The adsorption of atomic H above the carbon buffer layer in the graphene/SiC(0001) interface system is investigated within density functional theory through a set of realistic interface models that do not impose large artificial strains on the graphene. We find that hydrogen binding energies above the buffer layer are two to four times higher than on free-standing graphene and display important spatial variations across the unit cell. Adsorption on Si-bonded, fourfold-coordinated C atoms is strongly unfavorable (unstable, or metastable with very low barriers), while all threefold-coordinated C sites lead to stable configurations often showing H binding energies larger than in H2. We identify the origin of these large binding energies in the local strengthening of the graphene/SiC interface bonding around the adsorption site due to the H-induced deformation of the graphene buffer layer. The most stable adsorption sites are those having two or three C nearest neighbors (almost) atop the underlying surface Si atoms, because the presence of the adsorbed H atom favors the formation of a local sp3 arrangement of the graphene.
Graphene is a two-dimensional material with excellent physical properties, such as very high electron mobilities, thermal conduction power, and mechanical strength (). Epitaxial graphene grown on SiC surfaces by thermal decomposition offers a convenient template for future electronic applications because it does not require any transfer after growth [2, 3]. Indeed, some transistor prototypes based on epitaxial graphene on SiC have already been demonstrated [4-6] and show a great potential for high-frequency electronic applications (). In order to make these applications viable, one has to tackle the lower values and stronger temperature dependence of the electron mobility observed in epitaxial graphene on SiC compared to free-standing graphene produced by exfoliation methods (). This performance degradation is more significant on the Si-terminated face of the hexagonal SiC polytypes, where an interfacial carbon “buffer” layer forms between epitaxial graphene and the SiC(0001) surface during graphitization [3, 7]. Since about one-third of C atoms in the buffer layer form covalent bonds to the surface Si atoms, this layer is electrically inactive and partially decouples the subsequent graphene epilayers from the SiC substrate (). However, this decoupling is far from being complete, probably due to the presence of partially unsaturated Si dangling bonds, charge\parfillskip 0pt\par
puddles, or electron–phonon scattering from the substrate [8, 9]. A great advantage of growing graphene on the Si-terminated face of SiC is the possibility of a fine control on the graphene thickness resulting in uniform monolayers of micrometer size (). On the C-terminated face, most experiments found that the epitaxial graphene lies directly above a Si-adatom reconstruction of the SiC() surface (), but the existence of a carbon buffer-layer is still debated. The measured electron mobilities are significantly higher than on the Si-face () and the multilayer system shows a rotational stacking disorder which effectively decouples electronically one layer from the other. However, the development of applications on SiC() has been severely hindered by the difficulty of growing a specific number of layers in a uniform way ().
The practical realization of a quasi freestanding monolayer graphene (QFMLG) has represented an important step forward in the improvement of the electrical properties of epitaxial graphene on SiC(0001). It has in fact been shown that the carbon buffer layer can be decoupled from the SiC substrate and converted into an electrically active graphene layer by exposing the system to molecular hydrogen at elevated temperatures (between 600 and 1000C) [12, 13]. After a sufficiently long exposition time, the hydrogen intercalates underneath the buffer layer and saturates all Si dangling bonds on the surface, thus removing the covalent interaction between the carbon layer and the SiC(0001) surface. The resulting graphene monolayer presents mobilities significantly higher than standard epitaxial graphene on SiC(0001) and a slight p-doping (in contrast with the substantial n-doping of the latter), the origin of which is not completely understood until now (calculations give a tiny n-doping [14, 15]). Similarly, a single graphene monolayer and the buffer layer underneath can be converted into a quasi-freestanding graphene bilayer through hydrogenation of the SiC surface. An earlier attempt by Guisinger et al. () employing atomic hydrogen did not succeed in giving a complete conversion of the buffer layer into QFMLG. Successive experimental works achieved the production of QFMLG by exposing the system to hydrogen plasma () or to atomic hydrogen (). The surface structure of QFMLG was extensively investigated by Forti et al. (), who demonstrated the high structural quality and homogeneity of the graphene layer. The excellent electronic transport properties of QFMLG have been verified by Speck et al. (), who performed Hall-bar measurements and achieved a mobility of 3100 cm2 V−1 s−1 at room temperature, as well as a weak temperature dependence of the mobility.
