Hexagonal boron nitride on transition metal surfaces
Abstract
We validate a computational setup based on density functional theory to investigate hexagonal boron nitride (h-BN) monolayers grown on different transition metals exposing hexagonal surfaces. An extended assessment of our approach for the characterization of the geometrical and electronic structure of such systems is performed. Due to the lattice mismatch with the substrate, the monolayers can form Moiré-type superstructures with very long periodicities on the surface. Thus, proper models of these interfaces require very large simulation cells (more than 1,000 atoms) and an accurate description of interactions that are modulated with the specific registry of h-BN on the metal. We demonstrate that efficient and accurate calculations can be performed in such large systems using Gaussian basis sets and dispersion corrections to the (semi-)local density functionals. Four different metallic substrates, Rh(111), Ru(0001), Cu(111), and Ni(111), are explicitly considered, and the results are compared with previous experimental and computational studies.
Keywords
Density functional theory Nanomesh Boron nitride Interfaces Metal surfaces1 Introduction
Precise positioning and the control of interactions of individual molecules or small assemblies of atoms are of prime importance in the field of nano-devices. A promising way to obtain well-defined arrangements on a large scale is through template surfaces. These show a variation of the interaction strength on a nanometer scale. Optimally, the template will not interact too strongly with the nanostructures and should affect only weakly their electronic properties. Such functionalized surfaces have many possible applications in chemistry and biology and are essential in nano-electronics.
Monolayers of hexagonal boron nitride (h-BN) [1], as well as the isoelectronic carbon structure, graphene (gr), grown on transition metal (TM) surfaces have received much interest as possible templates for use in nano-devices. Chemical vapour deposition of precursor molecules, e.g., borazine in the case of h-BN, on a hot metallic surface leads to a spontaneous formation of the uniform epitaxial monolayers. Originally, the preparation of a single layer of h-BN was achieved on the Rh(111) surface [1, 2], but recently similar structures have been grown on Ru(0001) [3, 4, 5], Pt(111) [4, 6, 7], Ni(111) [8, 9, 10], Cu(111) [10], Pd(111) [11], and Ag(111) [12]. One-dimensional structures of h-BN have been produced using the same procedure on Cr(110) [13], Fe(110) [14], and Mo(110) [15]. Using similar recipes, graphene structures on most of these TM surfaces have also been obtained [5, 16].
Density functional theory (DFT)-based electronic structure calculations have been instrumental in the understanding of the structure and properties of the h-BN and gr nanomeshes [2, 5, 12, 17, 19]. Experimental techniques applied to characterize the nanomesh, i.e., scanning tunnelling microscopy (STM) and spectroscopy (STS), surface X-ray diffraction (SXRD), ultraviolet (UV), and X-ray photoemission spectroscopy (UPS, XPS), as well as X-ray absorption spectroscopy (XAS), all profit in interpretation from independent simulations. Previous simulations primarily used DFT with the generalized gradient approximation (GGA) and either the linearized augmented plane wave (LAPW) method [19, 20, 21, 22, 23, 24] or a plane wave (PW) basis set [25, 26, 27, 28].
We have developed an approach to investigate nanomeshes based on the Gaussian and plane wave (GPW) [29] formalism: A localized Gaussian basis positioned at each atom is used to expand the Kohn–Sham orbitals and a PW basis to describe the electron density to facilitate the calculation of the Coulomb interactions. This formalism leads to a very efficient description of the orbitals that can make use of locality in large systems and at the same time allows for the solution of the Poisson equation within linear time (in system size) [30]. By adding an empirical pair potential to account for long-range van der Waals (vdW) forces [31, 32] to a carefully chosen GGA functional, we achieve a balanced description of all important parts of the system energy. We will first show that the chosen model parameters give a faithful description of important properties of the individual systems, namely bulk and surfaces of metals and h-BN. We will then characterize four h-BN/TM systems (TM: Rh, Ru, Cu, and Ni), thereby also providing an overview of earlier calculations and experimental data.
