Ag and Au Atoms Intercalated in Bilayer Heterostructures of Transition Metal Dichalcogenides and Graphene

The diffusive motion of metal nanoparticles Au and Ag on monolayer and between bilayer heterostructures of transition metal dichalcogenides and graphene are investigated in the framework of density functional theory. We found that the minimum energy barriers for diffusion and the possibility of cluster formation depend strongly on both the type of nanoparticle and the type of monolayers and bilayers. Moreover, the tendency to form clusters of Ag and Au can be tuned by creating various bilayers. Tunability of the diffusion characteristics of adatoms in van der Waals heterostructures holds promise for controllable growth of nanostructures.


I. INTRODUCTION
In recent years graphene 1 has become one of the most attractive materials due to its unique properties such as high-mobility electron transport, 2,3 the presence of roomtemperature quantum Hall effect, 4 the strong lattice structure 5 and the extremely high in-plane thermal conductivity. 6 However, its highly active surface and the lack of a band gap in the electronic structure are emerging drawbacks for graphene. Recently, interests have now also focused on other two-dimensional systems having honeycomb structures, such as graphane, 7,8 halogenated graphenes, [9][10][11][12] silicene, 13 III-V binary compounds, 14  and NbSe 2 , Mott transition in 1T-TaS 2 and the presence of charge density wave in TiSe 2 . 19,20 It was also reported that the electrical and optical properties of TMDs are dramatically altered with the number of layers. [21][22][23] Although bulk hexagonal TMDs possess an indirect band gap, mono-layer TMDs exhibit a direct band gap which is crucial for optoelectronic devices, sensors and catalysts. In addition, n-type and p-type field-effect-transistors (FETs) based on monolayer and multilayer TMDs have been investigated. [24][25][26] It was also reported that many monolayer 2D crystals are reactive and segregation may occur easily. 27 Therefore, the investigation of bilayer structures which are chemically more stable than monolayer structures is of vital significance. Recent studies have shown that synthesis of heterostructures made of combinations of different TMD single layers, graphene, fluorographene and hexagonal-BN (hBN) is experimentally achievable. [28][29][30][31][32][33] Since TMDs and other two-dimensional structures have a lot of diverse monolayer structures, when they are combined together they are expected to exhibit very different properties. 34,35 Since the intercalation and migration of foreign atoms is inevitable during the formation of such lamellar materials and heterostructures, the investigation of the diffusion characteristics of various impurities is essential. Early studies revealed that alkali-metal doping of bulk TiSe 2 and MoS 2 can be utilized as an efficient way to tune the Fermi level. 36,37 The electrical conductivity of MoS 2 can be altered by substitutional doping. 38,39 Furthermore, decoration of the surfaces of few layer TMDs by metal nanoparticles like Au, Ag and Pt may provide p-and n-type doping. [40][41][42][43] The metal-atom adsorbed TMDs find their application in various areas including energy storage, 44 photonics, 45,46 biosensing, 47 and catalysis. 48 In a recent study, it has been demonstrated that, the presence of various impurities at the interface between MoS 2 /graphene/hBN and WS 2 /graphene/hBN heterostructures may modify the mobility of charge carriers. 49 It was also reported that contamination and migration of various molecules are inevitable during the formation of graphene based heterostructures and trapped hydrocarbons segregate into isolated pockets, leaving the rest of the interface atomically clean. 50 In addition, it was found that, attached metal nanoparticles on TMDs/Graphene stacks can be suitable for enhanced optoelectronic properties. 51,52 Despite some recent studies on adatom adsorption on various TMDs, intercalation and migration of foreign atoms in heterostructures have not been investigated. In this study, using density functional theory based electronic structure method, we investigate the diffusion characteristics of heavy metal atoms (Au and Ag) on monolayers and intercalated in such bilayer heterostructures. The paper is organized as follows: In Sec. II we give details of our computational methodology. In Sec. III the energetics of the metal atoms Ag and Au on monolayers of graphene and TMDs are presented. In Sec. IV diffusion characteristics of those metal atoms inside bilayer heterostructures are shown and in Sec. V we summarize and conclude our results.