While the practical procedure for converting the carbon buffer layer into QFMLG seems established and the nature of the final system appears to be sufficiently clear, the interaction of hydrogen with the graphene/SiC(0001) interface and the hydrogenation process have been addressed only partially. Lee et al. () studied the preferential sites of hydrogen incorporated in epitaxial graphene, reaching the conclusion that the adsorption of hydrogen at the interface becomes more favorable than above the buffer layer at very high hydrogen concentrations. Because of the very large periodicity of the actual interface structure, which is given by a SiC reconstruction [3, 7], they used two model interfaces where the lattice constant of the SiC substrate is either compressed or expanded by about 8% in order to match the lateral size of the graphene overlayer. One of the two interface models reproduces the experimentally observed rotation of 30\circ between the SiC and graphene lattices, while the second has no rotation. A realistic interface system with the correct periodicity was employed by Deretzis and La Magna () to investigate the electronic band structure of QFMLG within density functional theory (DFT), but the adsorption energetics of H was not considered there. More recently, the same authors studied the hydrogenation process through Monte Carlo techniques using a sophisticated model, but the input parameters (such as binding energies, adsorption/desorption barriers, etc.) were taken from ab initio calculations of interface models with unrealistic graphene or SiC strains (). In general, a high graphene strain may influence the relevant energetics in at least two ways: (i) it implies an energy cost to stretch or compress the graphene lattice; (ii) it modifies the chemical reactivity of graphene. For instance, in the commonly used model (which we will call R1 here), the graphene lattice constant is stretched by more than 8%, which corresponds to an energy cost of about 1 eV per surface Si atom (0.8 eV per graphene unit cell) () and a 0.7 eV larger binding energy of H (). Moreover, given its small periodicity compared to the reconstruction, a single unit cell can just mimic the strongly bound regions of the moiré (), and is thus not representative of the variations of height and register (lateral shift) of the graphene with respect to the SiC(0001) surface across the larger unit cell.
To make a step forward in these respects, we investigate here the interaction of atomic H on graphene/SiC(0001) by employing atomistic models characterized by negligible graphene strains (). The selected interface models have a surface periodicity smaller than the experimentally observed . Nevertheless, these models allow us to keep into account the local variation of the graphene–SiC interaction related to the moiré and to explore a large number of adsorption configurations from first principles at a reasonable computational cost. Two interface models are compared: a first one displaying a graphene/SiC rotation angle close to the experimental value of and thus also possessing a high energetic stability (); a second one having a much smaller rotation angle and a lower stability. This comparison allows us to study how the rotation angle and the interaction strength between graphene and SiC affect the interaction of H with the buffer layer. Adsorption of atomic H on the buffer-layer C atoms is addressed through these two models and the spatial variations of the binding strength of H are interpreted through the local atomic structure of the interface.
The paper is organized as follows. In Section 'Methods', we describe the computational parameters and approximations. In Section 'H adsorption on strained graphene', we report a set of reference calculations of H adsorption on pristine graphene at different strains. In Section 'H adsorption on the buffer layer', the results for the graphene/SiC interface are presented and interpreted. Finally, conclusions are drawn in Section 'Conclusions'.
The calculations are performed within density functional theory at the gradient-corrected level () using the Quantum ESPRESSO suite of codes (). We use ultrasoft pseudopotentials and plane waves basis sets with the computational parameters described previously in Ref. ().
The pristine graphene sheet is described by a periodic supercell with a vacuum layer of about 15 Å along the direction perpendicular to the graphene plane. The two-dimensional Brillouin zone (2D-BZ) is sampled with a Monkhorst–Pack grid () of uniformly spaced k-points corresponding to a mesh for the cell. The reference energy for the isolated hydrogen atom is obtained from a spin polarized calculation of one H atom inside a large enough cubic cell. Using a theoretical equilibrium distance of 0.753 Å for the H2 molecule, we find a binding energy of 2.27 eV per H atom, in agreement with recent calculations ().
The graphene/SiC interfaces are built by overlaying a SiC(0001) surface supercell with a rotated graphene layer and then slightly stretching or compressing the graphene lattice constant to match the lateral size of the SiC supercell ().
