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Current Applied Physics 13 (2013) 1512e1519

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Current Applied Physics

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Electronic properties of graphene on the C-decorated Si(111) surface:An ab initio study

J. Liu, C.Y. He, W. Wang, N. Jiao, C.X. Zhang, L.Z. Sun*

Department of Physics, Xiangtan University, Xiangtan 411105, Hunan, China

a r t i c l e i n f o

Article history:Received 4 February 2013Received in revised form30 April 2013Accepted 16 May 2013Available online 29 May 2013

Keywords:Si(111) surfaceGrapheneCarbon decorationDensity functional theoryElectronic properties

* Corresponding author. Tel.: þ86 731 52665818; faE-mail address: lzsun@xtu.edu.cn (L.Z. Sun).

1567-1739/$ e see front matter � 2013 Elsevier B.V.http://dx.doi.org/10.1016/j.cap.2013.05.012

a b s t r a c t

First principles calculations based on the density functional theory are performed to study electronicstructures of graphene adsorbed on clean or C-decorated Si(111) surface. Two types of surface re-constructions, 2 � 2 and

ffiffiffi

3p

�ffiffiffi

3p

, are considered to be decorated by carbon atoms with differentconcentrations. We find that graphene adsorbed on ideal clean Si(111) surface tends to induce a 2 � 1reconstruction, and its electronic dispersion characteristics are preserved. Moreover, the decoration ofcarbon atoms on the Si(111) surface can effectively passivate the Si dangling bonds on the surface. Suchdecoration effects make the carbon decorated Si(111) surfaces promising substrate for graphene pre-serving its excellent electronic structure.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Graphene [1e4], a single layer of carbon atoms in a honeycomblattice, has been attracted wide range of research interests duringthe last decade due to its excellent properties, such as high elec-tronic mobility [1,5], quantum Hall effect [3,4,6,7], high thermalconductivity [8], and long distance scattering [9]. As the Si-basedsemiconductor technology and industry are approaching to theirfundamental limits in the process of device miniaturization, gra-phene is considered as a promising candidate to replace Si as basic-material for the next generation electronic device. However, notonly its application but also its growth depends on proper sub-strate, looking for proper substrate keeping the electronic propertyof graphene becomes one of the most interesting topics. The sur-faces of SiC, SiO2, and metal were usually used as substrates ofgraphene [10e18]. Deretzis et al. [19] found that although the firstlayer of graphene adsorbed on Si face of SiC(0001) ð6

ffiffiffi

3p

� 6ffiffiffi

3p

ÞR30� surface behaves as buffer layer due to the strong interactionbetween substrates and graphene, both H and Li intercalation canrestore the ideal structural characteristics of graphene. Markevichet al. [20] recently reported that hydrogen easily migrates betweenthe graphene layer and the SiC substrate and passivates the surface

x: þ86 731 58292468.

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Si bonds, thus causing the graphene layer decoupling fromSiC(0001) ð6

ffiffiffi

3p

� 6ffiffiffi

3p

Þ R30� and 4 � 4 SiC(0001) reconstructedsurface. By saturating the surfaces with external atoms such as Siadatoms, (2 � 2) and (3 � 3) reconstructed SiC ð0001Þ surfaces donot interact strongly with graphene and no buffer layer is formed[21,22]. Using local density approximation (LDA), Khomyakov et al.[23] found that the bonding of graphene to Al, Ag, Cu, Au, andPt(111) surfaces is so weak that the unique electronic structure ofgraphene is preserved, whereas the interaction between grapheneand Co, Ni, Pd, and Ti is relatively strong undermining the electronicstructure of graphene. However, using van der Waals densityfunctional (vdWDF) Vanin et al. [24] found that the graphene bandstructure is basically unaffected by all Co, Ni, Pd, Ag, Au, Cu, Pt, andAl(111) surfaces. The interaction between graphene and a-SiO2(0001) interface is also studied [25] that van der Waals forcedominates the interaction due to the atomic structure reconstruc-tion at the graphene/SiO2 interface. However, the interaction isstronger than the force between the graphene layers in graphite. Bysaturating the surfaces with external atoms or functions groupreducing the concentration of the unsaturated atoms, some litera-ture also reported that the single graphene layers adsorbed on thedecorated surfaces preserve their novel electronic characteristicswell [26e28]. In view of the important role of the siliconmaterial inthe future nano-technology, the combination of graphene and sil-icon substrate is a significant issue for the practical applications ofgraphene. There are a lot of experimental and theoretical studies

