Physics Letters A 378 (2014) 1841–1844
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Physics Letters A
www.elsevier.com/locate/pla
Significant interplay effect of silicon dopants on electronic
properties in graphene
Xiao-Lin Wei a,b,∗ , Xun Wen a , Li-Chun Xu b,c , Xiang-Yang Peng a , Li-Min Liu a ,
Ru-Zhi Wang b,c , Jue-Xian Cao a
a
Laboratory for Quantum Engineering and Micro–Nano Energy Technology, Department of Physics, Xiangtan University, Xiangtan,
Hunan 411105, China
b
Beijing Computational Science Research Centre, Beijing 100084, China
c
Laboratory of Thin Film Materials, College of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, China
a r t i c l e
i n f o
Article history:
Received 14 January 2014
Received in revised form 10 April 2014
Accepted 28 April 2014
Available online 6 May 2014
Communicated by R. Wu
a b s t r a c t
Using first-principles calculations, we have systematically studied the effects of the interplay between Si
dopants in graphene. Four stable Si-pair doping configurations have been predicted and investigated. It is
shown that the Si dopants tend to agglomerate in graphene. In particular, the band structures can be remarkably modulated by the doping sites of Si atoms in graphene. With the change of the Si–Si distance,
the electronic structures can be widely tuned to exhibit isotropic, direction-dependent, and semiconducting properties. Based on this unique interplay effect, we reveal two ordered C–Si alloys, CSi and C3 Si. It is
found that CSi has an indirect band gap of 2.5 eV while C3 Si still retains the Dirac features. Our results
suggest that more remarkable electronic properties of graphene can be obtained by controllable tuning
of the multi-doping of Si in graphene.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Due to the linear dispersion relation obeyed by the electrons
in graphene, this special material has been endowed the most
important role in next generation devices [1]. The charge carriers behave like massless relativistic particles. However, the lack
of band gap renders the construction of graphene-based devices
difficult. Numerous efforts have been devoted to modulating the
electronic properties of graphene [2–5]. Especially, the doping with
heteroatoms is a very efficient way to tailor the properties of
graphene [6–13]. The atoms substitutionally doped in graphene
will lead to a disruption of the ideal sp2 hybridization of carbon
and hence have significant influence on graphene. In particular,
silicon atoms, which are frequently introduced into graphene as
heteroatoms, can improve and tune the properties of graphene [8].
For graphene prepared by chemical vapor deposition, Si is one
of the most common impurities [14]. Due to the existence of Si
sources, such as the Si wafer substrate, Si impurities are easily
introduced during the growth process at high temperatures. In addition, silicene, a two-dimensional (2D) honeycomb arrangement
of silicon atoms, has been successfully synthesized [15]. It provides a possibility of graphene–silicene 2D compound, like the
graphene–BN compound [16]. All these possible implementations
*
Corresponding author.
http://dx.doi.org/10.1016/j.physleta.2014.04.056
0375-9601/© 2014 Elsevier B.V. All rights reserved.
of Si doping in graphene require a clear understanding of the effect
of silicon atoms on graphene. The picture of individual Si impurity atoms has been derived experimentally [17]. It is found that
threefold coordinated Si in graphene results in sp3 hybridization.
Besides the single Si impurity in monolayer graphene, Si doped
bilayer–graphene has been investigated, which shows that there is
a covalent bonding of Si atoms between different layers [18]. This
stable linked structure strongly suggests the importance of interaction between Si impurity atoms in graphene. However, there are
few studies of multi-Si atoms doping in graphene, including the
structural stability and the interaction between the different doping sites. Therefore, it is important to give new insights into the
electronic structure and the chemical bonding of multi-impurities.
In this paper, we investigate the interplay between silicon
atoms in graphene by systematical calculation of possible structures using first-principles calculations. Base on this interplay effect, we predicted four related stable Si-doped graphene configurations and two C–Si alloys and discussed their electronic structures,
which indicates that the modulation of doping sites should be very
important to design new 2D electronic materials.
2. Models and methods
To investigate the effect of two substitutional silicon atoms,
we use a 9 × 9 graphene supercell with a vacuum layer of 15 Å
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Fig. 1. Doping model of graphene. Two C atoms are substituted by two Si atoms.
