Ab initio Study of Graphene on SiC
Ab initio Study of Graphene on SiC
Alexander Mattausch∗ and Oleg Pankratov
Theoretische Festkörperphysik, Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
(Dated: October 30, 2018)
Employing density-functional calculations we study single and double graphene layers on Si- and
C-terminated 1 × 1 - 6H-SiC surfaces. We show that, in contrast to earlier assumptions, the first
carbon layer is covalently bonded to the substrate, and cannot be responsible for the graphene-
type electronic spectrum observed experimentally. The characteristic spectrum of free-standing
graphene appears with the second carbon layer, which exhibits a weak van der Waals bonding to
the underlying structure. For Si-terminated substrate, the interface is metallic, whereas on C-face
it is semiconducting or semimetallic for single or double graphene coverage, respectively.
PACS numbers: 68.35.Ct, 68.47.Fg, 73.20.-r
The last years have witnessed an explosion of inter-
est in the prospect of graphene-based nanometer-scale
electronics [1, 2, 3, 4]. Graphene, a single hexagonally
ordered layer of carbon atoms, has a unique electronic
band structure with the conic “Dirac points” at two in-
equivalent corners of the two-dimensional Brillouin zone.
The electron mobility may be very high and lateral pat-
terning with standard lithography methods allows de-
vice fabrication [1]. Two ways of obtaining graphene
samples have been used up to now. In the first “me-
chanical” method, the carbon monolayers are mechani-
cally split off the bulk graphite crystals and deposited
onto a SiO2/Si substrate [4]. This way an almost “free-
standing” graphene is produced, since the carbon mono-
layer is practically not coupled to the substrate. The sec-
ond method uses epitaxial growth of graphite on single-
crystal silicon carbide (SiC). The ultrathin graphite layer
is formed by vacuum graphitization due to Si depletion
of the SiC surface [5]. This method has apparent techno-
logical advantages over the “mechanical” method, how-
ever it does not guarantee that an ultrathin graphite (or
graphene) layer is electronically isolated from the sub-
strate. Moreover, one expects a covalent coupling be-
tween both which may strongly modify the electronic
properties of the graphene overlayer. Yet, experiments
show that the transport properties of the interface are
dominated by a single epitaxial graphene layer [1, 2].
Most surprisingly, the electronic spectrum seems not to
be affected much by the substrate. As in free-standing
graphene one observes the “Dirac points” with the linear
dispersion relation around them. The electron dynamics
is governed by a Dirac-Weyl Hamiltonian with the Fermi
velocity of graphene replacing the speed of light. This
leads to an unusual sequence of Landau levels in a mag-
netic field and hence to peculiar features in the quantum
Hall effect [1, 4].
The growth of high-quality graphene layers on both
Si-terminated or C-terminated SiC{0001} surfaces oc-
curs in vacuum at annealing temperatures above 1400◦C.
The geometric structure of the interface is unclear. For-
beaux et al. [5] proposed that on the Si-face the graphite
FIG. 1: (Color online) Side view (a) and top view (b) of a
graphene layer on the SiC(0001) surface. The
3R30◦
surface unit cell is highlighted.
layer is loosely bound by van der Waals-forces to the√
3R30◦-reconstructed substrate. On the con-
trary, combining STM and LEED data with DFT cal-
culations Chen et al. [6] came to the conclusion that the
graphite sheet is formed on a complex 6 × 6-structure,
from which originates the observed 6
3 × 6
3R30◦ re-
construction that precedes the graphite formation. On
the C-terminated SiC(0001̄) face, graphite growth on top
of a 2 × 2 reconstruction was reported [5, 7]. Berger
et al. [1, 2] observed the formation of large high-quality
graphene islands on top of a 1×1 C-terminated SiC sub-
strate with a
3R30◦ interface reconstruction.