J. Liu et al. / Current Applied Physics 13 (2013) 1512e1519 1513

for the adsorption of materials on the silicon substrate [29e33]. Inprevious work [34], we study the configuration and electronicproperties of graphene nano-ribbons (GNRs) on Si(211) surface. Wefind that the substrate effectively affects the edge states of GNRsand tends to depress the metallic nature of zigzag GNRs (Z-GNRs)and metallize the armchair GNRs (A-GNRs). More recently, a singlelayer of graphene has been successfully transferred to the 7 � 7reconstructed Si(111) surface by Ochedowski et al. [35], and itsstructural and electronic properties are investigated thoroughly.Si(111) surface possess low Miller indices and hexagonal structurematching the lattice constant of graphene well. Each Si atom on theideal Si(111) surface forms three SieSi bonds with three inner-bulkSi atoms and leaves a dangling bond. The high density of danglingbonds makes Si(111) surface easy reconstruct. For example, (2 � 1)[36] and (2n þ 1) � (2n þ 1) [37e41] reconstructions of the Si(111)surface can be achieved by adjusting the annealing temperature atultra-high vacuum condition, and 2 � 2, 2 � 4, and

ffiffiffi

3p

�ffiffiffi

3p

re-constructions [39e43] can also be obtained by absorbing externalatoms on the surface.

In present work, first-principles calculations are performed toinvestigate the modulation effects of clean and C-decorated Si(111)surfaces on the electronic property of graphene adsorbed on it. Wefind that the graphene adsorption can induces a 2 � 1 recon-struction of the ideal clean Si(111) surface and its electronic prop-erties are preserved very well, implying that the reduction ofdangling bonds effectively weaken the interaction between gra-phene and Si(111) substrate. We further use external carbon atomsto saturate the dangling bonds at the Si(111) surface in views of itssp2 bonding characteristics. The aim of our present work issearching for proper substrates to support graphene for electronicdevice application. Eight substrates are evaluated in both theirviability and ability of keeping the electronic property of graphene.We find that some of them are hoping to be good substrates infuture graphene based nano-electronics.

2. Models and method

In our present work, eight Si(111) substrates are considered,including Si(111)2 � 1 surface (which is reconstructed from theideal clean Si(111) surface induced by the graphene adsorption),Si(111)2 � 2 surface decorated by carbon atoms with concentra-tions of 1/4, 1/2, 3/4 and 4/4 ML (The decorated concentration isdefined as the ratio of the number of the decorating carbon atomsand the total Si atoms in the surface.), and Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surfacesdecorated by carbon atoms with concentrations of 1/3, 2/3 and 3/3 ML. We firstly optimize these substrates to find out their stablereconstructed configurations. And then we investigate the in-teractions between these substrates and the adsorbed graphenesingle layers, especially the modulation effects of the substrates onthe electronic property of graphene. Considering the difference inlattice constants, 3 � 3 graphene supercell is adopted to match the1 � 1 unit cell of Si(111) 2 � 2; 3

ffiffiffi

3p

� 3ffiffiffi

3p

graphene supercell ischosen to match the 2 � 2 supercell of Si(111)

ffiffiffi

3p

�ffiffiffi

3p

. We stretchthe 3 � 3, 3

ffiffiffi

3p

� 3ffiffiffi

3p

graphene supercell lattice for 2.60% and2.89%, respectively, at the same time compress the correspondingsubstrate lattice for 2.02% and 1.75%, the change of graphene andsubstrate lattice is maintained within 3% the errors of calculationsbased on first-principles method. The thicknesses of the inner-bulkSi atomic layers are chosen to be 8 Si atom layers with the H-terminated bottom surface for the purpose of keeping their bulkproperties. The vacuums layers in our models are set to be largerthan 11 �A to avoid the spurious interactions between the adjacentimages.