2 Computational details and methods of analysis
Calculations are performed using Kohn–Sham DFT [33, 34] within the GPW formalism as implemented in the Quickstep module in the CP2K program package [35]. Dual-space pseudopotentials [36, 37, 38] are used to describe the interaction of valence electrons with atomic cores. The pseudopotentials for boron and nitrogen assume 3 and 5 valence electrons, respectively. The atomic cores of the metals are described by either a large- or medium-size core pseudopotential. In particular, for Rh we use potentials with 9 or 17 explicit valence electrons (q9, q17), for Ru 8 or 16 (q8, q16), 18 for Ni (q18), and 11 for Cu (q11). The PW energy cutoff for the expansion of the density is set at 500 Ry. If not stated otherwise, the Brillouin zone is sampled only at the \(\Upgamma\) point. Exchange and correlation contributions are calculated with the Perdew-Burke-Ernzerhof (PBE) [39, 40] and revised PBE (revPBE) [41] GGA exchange-correlation (XC) functionals. The latter is used together with the corrections for the long-range dispersion interactions, computed using either the DFT-D2 [31] or DFT-D3 formalisms [32], that are missing in GGA’s. The XC functional and its derivative are calculated on the same uniform density grid that is used for the Hartree energy and defined by the choice of the PW energy cutoff. In order to improve the accuracy and reduce numerical noise in the evaluation of the XC terms, a nearest neighbour smoothing procedure is employed. More details about these techniques are illustrated in Ref. [30]. The Fermi–Dirac smearing of occupation numbers with a 300 K electronic temperature is used in all calculations. Broyden density mixing [42] is used to facilitate smooth convergence within a reasonable number of iterations. Periodic boundary conditions are applied in all calculations. In calculations with slab-like models, interactions with periodic images in the direction perpendicular to the exposed surface are avoided by adding about 20 Å of vacuum space above the slab.
3 Assessment of the computational setup
Atomic basis sets, pseudopotentials and the employed density functional are the most important parameters for the model used in the nanomesh calculations. Basis sets and pseudopotentials have to be chosen carefully to find a balance between accuracy, transferability and computational efficiency. The largest systems will have a size of several thousand atoms and tens of thousands of electrons, and any justified reduction in the basis and the number of explicitly treated electrons will result in huge gains in computer time.
The Gaussian basis sets chosen for this type of application are of the molecularly optimized type [46] (Molopt basis). These basis sets are generally contracted and have a single set of exponents for all angular quantum numbers (family basis). The full contraction avoids single functions of diffuse character and results in well-conditioned overlap matrices for all kinds of systems. The basis sets include 4 primitives (B), 5 primitives (N), 6 primitives (Cu, Ni, and Rh), and 7 or 6 primitives (Ru) of s, p, d, and f type functions. The primitives are contracted to a small number of basis functions, and we denote the basis sets with [n|ijkl], where i, j, k, and l are the number of contractions of the s, p, d, and f type and n is the number of primitives. The exponents and contraction coefficients have been globally optimized with respect to the total energy of a small set of reference molecules. The basis sets used are for B [4|221], N [5|221], Cu [6|2221], and Ni [6|3221]. For Rh, either the [6|212] and [6|2221] basis sets with the large core pseudopotential (9 electrons, q9) or the [6|3221] basis with 17 electrons (q17) are employed; for Ru, either the [6|212] basis with 8 electrons (q8) or the [7|3221] with the q16 pseudopotential (q16).
Core electrons are described by dual-space pseudopotentials [36, 37, 38]. The potentials have been optimized in atomic calculations using the PBE [39, 40] functional. It is expected that the potentials perform equally well for the closely related revised PBE [41] functional.
3.1 Metals
Optimized lattice constants [Å]
PBE | revPBE | revPBE+D2 | revPBE+D3 | Experiments | ||||
---|---|---|---|---|---|---|---|---|
Ni | q18 | [6|3221] | 3.479 | 3.501 | 3.429 | 3.440 | 3.5171 [51] | |
PW-PP | 3.522 | 3.548 | 3.465 | |||||
PW-PAW | 3.520 | 3.546 | 3.465 | |||||
Cu | q11 | [6|2221] | 3.620 | 3.640 | 3.558 | 3.539 | 3.6149 [52] | |
PW-PP | 3.648 | 3.673 | 3.584 | |||||
PW-PAW | 3.644 | 3.676 | 3.589 | |||||
Ru | q16 | [7|3221] | a | 2.718 | 2.730 | 2.685 | 2.700 | 2.7059 [53] |
c | 4.292 | 4.311 | 4.240 | 4.265 | 4.2815 [53] | |||
PW-PP | a | 2.759 | 2.769 | |||||
c | 4.366 | 4.382 | ||||||
Rh | q17 | [6|3221] | 3.847 | 3.864 | 3.796 | 3.804 | 3.803 [54] | |
PW-PP | 3.834 | 3.851 | 3.781 | |||||
q9 | PW-PP | 3.860 | 3.869 | 3.802 | ||||
PW-PAW | 3.843 | 3.854 | 3.785 |
With the revPBE functional, the optimized lattice constants are consistently larger than with the PBE functional. When either of the empirical vdW potentials is added, the lattice constants become smaller, as expected. The Molopt basis set calculations usually result in slightly smaller lattice constants when compared to PW calculations using the same pseudopotential. The only exception is Rh where we find a larger value. The contraction induced by the vdW potentials is typically 1.5 % and slightly larger for the D2 than for the D3 correction. However, in copper the effect is reversed. The final lattice constant calculated with GPW and the revPBE+D3 functional is very close to the experimental value for Rh and Ru, whereas it is about 2 % too small for Cu and Ni.