Two among the low-strain interfaces identified in Ref. () are here considered and compared: (i) the R4” interface (Fig. 1) with a SiC periodicity and a graphene/SiC rotation angle , close to the rotation of corresponding to the experimentally observed reconstruction; (ii) the R2 interface (Fig. 2) with a SiC periodicity and . In the former, the graphene is uniformly stretched by about 1.4%, while in the latter it is compressed by about 0.6%. In both cases, the energy cost to strain the graphene is less than 50 meV per surface Si atom and is therefore negligible with respect to graphene/SiC interaction energies () and typical binding energies of H (see Section 'H adsorption on the buffer layer'). Moreover, in Section 'H adsorption on strained graphene', we will show that for strains below 1.5% the binding energy of H increases by less than 0.1 eV and thus the reactivity of graphene does not differ much from that of the unstrained system.
The slab models used here contain four SiC-bilayers (of which the upper two were relaxed), which are sufficient to account for the substrate relaxations upon adsorption. The 2H-SiC used in this work can be taken as representative of the 4H-, 6H-, and 3C-SiC substrates, which are usually employed to produce epitaxial graphene. Indeed, test calculations show that H binding energies generally differ by 0.05 eV and at most by 0.2 eV. The 2D-BZ was sampled using the -point for R4” and a shifted grid for R2, but we verified for selected configurations that a denser k-point mesh gives the same binding energy within 0.1 eV or better.
H adsorption on strained graphene
In this section, we report some reference calculations of H adsorption on a pristine graphene sheet as a function of the H coverage and the graphene strain. The structure ( graphene units and one H atom per cell) is fully relaxed and only adsorption atop C atoms is considered because it is by far energetically favored with respect to the other high symmetry sites (hollow or bridge) (). The binding energy of H in the graphene cell is given by:
where is the energy of one graphene unit cell, is the energy of the isolated H atom, and is the energy of the full system after relaxation. In Eq (1), we explicitly indicate the dependence on the graphene strain , where and are the lattice spacings of strained graphene and of graphene at the equilibrium, respectively. In order to minimize the BZ sampling error, the k-point mesh has been chosen according to the supercell size (e.g., , for ).
In Fig. 3, we report as a function of the strain s between (1% of compressive strain) and (8% of tensile strain) for several supercell sizes (), as obtained with spin-unpolarized calculations. For tensile strains, the reactivity increases with strain following the same trend for every value of n, although not exactly in a linear fashion as found by de Andres and Vergés (). For compressive strains, instead, we see a varying behavior depending on n: the reactivity is smaller than in the unstrained case up to , but it becomes larger at . This behavior is likely due to the rippling of graphene induced by H adsorption, which becomes more pronounced for larger n and is suppressed by a tensile strain. We notice that for the differences in with respect to unstrained graphene stay below 0.1 eV, while for it is about eV. Therefore, in the R1 interface the reactivity of graphene can be severely overestimated, while in our models it should be described with an acceptable level of accuracy.
We also checked spin-polarized calculations for and at two representative values of strain ( and ), finding that the trend of as a function of strain (not shown) is the same as in the non-polarized case. We also find that the values of in the spin-polarized case converge much faster as a function of the cell size compared to the spin-unpolarized case, even if the relaxed geometries do not differ appreciably. For large cell sizes the two approaches give the same within few tenths of eV, resulting in an error of about eV for and below eV for . This justifies the usage of spin-unpolarized calculations for the estimate of when large enough graphene periodicities are involved, such as in the graphene/SiC interface systems considered here.
H adsorption on the buffer layer
We examine now the binding energy of H above the buffer layer in the two interface models introduced in Section 'Methods'. First, some relevant structural properties of the relaxed interface systems (without adsorbates) will be presented (). In Fig. 4, we show the distributions of the pyramidalization angle () of the C atoms in the buffer layer for the two interfaces. The atoms with higher are fourfold-coordinated C atoms which make bonds to surface Si atoms (shaded areas in the histograms) and thus contribute to the interface stability (). The remaining C atoms are threefold coordinated but have a non-vanishing , thus one may expect that they exhibit a chemical reactivity larger than in free-standing graphene (, pure hybridization). Also, the spread in the value of might point to a large variation of the reactivity across the unit cell of the graphene/SiC interface.