Our calculations of both the optimizations and the total energyare performed within the density functional (DFT) based ab initio

simulation package (VASP) [44e46]. The interactions between thenucleus and valence electrons are described by the projectedaugmented wave (PAW) method and the exchange correlation ef-fects between valence electrons are described by the P.B.E [47] typegeneralized gradient approximations (GGA) functional. A plane-wave basis with cutoff energy of 450 eV is used to expand thewave functions. The Brillouin Zone (BZ) sampling meshes are set tobe dense enough to ensure the accuracy of our calculations. For thesystems based on the Si(111) 2 � 2 surfaces, gamma centeredMonkhorstePack grids of 5 � 5 � 1 and 11 �11 �1 are used in theoptimization and total energy calculations, respectively. For thesystems based on the Si(111)

ffiffiffi

3p

�ffiffiffi

3p

, the grids are set as 3 � 3� 1for both the calculations of optimization and total energy. All thesystems are optimized up to the residual force on every atoms to beless than 0.01 eV/�A. To eliminate the fictitious interactions betweenthe surface dipoles in adjacent surfaces, the dipole and potentialcorrection (DPC) method [48] is considered in our present work. Allcomputational parameters used in our present work are optimized.Moreover, we also test the influence of van der Waals correction(DFT-D2 [49] and VDW-DF2 [50]) on the configurations of grapheneadsorbed on clean Si(111)2 � 1 and 1/4 ML C-decorated Si(111)2 � 2. We find that the distance between the substrate and gra-phene, the adsorption energy and gap of the band structure of thegraphene only slightly changed. van der Waals correction is notconsidered in our present work.

3. Results and discussions

3.1. Carbon atoms decorated Si(111) 2 � 2 and Si(111)ffiffiffi

3p

�ffiffiffi

3p

surfaces

Firstly, we obtain the optimized configurations offfiffiffi

3p

�ffiffiffi

3p

and2 � 2 supercell of ideal Si(111) surfaces decorated by carbon atomswith different concentrations. In our calculations, we consider allpossible configurations for each concentration and choose the mostenergetically favorable one to be used as substrate for adsorbinggraphene. Typical adsorption sites are denoted in Fig. 1(a). For boththe

ffiffiffi

3p

�ffiffiffi

3p

and 2 � 2 supercell of Si(111) surfaces, the firstadsorption carbon atom is more favorable to adsorb on top positionthan hollow and hcp ones. The adsorption induces the surfaces occurffiffiffi

3p

�ffiffiffi

3p

and2�2 reconstructions, respectively, as shown inFig.1(d)and (e). The first adsorption carbon atomon Si(111)

ffiffiffi

3p

�ffiffiffi

3p

(Si(111)2 � 2) surface bond to three neighboring hcp Si atoms with bondlengths of 1.972�A,1.972�A and 1.972�A (2.085�A, 2.085�A and 1.892�A),drastically saturating 100% (75%) dangling bonds of the surface.