Bulk modulus B [GPa], surface energy \(\Upphi\) [eV/Å^{2}], and work function \(\Upphi\) [eV] in the studied metal system
Method | Functional | Cell | B | ϕ | \(\Upphi\) | |
---|---|---|---|---|---|---|
Ni | GPW | revPBE | exp. | 227 | 0.082 | 4.83 |
revPBE+D3 | exp. | 285 | 0.165 | 4.81 | ||
PW-PP | revPBE | exp. | 0.106 | 4.87 | ||
PW-PAW | revPBE | exp. | 0.109 | 4.92 | ||
revPBE+D2 | exp. | 0.174 | 4.90 | |||
exp | 186 | 0.149, 0.153 | 5.35 | |||
Cu | GPW | revPBE | exp. | 149 | 0.073 | 4.68 |
revPBE+D3 | exp. | 203 | 0.136 | 4.69 | ||
PW-PAW | revPBE | exp. | 0.068 | 4.81 | ||
revPBE+D2 | exp. | 0.126 | 4.80 | |||
exp | 137 | 0.112, 0.114 | 4.98, 4.92 | |||
Ru | GPW | revPBE | opt. | 307 | ||
revPBE+D2 | opt. | 323 | 0.225 | 5.01 | ||
revPBE+D3 | opt. | 345 | ||||
exp | 311 | 0.190 | 4.47 | |||
Rh | GPW | revPBE | opt. | 235 | ||
revPBE+D2 | opt. | 250 | 0.178 | 5.13 | ||
revPBE+D3 | opt. | 267 | 5.12 | |||
PW-PAW | revPBE | opt. | 238 | 0.124 | 5.01 | |
revPBE+D2 | opt. | 256 | 0.206 | 5.02 | ||
exp | 270 | 0.166, 0.169 | 5.0 |
As we are interested in very large systems and the properties of the metal support are often only of minor concern, we have also investigated the performance of pseudopotentials with fewer valence electrons for Ru and Rh. This basis set/pseudopotential setup is particularly interesting for the study of molecules interacting with the nanomesh. In these cases, we can trade in a slightly reduced accuracy in the description of the metal surface for an increased computational performance. However, as we are dealing with a large metallic system, the computational cost is dominated by the diagonalization of the Kohn–Sham matrix.
Even when not the entire eigenvalue spectrum is needed, the computational cost will scale cubically with the total number of basis functions. Hence, simply reducing the number of explicitly treated electrons by changing the pseudopotential is unlikely to improve performance significantly. Smaller basis sets also have to be used together with the q8 pseudopotential for Ru and the q9 pseudopotential for Rh. The new setup for Ru is [6|212] with the q8 pseudopotential and the two new setups for Rh [6|2221] or [6|212] together with the q9 pseudopotential.
Properties of Ru and Rh calculated with different basis sets and pseudopotentials using the revPBE+D2 approach
a | B | ϕ | \(\Upphi\) | ||
---|---|---|---|---|---|
Ru | q16 [7|3221] | 2.685 | 323 | 0.225 | 5.01 |
q8 [6|212] | 2.718 | 320 | 0.218 | 5.00 | |
Rh | q17 [6|3221] | 3.796 | 250 | 0.178 | 5.13 |
q9 [6|2221] | 3.813 | 250 | 0.172 | 5.14 | |
q9 [6|212] | 3.836 | 234 | 0.167 | 5.20 |
3.2 Hexagonal boron nitride
GPW: revPBE | PAW: revPBE | PW-LDA | Experiments | ||||
---|---|---|---|---|---|---|---|
DFT | DFT-D2 | DFT-D3 | DFT | DFT-D2 | [59] | ||
h-BN: (AA′) | |||||||
a | 2.516 | 2.512 | 2.511 | 2.521 | 2.515 | 2.486 | 2.50 [60] |
d_{layers} | 4.145 | 3.154 | 3.224 | 5.262 | 3.076 | 3.219 | 3.33 [60] |
d_{B−N} | 1.453 | 1.450 | 1.450 | 1.455 | 1.452 | 1.435 | 1.44 [61] |
GPW: revPBE | PAW: revPBE | PW-LDA | Experiments | ||||
---|---|---|---|---|---|---|---|
DFT | DFT-D2 | DFT-D3 | DFT | DFT-D2 | [62] | ||
h-BN: (AB) | |||||||
a | 2.516 | 2.511 | 2.510 | 2.521 | 2.514 | 2.478 | |
d_{layers} | 4.148 | 3.135 | 3.199 | 5.318 | 3.041 | 3.279 | |
d_{B–N} | 1.453 | 1.450 | 1.449 | 1.455 | 1.451 | 1.431 |
The dispersion correction is essential to obtain good agreement with experiment for the interlayer distance because the GGA functionals do not describe the vdW interactions. In particular, both variations of the Grimme potential (D2 and D3) give a slightly too short interlayer separation between the hexagonal BN planes, while the calculated bond lengths are not affected by the dispersion correction and agree well with experiment and previous theoretical estimates.
