zero, this is also seen from Fig. 7(b). Interfacial interactions change Mulliken charges on both nickel and graphene atoms. This was first noticed in Ref. [1]. Redistribution of Mulliken charges in nickel-graphene system as a function of interface distance is shown in Fig

12 Figure 7. (A) Mulliken charges for top two layers of nickel substrate. Deeper layers are not much influenced by graphene. (B) Mulliken charges on carbon atoms. Dashed line marks equilibrium interface distance. 5. Conclusions Graphene is hoped to be used in nanoelectronics applications, for which it is necessary to be able to grow large, high quality graphene sheets. This can be done epitaxially on metal substrates, although the graphene-metal interfacial interactions remain to be fully understood. In this work we identified stable configurations of graphene on nickel substrates. Fcc stacking was found to be the favored configuration, also hcp has only small difference in adhesion work. This agrees with experiment [4], where both fcc and hcp graphene stackings were observed. We found an increase in graphene-substrate binding caused by deposition of metal adlayers atop graphene. Both nickel and copper adlayers increase the adhesion work, but nickel has more pronounced effect. We also observed interesting magnetic effects at graphene-nickel interfaces. Magnetic moments of interfacial nickel atoms decrease. Carbon atoms in graphene experience an induced magnetic moment caused by the interfacial interaction. This work aims to contribute to future efforts in growing epitaxial graphene on metal substrates. For induced magnetism in carbon, additional theoretical work is needed to explain ferrimagnetic induced spin alignment in graphene lattice. 12

13 6. References 1. P. A. Khomyakov, G. Giovannetti, P.C. Rusu, G. Brocks, J. van den Brink, P. J. Kelly, Phys. Rev. B 79, (2009). 2. G. Bertoni, L. Calmels, A. Altibelli, V. Serin, Phys. Rev. B 71, (2004). 3. M. Weser, Y. Rehder, K. Horn, M. Sicot, M. Fonin, A. B. Preobrajenski, E. N. Voloshina, E. Goering, Yu. S. Dedkov, Appl. Phys. Lett. 96, (2010). 4. J. Lahiri, Y. Lin, P. Bozkurt, I. I. Oleynik, M. Batzill, Nat. Nanotechnol. 5, 326 (2010). 5. J. Lahiri, T. Miller, A. Ross, L. Adamska, I. I. Oleynik, M. Batzill, New Journal of Physics, submitted. 13