Following the definition of surface decorated concentration, thedecorated concentration of one carbon atomdecorated Si(111)

ffiffiffi

3p

�ffiffiffi

3p

and Si(111) 2 � 2 surfaces is 1/3 and 1/4 ML, respectively. Basedon the stable configurations of one carbon atom decorated Si(111)ffiffiffi

3p

�ffiffiffi

3p

and Si(111) 2 � 2 reconstructed surfaces obtained above,we further increase the decorated carbon atoms on the surfacesgradually up to 2/3 and 3/3ML for Si(111)

ffiffiffi

3p

�ffiffiffi

3p

, and 2/4, 3/4, and4/4 ML for Si(111) 2� 2 surfaces. The second adsorbed carbon atomon both Si(111)

ffiffiffi

3p

�ffiffiffi

3p

and Si(111) 2� 2 surfaces bonds to the firstadsorbed one forming a C^C dimer with triple bond whose bondlengths are all about 1.251�A (the acetylenic bond length is 1.23�A). Asshown in Fig. 1(d) and (e), the C^C bond of the dimer in both sys-tems spans two hcp positions and the two carbon atoms bond toadjacent hcp Si atoms with bond length of 1.863 �A and 1.867 �A forSi(111)

ffiffiffi

3p

�ffiffiffi

3p

and Si(111) 2 � 2, respectively. The third adsorbedcarbon atom on Si(111)

ffiffiffi

3p

�ffiffiffi

3p

(Si(111) 2� 2) surface bonds to thepreviously adsorbed CeC dimer with (equivalent) CeC bonds of1.416�A,1.416�A, and 1.462�A (1.416�A,1.416�A, and 1.416�A), forming anisosceles (equilateral) triangle. The center of the carbon isosceles(equilateral) triangle locates at the top (hollow) position and

Fig. 1. (a) and (b) are the stable structure offfiffiffi

3p

�ffiffiffi

3p

and 2 � 2 supercell of ideal clean Si(111) surface, respectively. (c) is 1 � 2 supercell of Si(111) 2 � 1 surface. (d) is C-decoratedSi(111)

ffiffiffi

3p

�ffiffiffi

3p

surface with different concentrations. (e) is C-decorated Si(111) 2 � 2 surface with different concentrations. (f) is the adsorption energy of C-decorated Si(111)surface in function of carbon concentration.

J. Liu et al. / Current Applied Physics 13 (2013) 1512e15191514

saturates 100% (75%) surface Si dangling bonds for Si(111)ffiffiffi

3p

�ffiffiffi

3p

and Si(111) 2� 2 surface, respectively. Tofind out themost favorableconfiguration of 4 carbon atoms adsorbed Si(111) 2 � 2 surface, weconsider “3 þ 1” (carbon trimer plus an isolated carbon atom) and“2þ 2” (two carbon dimers) configurations.We find that the “2þ 2”configuration is the most favorable one, as shown in Fig. 1(e). Fourcarbon atoms form two equivalent CeC dimers and bond to theadjacent hcp Si atoms with bond length of 1.861 �A and 1.865 �A,saturating all the dangling Si bonds of the surface.

To evaluate the relative stability of all above equilibrium con-figurations of the Si(111) surfaces with different reconstructions

and decorating carbon concentrations, we calculate their adsorp-tion energies for each carbon atom as:

Ead ¼ EðsubþnCÞ � n� EC � ðm�mÞ � Esubn�m�m

; (1)

where E(subþnC), EC and Esub represent the total energies of the C-decorated system, isolated C atom, and the ideal clean Si(111)substrate, respectively. n andm are the numbers of the decorating Catoms and the size index of the supercell used in calculations (

ffiffiffi

3p

and 2), respectively. The calculated results are shown in Fig.1(f). We

J. Liu et al. / Current Applied Physics 13 (2013) 1512e1519 1515

can see that the most favorable concentrations of the decoratingcarbon atoms to stabilize the surface are 2/3 and 1/2 ML for theSi(111)

ffiffiffi

3p

�ffiffiffi

3p

and Si(111) 2 � 2, respectively. The adsorptionenergies of the

ffiffiffi

3p

�ffiffiffi

3p

reconstructed systems are lower thanthose of the 2 � 2 reconstructed ones, implying that the

ffiffiffi

3p

�ffiffiffi

3p

reconstructions possess relatively high probability to be induced byexternal carbon atoms in comparisonwith the 2� 2 one. Moreover,the energy releases of the C-decorated Si(111) surface substratesimply that the carbon decoration is a possible and helpful way tostabilize the Si(111) surface.