4 h-BN/metal interface
Thermal decomposition of borazine on hot TM surfaces can lead to the formation of a Moiré lattice of a highly regular and corrugated h-BN monolayer on the hexagonal metallic surface (for the fcc metals (111) and for Ru the hcp(0001) orientation). The periodicity of such superstructures at the h-BN/metal interface depends strongly on the lattice constant mismatch between h-BN and metal, but can also be influenced by the preparation details [63]. We investigate four systems: two where the lattice constant mismatch is almost 10 % and the h-BN overlayer is strongly corrugated (Rh, Ru), forming the so-called nanomesh [1], and two with small mismatch and practically no corrugation (Ni, Cu). These systems have previously been investigated using different simulation methods and models. Structures and bonding of h-BN/Rh(111) and h-BN/Ru(0001) were studied in detail by applying LAPW models [22, 24]. The h-BN/Ni(111) system has attracted attention due to the surface magnetization [20, 21, 25, 26], which is retained after h-BN growth. Results on the h-BN/Cu(111) systems have been reported within an extended study on several TMs [21]. More theoretical work on these systems is available in the context of additional molecular interactions (water on h-BN/Rh(111) [64, 65], metal atoms on h-BN/Rh(111) [27, 66], hydrogen adsorption and intercalation [18, 67]), and in direct connection with experiments [2, 5, 10, 19, 23, 68].
The mismatch between h-BN and metal is a fundamental parameter that determines binding and corrugation of the h-BN monolayer. For this reason, we choose the size of the simulation cell that reproduces exactly the experimental mismatch using as reference value the equilibrium lattice constant of h-BN as obtained with our setup, i.e., 2.517 Å. This results in an effective lattice constant a of 3.801 Å for Rh, 3.628 Å for Cu, 3.543 Å for Ni, and 2.724 Å for Ru. Structural optimizations are typically started from a flat h-BN terminating a slab of four or seven metallic layers and are stopped when the largest gradient is smaller than 4 × 10^{−4} Hartree/Bohr. The revPBE-GGA is used as the exchange-correlation functional and is augmented with the empirical DFT-D3 dispersion correction unless otherwise stated.
4.1 h-BN adsorbed on Rh(111)
Full models of the h-BN/Rh(111) unit cell have been studied previously [22, 24, 27]. In this section, we will extend our results [64] and compare them to other studies.
The lattice mismatch between h-BN and Rh(111) is quite large, the (111) lattice constant of Rh being −7.0 % larger than that of h-BN. Such a mismatch does not allow a commensurate growth of the overlayer. Instead, a superstructure constituted of 13 × 13 h-BN units on a 12 × 12 Rh(111) surface has been observed. In principle, only a slight distortion of the B-N bond length would be required to match with a flat 13 × 13 h-BN layer on top of the 12 × 12 Rh(111) units. This is an overall contraction of the bonds by 1.4 % from 1.45 to 1.43 Å and corresponds to an energy increase of 0.02 eV per BN pair. This has to be compared with a stretching energy of 0.40 eV/BN for the 1 × 1 commensurate structure. In fact, the adsorbed h-BN layer is corrugated, in order to optimize the BN-Rh binding over a larger area. The extent of this area depends on the registry of h-BN over the Rh(111) surface.
4.1.1 Quasi-commensurate adsorption of h-BN on Rh(111)
Properties of the quasi-commensurate h-BN/Rh(111) system, using the symmetric slab model at the four registries: Interaction energies [eV/BN], work function \(\Upphi\) [eV], and distances and buckling [Å]
N | B | E_{int} | \(\Upphi\) | d_{min}(N) | b_{B–N} |
---|---|---|---|---|---|
top | fcc | −0.621 | 3.07 | 2.184 | 0.139 |
top | hcp | −0.587 | 3.07 | 2.193 | 0.141 |
fcc | top | −0.323 | 3.83 | 2.590 | 0.088 |
hcp | top | −0.325 | 3.76 | 2.608 | 0.085 |
The stretched overlayer remains overall flat in all the registries, even though the B–N bond buckles. The most stable structure is the (N-top,B-fcc) registry, with a minimum N-Rh distance of about 2.18 Å. The (N-top,B-hcp) is very similar, only 0.034 eV/BN less stable than the (N-top,B-fcc) registry. Since the energy cost for a 1-to-1 matching of h-BN on Rh(111) is quite large, the adsorption energy is only about −0.14 eV per BN pair in the N-top structures, while it is positive in all the N-hollow models. In the latter case, the weak binding is not sufficient to compensate the energy cost for the distortion of the h-BN layer. When N occupies hollow sites, the vertical distance from Rh(111) increases and the buckling is reduced. The buckling can be explained considering the weakened B–N bond, due to the stretching of the h-BN layer and a partial charge redistribution. Indeed, due to the presence of the metal, the electronic charge localized around the N atoms is polarized towards the Rh slab. Hence, the positively charged B atoms get attracted towards the negatively charged interlayer region. This effect is more evident in the N-top registry, where the N-Rh interactions and the polarization of N-p_{z} electrons are stronger. In this case, we can consider the N-p band as hybridized with the metal d band.