In this work we employ an ab initio density-functional
theory approach to study the bonding and electronic
structure of graphene on SiC. We find that a strong co-
valent bonding of the first carbon layer to the substrate
removes the graphene-type electronic features from the
energy region around the Fermi level. However, these
features reappear with the second carbon layer. We also
compare the electronic properties of graphene on Si- and
C-terminated surfaces.
Our calculations were performed with the density-
functional theory program package VASP [8, 9, 10, 11] in
the local spin density approximation (LSDA). Projector
augmented wave (PAW) pseudopotentials [12] were used.
A special 7× 7× 1 k-point sampling was applied for the
Brillouin-zone integration. The plane wave basis set was
http://arxiv.org/abs/0704.0216v2
restricted by a cut-off energy of 400 eV. We have chosen a
6H-SiC polytype, which is most often used in experimen-
tal studies. The supercell was constructed of 6 bi-layers
of SiC in the S3-structure [13], one or two carbon mono-
layers and a vacuum interval needed to separate the slabs.
The vacuum separation varied, depending on the carbon
coverage, between 10 to 15 Å. The graphene layer was
placed on top of the unreconstructed 6H-SiC substrate
such that the structure had a lateral
3R30◦ el-
ementary cell (Fig. 1a). Due to the lattice mismatch
of 8% between SiC and graphite, this requires stretching
the graphene layer. We verified that for the free-standing
graphene layer the stretch reduces the total bandwidth
from 19.1 eV to 17.3 eV but does not affect the electronic
spectrum close to the Fermi energy. The elastic energy
is 0.8 eV per graphene unit cell.
The interface unit cell (cf. Fig. 1b) contains three sur-
face atoms of the substrate and four elementary unit cells
of graphene. The dangling bonds of the substrate atoms
at the corners of the unit cell are unsaturated, while the
other surface atoms bind to two carbon atoms of the
hexagonal graphene ring. In case of the Si-terminated
SiC(0001) surface, we find that the graphene layer is sep-
arated by 2.58 Å from the SiC substrate. The carbon
atoms covalently bonded to the substrate relax towards
the SiC surface, such that the bond length is 2.0 Å. This
is only slightly longer than the bond length 1.87 Å in SiC.
The graphene bonding releases 0.72 eV per graphene unit
cell. For the C-terminated SiC(0001̄) face, the graphene
layer is somewhat closer (2.44 Å) to the substrate and the
bond length between the bonding carbon atoms reduces
to 1.87 Å. The energy gain is 0.60 eV per graphene unit
cell. On both interfaces, the bonding atom of the sub-
strate relaxes outwards, whereas the partner graphene
atom moves towards the substrate. The bonding ener-
gies are quite close but somewhat smaller than the elastic
deformation energy of the graphene layer. However, the
latter can be drastically lessened by defects which result
from the lattice mismatch.
For a second graphene layer placed in the graphite-
type AB stacking, we find a weak bonding at a distance
of 3.3 Å, very close to the bulk graphite value 3.35 Å.
This conforms to the fact that LSDA, despite the lack
of long-range non-local correlations, produces reason-
able interlayer distances in van der Waals crystals like
graphite [14, 15] or h-BN [16]. As shown by Marini et
al. [16], a delicate error cancellation between exchange
and correlation underlies this apparent performance of
the LSDA. The semilocal GGA, which violates this bal-
ance, fails to generate the interplanar bonding in both
graphite [15] and h-BN [16], while producing a band
structure identical to LSDA [15]. It is thus natural to
assume that in our situation the bonding between the
graphene layers is the same as in bulk graphite with the
same interplanar distance. To reduce the calculational
cost, we fixed the interplanar distance at this value.
The first graphene layer, which is covalently bonded to
the substrate, thus serves as a buffer separating the SiC
crystal and the van der Waals bonded second graphene
sheet. Most probably, the 6
3R30◦ reconstructed
carbon-rich Si-terminated surface observed as a precur-
sor of graphitization is a natural realization of this buffer
layer in the epitaxial process. The 6
3 structure is
practically commensurate with graphene since 13 times
the graphene lattice constant almost precisely fits 6
times the SiC lattice parameter. In any case, there is
no stress in the second carbon layer. Even placed on a
strongly stretched buffer layer, the upper layer relaxes to
its natural lattice constant due to the weak interlayer in-
teraction. For the C-face Berger et al. [1] found graphene
formation on a 1× 1 substrate with a
3 interface
unit cell. This structure is the same as we used in our
calculations.