3.2. Electronic properties of carbon atoms decorated Si(111) surface

Based on the optimized configurations of the C-decoratedSi(111) surfaces, we then calculate their electronic band structures.The electronic band structures of the free-standing graphene (inboth 3� 3 and 3

ffiffiffi

3p

� 3ffiffiffi

3p

supercell) and ideal clean Si(111) surface(in

ffiffiffi

3p

�ffiffiffi

3p

and 2 � 2 supercell) are shown in Fig. 2. From Fig. 2(a)and (b), we can see that graphene is a semimetal that its bandstructure shows linear dispersions near the Fermi level where the pand p* bands touch each other at the highly symmetric G and G0

points in the Brillouin zone. When the graphene supercell is3m � 3m and

ffiffiffi

3p

n�ffiffiffi

3p

n (m, n are integers larger than zero) unitcell, the K and K0 points are backfolded on the Gamma point. (Thedetails of the band folding can be found in the Supplementarydata.) Fig. 2(cee) shows the band structures of Si(111) 2 � 2,Si(111)

ffiffiffi

3p

�ffiffiffi

3p

, and Si(111) 2 � 1. The results indicate that thereare obvious localized surface states in its band gap, which arearoused from the unsaturated surface Si atoms.

In comparison with the clean Si(111) surfaces, local surfacestates around the Fermi level of the C-decorated Si(111) are

Fig. 2. Band structure for the free-standing graphene with (a) 3 � 3 supercell (b) 3ffiffiffi

3p

� 3p

band structures of the clean 1 � 2 supercell of Si(111) 2 � 1 surface. (f), (g), and (h) are the3 ML, 3/3 ML, respectively; (i), (j), (k), and (m) are the band structures of the C-decorated Spoint (green) and round dot (amaranth) represent the contribution of surface Si atom andinterpretation of the references to color in this figure legend, the reader is referred to the

obviously reduced. The decoration of the carbon atoms can saturatethe dangling bonds on the Si(111) surface. Before the decoration,there are 4(3) Si dangling bonds on the ideal clean Si(111) surfaceper 2 � 2 ð

ffiffiffi

3p

�ffiffiffi

3p

Þ supercell. After decoration by the carbonatoms of concentrations of 1/4, 1/2, 3/4 and 4/4 (1/3, 2/3 and 3/3)ML for 2 � 2 ð

ffiffiffi

3p

�ffiffiffi

3p

Þ, the remnant Si dangling bonds reduce to 1,2, 1 and 0 (0, 1 and 0), respectively. The results indicate that thedecorating carbon atoms also introduce some C dangling bonds insome concentration and contribute some local states around theFermi level in the band structures, as shown in Fig. 2(f), (h), (i), and(k). Namely, using carbon atom adsorption to passivate thedangling bond of Si(111) surface is dependent on the adsorptionconcentration. However, we also find that decorating the Si(111)surface by carbon atoms with proper concentration can effectivelysaturate the surface Si dangling bonds, for example, the Si(111)2 � 2 and Si(111)

ffiffiffi

3p

�ffiffiffi

3p

decorated by 4 and 3 carbon atoms arepromising substrates of supporting graphene preserving its novelelectronic properties due to their passivated surfaces.