In order to characterize the electronic structure, we make use of the MLWFs. The displacements of the centres of charge, or Wannier centres (WC) of the MLWFs, with respect to the nuclear cores in different chemical environments can be used as an indicator of polarization. In free-standing h-BN, three such WCs are found along the three in-plane B–N bonds of each nitrogen atom. The fourth centre, representing the nitrogen lone pair, is located at the N atom. In the N-top structure, instead, the lone-pair WC is displaced into the interlayer region, indicating a polarization of the electronic charge distribution due to the interaction with the metal. As a consequence, the work function of the system is reduced from 5.01 eV of bare Rh(111) to 3.07 eV. Such N–Rh binding interaction is not observed in the N-hollow configurations, and the lone-pair WC is located within the h-BN plane like in the free-standing h-BN. The work function in this case is 3.8 eV, almost independent of the specific registry.
4.1.2 h-BN/Rh(111) nanomesh
The full supercell for the nanomesh is constructed with the metallic slab of 12 × 12 lateral unit cells of Rh(111) terminated with a 13 × 13 h-BN overlayer. We tested several different models by changing the thickness of the slab, from four to seven layers, and pseudopotential and basis set of Rh, i.e., both q17 and q9 pseudopotentials with the [6|3221] and [6|212] basis sets, respectively. For B and N, we always use q3 and q5 pseudopotentials and [4|221] and [5|221] basis sets. The largest tested model is a symmetric slab of 7 layers (1008 Rh atoms) and one h-BN overlayer per side (338 BN pairs), for a total of 1,684 atoms. With the q17 pseudopotential and the largest [6|3221] basis set for Rh, this amounts to 19,840 electrons and 34,996 basis functions. Nevertheless, similar structural and electronic properties of the nanomesh are obtained with the computationally more convenient setup employing q9 pseudopotential and [6|212] basis set. In what follows, we report the results for the seven layer slab with h-BN on one side only (non-symmetric system) and the bottom-most layer is kept fixed with the atoms in bulk positions. With this model, we allow the relaxation of the metal layers deeper inside the slab. This is important in order to be able to estimate how much the interaction with h-BN affects the substrate.
4.2 h-BN adsorbed on Ru(0001)
The a parameter of the Ru hexagonal lattice is 8.2 % larger than that of h-BN. Hence, it is reasonable to expect that similar structures as those observed on Rh(111) can be formed on the Ru(0001) surface. Indeed, the formation of a nanomesh of h-BN on Ru(0001) was reported first in 2007 [3]. The periodicity of 13-on-12 was considered to be the most likely [70] and was therefore subsequently used in the theoretical studies by Laskowski and Blaha [24] and Wang and Bocquet [27]. Comparison with experiments also supported this periodicity, as h-BN deposited on thin Rh(111)-films grown on yttrium-stabilized zirconia on Si(111) [63] resulted in a 14-on-13 structure: It was argued that the slightly smaller lattice constant of the Rh-film compared to bulk Rh(111) and the slightly different thermal expansion coefficients are responsible for the formation of this larger superstructure. Extrapolating this line of argument to a Ru(0001) single crystal, it was predicted that either a 12-on-11 or a 13-on-12 nanomesh superstructure would be formed at the growth temperature of 900 K. However, using surface X-ray diffraction [71], a 14-on-13 structure was found. According to the proposed interpretation, energy minimization from the stronger bonding of h-BN to Ru in comparison with h-BN/Rh(111) overcomes the increased strain energy and leads to the formation of a larger superstructure, 14-on-13, rather than the smaller 13-on-12.