The distance between the doping sites is denoted by r.
to avoid the long-range interaction between silicon atoms and
their images in the periodic supercells. The search of doping sites
is done in a way as shown in Fig. 1: the first Si atom is fixed
at one site, and the second one is put on the sites with a distance of r from the first one. These sites are equivalent due to the
symmetry. The non-equivalent doping configurations of bi-silicon
atoms can be obtained by changing the distance r. For all doping configurations, first-principles calculations were carried out using density functional theory and the projector-augmented-wave
(PAW) method [19] as implemented in VASP code [20]. For the
exchange-correlation function, the GGA-PBE [21] was employed.
The standard PAW pseudopotentials for C with 2s2 2p2 and Si with
3s2 3p2 were adopted. A kinetic-energy cutoff of 500 eV and a
Monkhorst–Pack k-point mesh [22] of 3 × 3 × 1 were chosen. The
convergence criterion of the SCF process was set to 10−5 eV. The
atoms were relaxed until the calculated forces were smaller than
0.01 eV/Å.
Fig. 2. (a) Interaction energy between the doped Si pair in graphene. (b) 1, (c) 2,
(d) 3, and (e) 4 indicate four configurations in which the interaction of Si atoms
leads to an exothermic doping.
3. Stable structure of Si substitutionally doped graphene
All possible configurations of Si–Si atoms doping have been investigated in the 9 × 9 graphene cell. Due to the periodicity of the
supercells, we only considered the configurations in which the separation of the two Si atoms is less than 11 Å. In this work, the effects
of concentration of silicon atoms and the shape of supercell keep constant, and only the interactions effect of two silicon atoms are studied by
tuning the distance between two silicon atoms. For each configuration,
the atoms have been fully relaxed. To investigate the possibility
of aggregation of substitutional silicon atoms, the interaction energy E of two doped Si atoms is calculated by [9]
E = E 2 + E 0 − 2E 1 ,
(1)
where E 0 , E 1 and E 2 are the total energies of the systems with
zero, one and two substitutional Si atoms, respectively. Fig. 2(a)
gives the relation between E and the Si–Si pair distance. It can
be seen that E is positive except at some special points, such
as 1, 2, 3 and 4. These four configurations are thermodynamic stability systems. Beside the thermodynamic stability, the dynamic stability of
four configurations have also been checked by the Ab Initio Molecular
Dynamics calculation. The lattices remain very stable after 15 ps simulations at heating up to 500 K. It can be confirmed that these configurations
are stable. When the two Si atoms replace the two adjacent C
atoms on the same edge of a hexagon, namely, when they are nearest neighbors, E reaches its maximum positive value, indicating a
strong repulsion between these two substitutional Si atoms. When
the distance of Si–Si pair is big enough, with the increase of the
distance between the Si pair, E oscillates and tends to decay to
zero. The four stable configurations with negative E are shown
Fig. 3. The band structures of the four stable configurations shown in Fig. 3. The
labels 1, 2, 3 and 4 correspond to those of in Fig. 2.
in Fig. 2. The configuration in which the two substitutional Si
atoms are third nearest neighbors [Fig. 2(c)], the interaction of
the Si–Si pair is strongest with E = −0.65 eV. This most stable configuration for Si-pair substitutional doping, in which two C
atoms located on the diametrically opposite vertices of a hexagon
are substituted, is also a stable configuration for N-pair substitutional doping in graphene. However, the substitution configuration
as shown in Fig. 3(d), which is the most stable one for N-pair
doping [9], is much less stable for Si-pair doping with an attractive interaction energy E as small as −0.075 eV. It is interesting
X.-L. Wei et al. / Physics Letters A 378 (2014) 1841–1844
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to note that in the configuration defined by Fig. 3(a), in which
the two substitutional atoms are second nearest neighbors, the
Si-pair still have attractive interaction (with negative E) while
the N-pair in this configuration are highly repulsive to each other
with a large positive E. There is a similar difference between
N-pair doping and Si-pair doping for the substitutional configuration as defined by [Fig. 2(d)]. A N atom has 5 valence electrons
and a higher electronegativity than C atom, while Si and C atoms
have the same number of valence electrons. Although a single
threefold-coordinated Si in graphene results in an out-of-plane sp3
hybridization [17], it is surprising to find that two Si substitutional
atoms are in the carbon plane due to the interaction between the
Si-pair, which is favorable for the application of the multi-layer devices based on the Si-doped graphene.
4. Energy band diversity in C–Si 2D structure from
To study the electronic structures of the four stable configurations as shown in Fig. 2, we calculated their band structures.
It was found that one Si atom doping in graphene will lead
to a local pyramidal coordination around the Si atom, and the
energy band structure has a small band gap of 0.054 eV [8].