3.3. Configurations of graphene adsorbed on C-decorated Si(111)surface

To find out the adsorption configuration of graphene ondifferent C-decorated Si(111) surface, we choose 3 � 3 graphenesupercell to adsorb on 2 � 2 supercell of ideal clean Si(111) and C-decorated Si(111) surfaces, whereas 3

ffiffiffi

3p

� 3ffiffiffi

3p

graphene supercellon 2� 2 supercell of C-decorated Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surface. Actually,the Si(111) 2 � 1 surface can be induced naturally by the grapheneadsorption on the ideal clean Si(111) surface, as shown in Fig. 3(a).Previous theoretical study [51] indicates that the energy barrier ofthe transformation from ideal Si(111) 1 � 1 to Si(111) 2 � 1

ffiffiffi

3 supercell; the ideal clean Si(111) (c) 2 � 2 supercell (d)ffiffiffi

3p

�ffiffiffi

3p

supercell. (e) is theband structures of C-modified Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surface with concentrations 1/3 ML, 2/i(111) 2 � 2 surface with concentration 1/4 ML, 1/2 ML, 3/4 ML, and 4/4 ML. Diamonddecorated C atom to the band structure, respectively. Fermi level is set to zero. (For

web version of this article.)

Fig. 3. Equilibrium adsorption structure for graphene adsorbed on (a) clean 2 � 1reconstructed Si(111) surface. Graphene adsorbed on C-modified 2 � 2 reconstructedSi(111) surface with concentration 1/4 ML (b), 1/2 ML (c), 3/4 ML (d), and 1 ML (e). (f),(g), and (h) are the adsorption configuration of graphene adsorbed on C-modifiedreconstructed Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surface with concentration of 1/3 ML, 2/3 ML, and 1 ML,respectively.

J. Liu et al. / Current Applied Physics 13 (2013) 1512e15191516

reconstructed surface is only 0.03 eV which can be easily overcomein experiments [52]. According to our calculations, the energy persurface atom of the clean Si(111) 2 � 1 reconstructed surface is0.276 eV smaller than that of ideal clean Si(111) 1 �1, however the2 � 1 reconstruction can not be found directly from the relaxationprocess of the ideal clean Si(111) 1 � 1 surface due to the energybarrier. When the graphene adsorbs on the top of the ideal cleanSi(111) 1�1 surface, the Si(111) 2� 1 structure will form regardlessof the size of the supercell. Such results indicate that although theinteraction between graphene and the Si(111) surface is relativelyweak, it is enough to promote the formation of the Si(111) 2 � 1reconstruction. The distance between the graphene and the Si(111)2 � 1 substrate is about 3.59 �A, which is larger than the interlayerdistance in graphite. The optimized configurations of grapheneadsorbed C-decorated Si(111) 2 � 2 surfaces with carbon concen-tration of 1/4, 2/4, 3/4 and 4/4 ML are shown in Fig. 3(bee),respectively. The distances between the adsorbed graphene and thesubstrate in these complex systems are 3.57 �A, 3.61 �A, 3.14 �A and3.81 �A, respectively. For the complex systems consisting of thegraphenes with 3

ffiffiffi

3p

� 3ffiffiffi

3p

supercell and the 2 � 2 supercells ofthe Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surfaces as shown in Fig. 3(feh), the distancesbetween the adsorbed graphene and the substrate are 3.59�A, 3.74�Aand 3.60�Awhen the concentrations of the decorating carbon atomsare 1/3, 2/3 and 3/3 ML, respectively. These distances are very closeto that between the adsorbed graphene and the 7� 7 reconstructed

Si(111) surface of 0.4 nm reported by Ochedowski et al. [35] in theirexperiments. On the whole, these distances are similar to theinterlayer distance in graphite so that the interaction between theadsorbed graphenes and the substrates is very weak physicaladsorption.