Starting from the relaxed interface structures, depicted in Figs. 1 and 2, we probe the chemical reactivity of each C atom in the buffer layer by adsorbing a H atom atop the selected C. The color of these atoms has been mapped to the corresponding binding energy of H, calculated as:
where and are the total energies of the relaxed graphene/SiC interface with and without the adsorbate, respectively. Hydrogen adsorption on most of the Si-bonded C atoms is unstable or metastable (i.e., a H atom initially placed atop those sites moves toward a neighboring stable site during structural optimization), while it is stable on any of the C atoms which do not form covalent bonds with the substrate. A general feature of the R4” interface (cf. Fig. 1) is the presence of two Si-bonded atoms as nearest neighbors (NNs) of the more reactive C atoms, while the less reactive ones often have only a single Si-bonded NN or none. In the R2 interface model (Fig. 2), also configurations with 3 Si-bonded neighbors are possible. This is at variance with the R4” model, where these configurations cannot occur because of the different rotation angle between graphene and SiC (see also below). If we collect the H binding energies for all stable sites into a histogram (Fig. 5), we see that in general is much larger than in free-standing graphene (cf. Section 'H adsorption on strained graphene') and can vary by roughly 1.5 eV (2.0 eV) across the R4” (R2) unit cell. In both unit cells, is larger than the H binding energy in the H2 molecule for many of the stable adsorption sites. If we assume that is not influenced much by the presence of other adsorbed H in the neighborhood, dissociative adsorption of H2 would be an exothermic process on those sites, in contrast to pristine graphene. Experiments showed that adsorbed hydrogen atoms on the buffer layer are remarkably stable upon sample annealing, desorbing from the buffer layer only above 750 K (). This is in line with our finding of much larger H binding energies on the buffer layer than on pristine graphene.
We now want to establish a connection between the local variations of and the structural properties of the interface in the vicinity of the adsorption site. In Fig. 6a, we plot the value of for each stable adsorption site against , the average of the xy-projected distances between its three nearest C neighbors and the respective surface Si atom at closest distance. In the R2 interface, a clear linear trend is found between and , with the most stable configurations having the lowest values of . One of these configurations is shown in Fig. 6b. Each of the three C NNs of the adsorption site is almost atop a surface Si atom. The corresponding C–Si bonds are strengthened by the local sp3 rearrangement of the C atom to which the H atom attaches, which generally presents a between and upon H adsorption. In the R4” interface, instead, the correlation is less clear. Nevertheless, most of the points follow the same trend as in the R2 interface. The smallest values that can be realized in this case are not as low as in the R2 case, because of the different graphene/SiC rotation which forbids configurations with all three C NNs directly atop surface Si atoms. One of the lowest energy configurations of H adsorbed on R4” is shown in Fig. 6c. One can argue that at most two NNs are very close to surface Si atoms. Such configurations correspond in most cases to the more reactive sites in the R4” interface. Instead, no clear correlation is found between the initial (or final) values of and the binding energy of H. Since the latter is about one order of magnitude larger than the interface energy per Si atom (cf. Fig. 4), the initial geometry of the interface near the adsorption site gets easily modified by H adsorption.
The interaction of atomic H at the graphene/SiC(0001) interface was addressed using model interfaces characterized by negligible graphene strains and two different graphene/SiC rotation angles. The threefold coordinated C atoms in the buffer layer display an increased chemical reactivity compared to free-standing graphene, resulting in two-to-four times larger binding energies of H. On most of the stable adsorption sites, H binds more strongly than in a H2 molecule, possibly resulting in an exothermic dissociative adsorption of H2. The enhanced binding energies of H were interpreted through the interaction between graphene and the underlying SiC(0001) surface, which makes energetically convenient local sp3 arrangements near the adsorption site. The most stable adsorption sites are those with all three nearest C neighbors directly atop surface Si atoms, since the corresponding C–Si bonds are strengthened by the local change of hybridization of the H-bonded C atom. Configurations with three C atoms atop a surface Si can occur only when the graphene/SiC rotation is close to , while for rotations close to at most two C atoms can be atop surface Si atoms, resulting in lower maximal values of the binding energy.
These findings demonstrate the utility of low-strain interface models for investigating H interaction at the graphene/SiC(0001) interface without resorting to the experimental periodicity, which would be much more demanding from the computational point of view. In addition to binding energies, other relevant chemical processes could be assessed within these models, such as, for instance, energetic barriers associated to diffusion, attachment and desorption of H.
Partial financial support is acknowledged from the Swiss National Science Foundation (Grant Nos. 200020–119733/1 and 206021–128743). We used the computational resources of CSEA-EPFL and CADMOS. The financial support for CADMOS and the Blue Gene/P system is provided by the Canton of Geneva, Canton of Vaud, Hans Wilsdorf Foundation, Louis-Jeantet Foundation, University of Geneva, University of Lausanne and École Polytechnique Fédérale de Lausanne.