II. COMPUTATIONAL METHODOLOGY
To determine ground state atomic structures and migration characteristics of monolayers and their bilayer heterostructures, first-principles calculations were performed using density functional theory (DFT) with a plane-wave basis set as implemented in the Vienna ab initio simulation package (VASP). 53 For the exchange correlation function generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof 54 was used together with the van der Waals correction. 55 Spin-unpolarized calculations were carried out using projectoraugmented-wave potentials (PAW). The plane-wave basis set with kinetic energy cutoff of 500 eV was used.
A 4×4 and 3×3 hexagonal supercells of single layer and bilayer structures are employed to model diffusion paths of metal atoms, respectively. The k-point samples were 3×3×1 for these supercells. It is calculated that a 12Å of vacuum space is enough to hinder long-range 3 dispersion forces between two adjacent images in the supercell. Lattice constants and total energies were computed with the conjugate gradient method, where atomic forces and total energies were minimized. The convergence criterion of our calculations for ionic relaxations is 10 −5 eV between two consecutive steps. The maximum Hellmann-Feynman forces acting on each atom were reduced to a value of less than 10 −4 eV/Å. All components of the external pressure in the unit cell was held below 1 kbar. For the electronic density of states Gaussian smearing was used with a broadening of 0.1 eV. The non-local correlation energies were determined by employing density functional theory plus the long-range dispersion correction (DFT+D2) method. 55 55,56 It is essential that long-range dispersion correction to the interlayer force is taken into account in order to obtain reliable layer-layer distances and electronic properties of the heterobilayers.
To study the adsorption and diffusion of metal atoms in these systems, total energies of monolayer TMDs (graphene) with adatom were calculated for 19 (12) different points which include the high symmetry points (H, M, B, and T). Total energies of bilayers with adatom were calculated for only 4 high symmetry points. In these different points, the adatom-surface distance was fully relaxed while the position of the adatoms parallel to the surface was kept fixed. To obtain accurate diffusion characteristics of heavy atoms on monolayer TMDs and graphene, calculations were performed using 4x4 supercells. In these calculations, first and second nearest neighbors of the adatom were fully relaxed while all the rest was kept fixed. On the other hand, in the bilayer calculations, all atoms of bilayers were free to move in all directions. Binding energies were calculated for the most favorable adsorption sites. These binding energies were calculated from the expression E B = E M onolayer + E A − E M onolayer+A , where E B is the binding energy of the metal atoms on the TMDs or graphene, E M onolayer is the energy of monolayer TMDs or graphene, E A is the energy of metal atoms, E M onolayer+A is the total energy of the metal atom-monolayer system.
We have chosen the following convention to define the diffusion energy barrier. The binding energy of an adatom was calculated at all high-symmetry points of the TMDs and the graphene surface. Since adatoms follow the lowest energy path, the difference of the energies between the most favorable site and the second most favorable site was considered as the diffusion energy barrier.
In order to obtain the correct value of the charge transferred between the metal atoms, the TMDs and the graphene, Bader charge analysis was performed. Rather than electronic orbitals in Bader methodology, charge partitioning is based on electronic charge density and therefore it is highly efficient, it scales linearly with the number of grid points, and is more robust than other partitioning schemes. Diffusion and mobility of impurities on a two-dimensional crystal surface can be described by quantities such as activation energy (E a ) and jump probability (P ) from the binding site over the lowest-barrier path at room temperature. The P value is a measure of the possibility of propagation by overcoming the energy barrier among the possible adsorption sites. Jump probability from one lattice site to another one can be calculated by using the formula P ≈ e −Ea/k B T where k B is the Boltzmann constant and it increases exponentially with increasing temperature. Here E a is the activation energy which is equal to the difference of the energy of the two lowest energy states.
Our calculated adsorption sites, binding energies, vertical adsorption position, charge transfer, energy barrier and jump probability (P ) values are listed in Table I. We see that the bonding of an Ag atom to graphene occurs at the B site and the H site is the least favorable adsorption site. In accordance with the previous DFT study, we found that the binding energy of Au on graphene is almost twice the binding energy of Ag on graphene. The Ag atoms lose (while the Au atoms gain) a small amount of charge when they bind to the graphene surface. 60 On the surface of TMDs, the most favorable bonding site for Ag atoms is the H site and the next largest adsorption energy is found for the M site. It is reasonable to assume that metal atoms diffuse through these two favorable adsorption sites. Therefore the energy difference between these two lowest-energy sites can be regarded as the diffusion barrier. Since the energy barrier for Ag between H and M sites is high (∼50 meV) diffusion through these symmetry points may not occur at low temperatures. It appears from Fig. 2 that Ag atoms on graphene migrate through the B and T sites with almost zero (∼2 meV) energy barrier, while migration on TMDs (MoS 2 , MoSe 2 and WS 2 ) occurs through H and M sites. As shown in Table I In addition, the migration barrier seen by Au atoms is ∼30 meV larger than the energy  nm, respectively. 44 In agreement with this experimental study, our calculations show that 7 the P value of the Au atoms on a WS 2 surface is higher than that of Ag atoms.

WAALS BILAYERS
The vertical stacking of graphene and other two-dimensional atomic crystals allows for the combination of different electronic properties. Recent studies have shown that, electronic and optical properties of TMDs can be altered dramatically by forming such heterostructures. 28,64 It appears that the intercalation and contamination of foreign atoms and functional groups at the interface of these heterostructures are unavoidable. As shown by recent experimental study, heavy atoms such as Au and Ag are quite mobile on TMD surfaces and they form clusters. 65 Therefore, understanding the diffusion characteristics of heavy atoms at the interface of these heterostructures is of importance for the ongoing research on heterostructure devices.
In this section, we investigate the diffusion characteristics of Au and Ag atoms intercalated First, we start with the heterostructure MoS 2 /Graphene. However, the determination of the most favorable atomic structure of MoS 2 /Graphene heterostructure is more complicated due to the lattice mismatch. Our calculations showed that bare DFT calculations are not capable of finding the ground state ordering of graphene placed on MoS 2 due to the presence of many local minima corresponding to metastable states. It was seen that low-temperature (100 K) molecular dynamic calculations are able to avoid local minima allowing to obtain the relaxed geometric structure of MoS 2 /Graphene as shown in Fig. 1(c). Due to the lack of symmetry in the MoS 2 /Graphene structure, twenty-seven inequivalent adsorption sites are considered for each Ag (and Au) atom adsorption. Table II lists the intercalation energies obtained by using a 3×3 unit cell of the most favorable site for each configuration. Here the intercalation energy is defined by the expression