Si and C atoms have four valence electrons, but Si tends to have a
tetrahedron coordination. This tendency is suppressed when there
are two interacting substitutional Si atoms, namely, the Si-pair
doped graphene keeps flat, even the relax calculations start from the
non-planar structures with the out-of-plane Si atoms. For the Si-pair
doping configuration as shown in [Fig. 2(b)], the band structure
still exhibits linear dispersion near Gamma point, which is not broken by the Si–Si interaction. With the increase of distance between
two Si atoms, the band structure of the configurations 2 and 3 undergo similar changes. The Dirac points are shifted from Gamma
point towards X- or Y-lines [Fig. 3], which are the mirror lines
in reciprocal space of graphene. When the Dirac point locates at
the Gamma point, the electronic properties of Si-doped graphene
are isotropic. If the Dirac point is shifted away from the Gamma
point, the electronic properties of graphene become anisotropic,
which implies direction-dependent properties similar to those of
6, 6, 12-graphene [2]. For the configuration shown in [Fig. 2(e)],
its band structure is different from those of the above three configurations with an indirect band gap of 90 meV. Since the two Si
atoms are far from each other [Fig. 2(e)] and the electronic structure tends to resemble that of single-Si-doped graphene. With the
different interaction between Si dopants, the electronic structures
of Si-pair-doped graphene exhibit isotropic Dirac cones, anisotropic
Dirac cones, and small indirect semiconducting band-gap in the
four stable configurations described in Fig. 3.
We can construct C–Si alloys by uniformly distributing Si
dopants in graphene in a way based on the stable Si-doping configuration discussed above [9]. These C–Si alloys are the extreme
case of the Si-doping in graphene. From the configurations 1 and 2,
we can construct CSi alloy [Fig. 4(a)] and C3 Si alloy [Fig. 4(b)],
respectively. The band structures and DOSs for the CSi and C3 Si
alloys are shown in [Fig. 4(c, d)] and [Fig. 4(e, f)], respectively. Interestingly, CSi is a semiconductor and has an indirect band gap of
2.5 eV with the VBM at K and CBM at M, respectively. The VBM is
mainly contributed by C p z orbitals, and the CBM is mainly contributed by Si p z orbitals. The distribution of valence electrons in
Si and C is similar in the CSi alloy, implying a C–Si hybridization
that leads to a reduction of the Coulombic repulsion and a big
band gap. Another alloy, C3 Si, is quite different from the CSi alloy. The band structure and DOS of C3 Si alloy [Fig. 4(e, f)] show
that the valence and conduction bands intersect at the K point at
the Fermi level to form a gapless Dirac cone. Accordingly, the DOS
of C3 Si is zero at the Fermi level. Similar distributions of valence
electrons in Si and C should be one of the reasons for the exis-
Fig. 4. Ordered C–Si alloys of (a) CSi, and (b) C3 Si. Their band structure and DOS are
shown in (c, d) for CSi and in (e, f) for C3 Si.
tence of Dirac point. The Dirac cone is still retained in the band
structure of C3 Si alloy, because the hexagonal symmetry still holds
for C and Si atoms and there are six-membered C rings in the alloy [Fig. 4(b)]. The fact, the distribution of Si atoms in C3 Si alloy has
not broken the symmetry between the A and B sublattice of hexagonal
lattice, contributes to the preservation of Dirac cone.
5. Conclusions
In summary, we have studied the effects of the interaction between the substitutional Si atoms doped in graphene and found
four stable Si-pair doping configurations. The band structure of
graphene can be remarkably modulated by different Si doping
configurations, leading to Dirac point shifting and even band-gap
opening. As a result, new electronic features arise via Si-doping
modulations, such as direction-dependent electronic properties
and band gap tuning. Further, we revealed two ordered C–Si alloys,
CSi and C3 Si derived from the stable Si-pair doping configurations,
in which different distribution symmetries of the atoms and interactions between Si and C atoms give rise to qualitatively different
electronic structures. CSi alloy has a large indirect band gap of
2.5 eV while in C3 Si alloy the gapless Dirac cone is still retained.
Our research proposes a novel, effective and simple approach to
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designing graphene-based devices that can be modulated by different Si-doping configurations.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11204262, 11275163, 11074017), the
Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20124301120006), the Open Fund
based on innovation platform of Hunan colleges and universities
(No. 12K045), and Hunan Provincial Natural Science Foundation of
China (No. 13JJ4046).
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