Summary and comparison of results for h-BN on Rh(111) and Ru(0001)
h-BN/Rh 13-on-12 | h-BN/Ru 13-on-12 | h-BN/Ru 14-on-13 | |
---|---|---|---|
E_{BNdist} | 0.022 | 0.0001 | 0.004 |
E_{ads} | −0.254 | −0.367 | −0.380 |
E_{int} | −0.310 | −0.520 | −0.542 |
E_{BNcorr} | 0.032 | 0.134 | 0.139 |
d_{min}(N) | 2.208 | 2.186 | 2.186 |
d_{min}(B) | 2.128 | 2.082 | 2.076 |
\(\Updelta h_{\rm N}\) | 1.082 | 1.665 | 1.497 |
\(\Updelta h_{\rm B}\) | 1.175 | 1.754 | 1.640 |
\(\Updelta h_{\rm 1stTM}\) | 0.153 | 0.258 | 0.247 |
\(\Updelta h_{\rm 2ndTM}\) | 0.157 | 0.248 | 0.256 |
\(\Updelta h_{\rm 3rdTM}\) | 0.125 | 0.202 | 0.212 |
\(\Updelta h_{\rm STM}\) | 1.0 | 1.7 | 1.6 |
\(\Updelta \Upphi\) | 0.5 | 0.36 | 0.35 |
pore % (<2.4 on Rh; <2.2 on Ru) | 20 | 43 | 46 |
wire % (>3.2 on Rh; >3.3 on Ru) | 52 | 23 | 19 |
4.3 h-BN adsorbed on Cu(111)
Compared with other metal substrates, copper has so far received little attention for h-BN adsorption. An experimental study using XAS and photoemission spectroscopy [8] revealed only weak chemisorption of h-BN on Cu(111) and a very flat layer. More recently, Laskowski et al. [21] included Cu in a systematic theoretical study of TM substrates for h-BN. They used the LAPW method to study 7-layer metal slabs with a commensurate 1 × 1 registry. They report results obtained with different XC functionals, LDA, PBE, and Wu-Cohen-GGA (WC-GGA) [72]. The LDA interaction energy is −190 meV/BN for h-BN adsorbed in the (N-top,B-fcc) registry, the height over the Cu(111) surface 3.10 Å, and the B-N buckling 0.02 Å. On the other hand, E_{int} is only −10 meV/BN with the WC-GGA functional and the monolayer turns out to be unbound (positive E_{int}) with PBE. We note that no dispersion correction was applied in these calculations.
Properties of the commensurate h-BN/Cu(111) system, using the symmetric slab model in the six registries: adsorption and interaction energies [eV/BN], work function \(\Upphi\) [eV], and distances, corrugation and buckling [Å]
N | B | E_{ads} | E_{int} | \(\Upphi\) | d_{min }(B) | d_{min} (N) | \(\Updelta h_{\rm N}\) | b_{BN} |
---|---|---|---|---|---|---|---|---|
top | fcc | −0.270 | −0.298 | 3.62 | 2.962 | 2.977 | 0.010 | 0.015 |
top | hcp | −0.265 | −0.262 | 3.63 | 2.966 | 2.980 | 0.020 | 0.015 |
fcc | top | −0.244 | −0.284 | 3.66 | 2.959 | 2.976 | 0.052 | 0.016 |
hcp | top | −0.229 | −0.273 | 3.67 | 2.969 | 2.985 | 0.043 | 0.016 |
fcc | hcp | −0.234 | −0.281 | 3.71 | 3.023 | 3.036 | 0.006 | 0.013 |
hcp | fcc | −0.234 | −0.280 | 3.69 | 3.019 | 3.032 | 0.045 | 0.013 |
As can be seen from both the adsorption energies and the h-BN-metal separation, the differences among the registries are quite small. E_{ads} is always negative (i.e. binding) and very close to E_{int}, which is about 30–50 meV smaller, except in (N-top,B-hcp) where the two energies are essentially equal. This is an indication that the monolayer remains largely unchanged upon adsorption, i.e., effective interaction is weak. The work function, \(\Upphi, \) spans a range of 0.1 eV from 3.62 to 3.71 eV. The systems are also similar in geometrical structure. In all registries, the adsorbate layer is approximately 3 Å (2.99–3.03 Å) from the metal surface and is very flat, as indicated by the small h-BN corrugation.
In contrast to previous studies, our work explicitly takes into account dispersion contributions to the adsorption energies. These appear to be significant in order to obtain a monolayer adsorbed in a stable way, as opposed to the very weakly bound or unbound systems. However, as vdW interactions are unspecific and only attractive, they do not make clear distinction among the various possible registries. Due to a small electronic effect, configurations with N atop turn out to be somewhat energetically favoured to the others, which confirms previous results [20, 21]. However, we cannot confidently distinguish between (N-top,B-fcc) and (N-top,B-hcp). The energetic differences between the remaining four registries are also too small to establish a well-defined hierarchy of stability.
We have investigated the influence of the h-BN–Cu interaction on the electronic structure of the h-BN by comparing the PDOS and the charge density distribution. In general, the observed effects are small, and therefore, we do not show plots of the results here. By mapping the total density differences, only a slight polarization of the monolayer upon adsorption is revealed, largely independent of the registry. The major difference in the PDOS on the p_{z} states of N between the (N-top,B-fcc) and the (N-fcc,B-hcp) configurations, the structures with the smallest and largest values of the work function, is a shift of the valence band by about 0.3 eV.