Figs. 2a and 2b show the electronic energy spectrum
of a single graphene layer on the two SiC surfaces. The
shaded regions are the projected conduction and valence
energy bands of SiC. The Kohn-Sham energy gap of
1.98 eV is smaller than the optical band gap (3.02 eV)
of the bulk 6H-SiC, which is a common consequence
of LSDA. The covalent bonding drastically changes the
graphene electron spectrum at the Fermi energy. The
“Dirac cones” are merged into the valence band, whereas
the upper graphene bands overlap with the SiC conduc-
tion band. Hence a wide energy gap emerges in the
graphene spectrum. A similar gap opening due to hy-
drogen absorption on a single graphene sheet was pre-
dicted in Ref. 17. The weakly dispersive interface states
visible in Figs. 2a and 2b result from the interaction
of the graphene layer with the three dangling orbitals
of the substrate. Two of them make covalent bonds,
while the third one in the center of the graphene ring
remains unsaturated (cf. Fig. 1b). A projection analysis
of the wave functions reveals that the gap states close to
the Fermi energy originate from the remaining dangling
bonds of the substrate. On the Si-face we find a half-filled
metallic state, whereas on the C-face the interface state
is split into a singly occupied (spin polarized) and an
empty state, making the interface insulating. In contrast,
on both clean SiC surfaces LSDA predicts a substantial
splitting of the surface states (0.86 eV for SiC(0001) and
0.45 eV for SiC(0001̄), see Table I). Actually, the gap
separating a singly occupied and an empty state is larger
due to the Hubbard repulsion of the electrons (about 2 eV
for the
3R30◦ reconstructed surface [18, 19]), but
already LSDA correctly reproduces the insulating char-
acter of both surfaces.
The reason for the striking difference between the two
graphene-covered surfaces becomes clear if one compares
the planar localization of the two gap states. As seen in
Fig. 3a for the Si-face the interface state electron density
is strongly delocalized. As the projection analysis shows,
this results from the hybridization with the graphene-
Γ Κ Μ Γ
SiC(0001)/Graphene
Γ Κ Μ Γ
SiC(0001)/Graphene
Γ ΓΚ Μ
SiC(0001)/2 graph. lay.
Γ ΓΚ Μ
SiC(0001)/2 graph. lay.
c) d)
FIG. 2: Energy spectrum of the interface states of a) the SiC(0001)/graphene interface, b) the SiC(0001̄)/graphene interface,
c) SiC(0001) with two layers of graphene and d) SiC(0001̄) with two layers of graphene. The Fermi energy is indicated by the
dashed line. K̄ and M̄ are the high-symmetry points of the surface Brillouin zone of the
3R30◦ surface unit cell.
FIG. 3: (Color online) Charge density of the interface states
at the Fermi energy for a single graphene layer on a) SiC(0001)
and b) SiC(0001̄).
induced electron states overlapping with the conduction
band (see Fig. 2a). Given the delocalized nature of the
interface state we expect the influence of Hubbard cor-
relations to be small. In contrast, at the C-terminated
substrate the electron state retains its localized charac-
ter, although it is smeared over a carbon ring just above
the unsaturated C-dangling bond. The localization fa-
vors the spin polarization and thus the splitting of the
gap state, whereas the interface state at the Si-face re-
mains spin-degenerate. In the former case, Hubbard cor-
relations may lead to a further splitting of the interface
state.