More recently, it has been shown [73] that the −2.2 % lattice mismatch between Cu(111) and h-BN causes the formation of Moiré patterns also at this interface, accompanied by small rotations of the overlayer with rotation angles from 1 to 10 degrees. The resulting superstructures have much larger unit cells and the simulations become much more challenging. Further discussion of this type of h-BN/Cu(111) superstructure, supported by both experiments and calculations, is reported in a separate work [73].
4.4 h-BN adsorbed on Ni(111)
Several theoretical [20, 21, 23, 25, 74] and experimental [8, 10, 26] studies on the adsorption of h-BN on nickel surfaces have been published, focusing on various structural, energetic, and spectroscopic aspects. Among the possible metal substrates, the Ni(111) in-plane lattice constant (2.49 Å) matches that of h-BN most closely, allowing the formation of an almost perfectly commensurate overlayer. Since the earliest experiments of h-BN/Ni [75, 77], the nature of the bonding of the monolayer to the surface has been discussed repeatedly. Some authors have argued for a weak physisorption-like interaction [8], while others have proposed a strong(er), chemisorption-like binding [10].
Adsorption energy [eV/BN], layer separation and corrugation [Å], and change in magnetic moment of the surface Ni atoms [μ_{B}] upon adsorption of the h-BN overlayer on Ni(111) at different registries
Method | XC | E_{ads} | d_{m}in(B) | b_{B-N} | \(\Updelta\mu_{\rm surf}\) per Ni | References |
---|---|---|---|---|---|---|
DFT | PBE-GGA | – | 2.08 | 0.11 | −0.08 | [20] |
DFT | PW91-GGA | −0.021–0.038 | 2.18 – 3.97 | – | −0.00 to −0.23 | [25] |
LDA | −0.420 to −0.141 | 1.95 – 3.11 | – | −0.02 to −0.43 | [25] | |
DFT | PBE-GGA | −0.04 | 2.04 | 0.11 | −0.06 | [21] |
WC-GGA | −0.19 | 2.03 | 0.11 | [21] | ||
LDA | −0.27 | 2.01 | 0.11 | [21] | ||
DFT | PBE-GGA | −0.04 | 1.99 | 0.10 | – | [74] |
DFT | revPBE+D3 | −0.392 | 2.008 | 0.124 | −0.08 to −0.23 | Present work |
LEED | – | 2.20 | 0.2 | – | [77] | |
XPD | – | 1.95 | 0.07 | – | [76] |
Adsorption and interaction energies [eV/BN], work function \(\Upphi\) [eV], and distances, corrugation and buckling [Å] in the h-BN/Ni(111) system, using a 6 × 6 symmetric slab model in the six registries listed
N | B | E_{ads} | E_{int} | \(\Upphi\) | d_{min}(B) | d_{min}(N) | \(\Updelta h_{\rm BN}\) | b_{B-N} | μ_{surf} per Ni |
---|---|---|---|---|---|---|---|---|---|
top | fcc | −0.390 | −0.470 | 3.58 | 2.006 | 2.130 | 0.001 | 0.123 | 0.519 |
top | hcp | −0.392 | −0.473 | 3.55 | 2.008 | 2.132 | 0.001 | 0.124 | 0.503 |
fcc | top | −0.283 | −0.257 | 3.84 | 2.903 | 2.921 | 0.010 | 0.022 | 0.635 |
hcp | top | −0.283 | −0.268 | 3.84 | 2.923 | 2.944 | 0.057 | 0.021 | 0.630 |
fcc | hcp | −0.285 | −0.269 | 3.90 | 3.015 | 3.028 | 0.028 | 0.016 | 0.651 |
hcp | fcc | −0.293 | −0.270 | 3.91 | 2.996 | 3.008 | 0.073 | 0.016 | 0.649 |
In the most stable registries, our results agree well with the published experimental values of interlayer distance and corrugation, being between the values determined from LEED and XPD. The distance between h-BN and Ni(111) and the corrugation of the overlayer also agree well with most previous computational studies [20, 21, 74] (cf. Table 8). The computed adsorption energies indicate also in the case of Ni(111) that the configurations with N atoms atop the surface Ni atoms are most stable. It is, however, not possible to definitively distinguish between B-fcc and B-hcp due to the very small differences in adsorption energy. h-BN turns out to be chemisorbed on Ni(111) in all six registries, with generally significantly stronger adsorption energies than previous studies have shown. This effect can be attributed to the contribution from the vdW correction, which was not considered in previous studies.