Figures 2c and 2d show that the second carbon layer
indeed possesses an electronic structure similar to free-
standing graphene. The characteristic conic point ap-
pears on the Γ̄ − K̄ line (note that since the Brillouin
zone corresponds to the
3R30◦ unit cell, the conic
point is not located at the K̄-point). The interface states
of the buffer layer remain practically unchanged since
the interaction of the carbon layers is very small. The
metallic interface state on the Si-terminated substrate
pins the Fermi level just above the conic point, making
the second graphene layer n-doped. On C-terminated
substrate the Fermi level runs exactly through the conic
point. Hence the interface is semimetallic just as for free-
standing graphene. Indeed, for a graphene-covered C-
face Berger et al. [1] found that the thin graphite layers
possess electronic properties of free-standing graphene.
The parameters of the electron states for the different
interfaces are summarized in Table I. For clean unre-
constructed surfaces we find work functions of 4.75 eV
(Si-terminated surface) and 5.75 eV (C-terminated sur-
face). The former value is practically the same as the
work function of the reconstructed SiC(0001) [20]. The
first graphene layer reduces this value to 3.75 eV, which
is 1.3 eV lower than the work function of free-standing
graphene. The drastic reduction of the work function
is caused by charge flow from graphene to the interface
region, which induces a dipole layer. On the C-face the
graphene overlayer also reduces the work function, but to
a lesser extent such that it remains above the graphene
value. Adding the second graphene layer makes the work
function closer to that of graphene for both faces.
The Fermi level pinning close to the conduction band
makes the graphitized Si-face especially suitable for
Ohmic contacts on n-type SiC, because it guarantees a
low Schottky barrier. Indeed, Lu et al. [21] find a very
low resistance for thermally treated SiC contacts with
TABLE I: Parameters of the unreconstructed and graphene-covered SiC{0001} surfaces in eV: work function φ, positions of
the occupied and the unoccupied surface and interface states above the valence band edge (Eo, Eu) and their corresponding
bandwidths (Bo, Bu).
Work function φ Eo Bo Eu Bu
SiC(0001) 1×1 4.75 Ev + 0.92 0.45 Ev + 1.78 0.53
SiC(0001)/Graphene 3.75 Ev + 1.64 0.35 − −
SiC(0001)/2 Graphene 4.33 Ev + 1.64 0.40 − −
SiC(0001̄) 1×1 5.75 Ev + 0.05 0.75 Ev + 0.50 0.45
SiC(0001̄)/Graphene 5.33 Ev + 0.43 0.13 Ev + 1.19 0.14
SiC(0001̄)/2 Graphene 5.31 Ev + 0.44 0.10 Ev + 1.19 0.15
Graphene (single layer) 5.11
nickel and cobalt, while other metals, which form car-
bides and thereby remove the graphitic inclusions, were
rectifying. Recently Seyller et al. measured the Schot-
tky barrier between n-type 6H-SiC(0001) and graphite
by photoelectron spectroscopy and found a low value of
0.3 eV [22]. On the contrary, the C-terminated face has
the Fermi level close to the middle of the band gap and
is semiconducting or semimetallic.
In conclusion, we investigated the interface between
1 × 1 - 6H-SiC{0001} surfaces and carbon layers em-
ploying ab initio density-functional theory. We find
that graphene overlayers on SiC(0001) and SiC(0001̄)
faces possess qualitatively different electronic structures.
While the former is metallic, the latter has semiconduct-
ing properties. The conic points at the Fermi energy,
which are specific for graphene, appear only with the sec-
ond layer. The first carbon sheet is covalently bound to
the substrate and plays the role of a transition region be-
tween a covalent SiC crystal and a van der Waals bonded
stack of graphene layers.
This work was supported by Deutsche Forschungsge-
meinschaft within the SiC Research Group. We are grate-
ful to L. Magaud and F. Varchon for communicating to
us similar results on the SiC/graphene system [23] and
fruitful discussions.
∗ Electronic address: Alexander.Mattausch@physik.uni-erlangen.de
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mailto:Alexander.Mattausch@physik.uni-erlangen.de