In the right column of Fig. 8, the electronic states are projected on the N p orbitals. We tried to adjust energy reference of the PDOS from the free-standing to one from the adsorbed h-BN by aligning the low-energy peaks, but when the peaks in the p_{x,y} match well, in p_{z} the main peaks are about 1 eV higher in energy in the free-standing h-BN; this indicates a different response in the two different kinds of p orbitals to the adsorption. Interestingly, the largest peaks more than 3 eV below the Fermi energy in the spin α and β p_{z} PDOS lie at the same energies, differences appearing only close and above the Fermi energy. Compared to a free-standing h-BN sheet, a number of weak gap states appears upon the adsorption, mainly originating from p_{z}. The shape of the curves remains otherwise quite similar, indicating that the electronic structure of the adsorbate is affected only weakly by the adsorption. We also note a small spin polarization of the PDOS, shifting the β channel to slightly higher energies, and some differences in gap states between the two spins.
Several related investigations of the density of states of h-BN/Ni have been published recently [21,23,74]. Our results are in good agreement with these reports. In particular, our data reproduce the approximate peak shape and position of the Ni \(d_{z^{2}}\) states reported in [21], both at the surface with h-BN (3 peaks) and the bare surface (2 peaks). The relative shifts of the peaks closest to the Fermi level upon adsorption are also comparable to those results. Concerning the nitrogen states, the small spin polarization that we find (discussed below) matches the results in Ref. [21]. Che and Cheng [74] found similar peaks in the N p_{z} states, only sharper and more pronounced than ours.
With regard to spin density, the most significant change of magnetism occurs—as expected—in the topmost Ni layer. The spin polarization in the \(d_{z^{2}}\)-symmetry orbitals increases, while spin polarization decreases in the d_{xz,yz} orbitals. Some decrease in spin polarization is also visible in the second Ni layer. More notably, however, the nitrogen atoms are also subject to some magnetic polarization, albeit much smaller in magnitude. In particular, the average magnetic moment (from Mulliken population analysis) of the N atoms is 0.027 μ_{B} while that of B is −0.020 μ_{B}. These observations are consistent with the PDOS results discussed above. The upshift of the peak in the \(d_{z^{2}}\)-symmetric β PDOS causes the increase in spin polarization of the corresponding orbitals, while the move of d_{xz, yz} orbitals to lower energies leads to the loss of spin polarization in these directions.
5 Summary
In this overview, we have shown that DFT calculations, when carefully set up, can be used to reproduce and explain experimental findings for the nanomesh systems. Our specific approach based on the Gaussian and plane waves method provides a similar accuracy of description as plane wave-based codes. Additionally, we apply a dispersion correction to semi-local density functionals.
General properties in the different h-BN/TM and nanomesh systems: mismatch between the equilibrium hexagonal lattice constants between the h-BN and the substrate [%], corrugation [Å], adsorption energy and interaction energy [eV/BN], smallest vertical TM-N and TM-B distances [Å], and the share of atoms forming the pore region (closer than 2.4 Å on Rh and 2.2 Å on Ru) [%]
Mismatch | \(\Updelta h_{\rm N}\) | E_{ads} | E_{int} | d_{min}(N) | d_{min}(B) | In-pore | |
---|---|---|---|---|---|---|---|
Ni | +0.5 | – | −0.39 | −0.47 | 2.13 | 2.07 | – |
Cu | −2.2 | 0.02 | −0.27 | −0.30 | 2.98 | 2.97 | – |
Ru | −7.6 | 1.5 | −0.38 | −0.54 | 2.19 | 2.08 | 46 |
Rh | −7.0 | 1.1 | −0.25 | −0.31 | 2.21 | 2.13 | 20 |
Rh^{*} | 0.0 | – | – | −0.62 | 2.61 | – |
In order to better understand the nature of the interaction between h-BN and the four substrates, we have considered how the electronic structure of the overlayer is modified. On Rh and Ru, the regions where good contact is possible are characterized by strong re-hybridization of the p-states on the N atoms. In particular, we observe that these areas are more extended on Ru, where the 14-on-13 reconstruction turns out to be the most favourable. Like previous studies, our calculations yield the magnetization of the h-BN overlayer on Ni(111). This surface magnetization could lead to applications including spin filtering, as adsorbates on this system would experience a weak, mainly insulating but yet spin-polarized interaction with the h-BN/Ni(111). Our results confirm that in the spectrum of h-BN–TM electronic interaction strength, Cu resides at the very low end and shows the weakest effects on h-BN of all metals discussed in this study.
Having established reliability and accuracy of the computational method for the overlayer arrangement of h-BN on metal supports, we can go further and use this approach not only to verify and explain experimental findings but also to predict new arrangements and trends of similar nanostructures and for example adsorption and assembly of molecules on them. The first examples have already appeared in the literature: Disappearance of the corrugation in the nanomesh on Rh(111) upon hydrogen intercalation [18] and water interacting with the nanomesh [64, 65, 68].
Notes
Acknowledgments
This work is supported by Swiss National Science Foundation under Grants No. CRSI20 122703 and No. 140441. The authors thank the Swiss National Supercomputer Centre (CSCS) and University of Zurich for generous allocations of computer time.
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