The results of the bond lengths and bond angles of the grapheneadsorbed on the surfaces show that the distortions of the sp2 hy-bridization of the carbon atoms are negligible. The changes in bondlengths and bond angles in graphenes adsorbed on the C-decoratedSi(111) 2 � 2 surfaces are not exceeding 0.004 �A and 0.01�,respectively. In the complex systems consisting of the graphenewith 3

ffiffiffi

3p

� 3ffiffiffi

3p

supercell and the 2 � 2 supercell of the recon-structed Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surfaces, graphene keeps almost theperfect sp2 configurations when the concentration of the deco-rating carbon atoms is 1/3 ML. When the concentration of thedecorating carbon atoms are 2/3 and 3/3 ML, the decorated Si(111)surface distort the bond lengths and angles of the adsorbed gra-phenes, inducing small changes in bond lengths not exceeding0.02 �A and the bond angle is 1.3�, respectively. The adsorptionenergies of these complex systems are also calculated as:

Ead ¼ EðsubþgrapheneÞ � EðgrapheneÞ � Esubm�m

; (2)

where E(subþgraphene), Egraphene and Esub represent the total energiesof the complex system, isolated graphene, and the Si(111) substrate,respectively.m is the number of the size index of the supercell usedin the calculations (2

ffiffiffi

3p

and 2). We find that in all the complexsystems the graphene physically adsorb on the substrates. In de-tails, 3 � 3 supercell graphene adsorbed on the 1 � 2 supercell ofthe reconstructed Si(111) 2 � 1 surface release energy of 6.26 meV/u.c. The 3

ffiffiffi

3p

� 3ffiffiffi

3p

graphene adsorbed 2 � 2 supercells of theSi(111)

ffiffiffi

3p

�ffiffiffi

3p

reconstructed surface release energies of 14 meV/u.c, 106 meV/u.c and 75 meV/u.c when the decorating carbonconcentration is 1/3, 2/3, and 3/3 ML, respectively. The 3 � 3 gra-phene supercell releases 5 meV/u.c when it adsorbs on the 1/4carbon ML modified Si(111) 2 � 2 surface. It releases 13 meV/u.c,6 meV/u.c and 27meV/u.c energy when the graphene adsorbs on 2/4, 3/4, and 4/4 carbon ML decorated Si(111) 2 � 2 surfaces,respectively. We can see that the complex systems consisting of the3

ffiffiffi

3p

� 3ffiffiffi

3p

graphenes and the 2 � 2 supercells of Si(111)ffiffiffi

3p

�ffiffiffi

3p

surfaces release relatively higher energies, implying the relativelystrong interactions between graphenes and substrates in thesesystems, which is in agreement with the above analysis.

3.4. Electronic properties of the graphene/substrate complexsystems

After achieving the stable graphene/substrate complex systems,we investigate their electronic properties. The calculated bandstructures are shown in Fig. 4. The origin of the bands is alsoindicated in the figures. From these results we can see that the bandstructures of the complex systems consisting of the graphenes andthe Si(111) 2� 1 surface and the Si(111) 2� 2 surfaces decorated bycarbon atoms with concentration of 1/4, 2/4, 3/4 and 4/4 ML can beconsidered as simple combinations of the band structures of thefree standing graphene and the substrates. We can see that in thesesystems, graphenes preserve their electronic characteristics well.The results indicate that there are only weak interactions betweengraphene and the substrate. Further analysis show that althoughthe interaction is weak, it can open small band gap (23.9e45.7 meV) in the band structures of graphene. The weak in-teractions also induce electron exchange which shifts the energystates of the substrates to low energy and results in hole-dopingeffects on graphene whose Dirac cones shift above the Fermi levels.

Fig. 4. (a) Band structures and partial density of states for graphene adsorbed on Si(111) 2� 1 surface. Band structures and partial density of states of graphene adsorbed on C-decoratedSi(111)2� 2 surfaceswith concentrationof1/4ML,1/2ML, 3/4ML, and4/4MLare shown in (b), (c), (d), and (e), respectively. (f), (g), and (h) represent theband structuresandpartial densityof states of grapheneadsorbedonC-decorated Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surfacewith concentrationof 1/3ML, 2/3ML, 3/3ML, respectively. Blue doton theband structure represent the contributionof graphene to the band structure. Fermi level is set to zero. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

J. Liu et al. / Current Applied Physics 13 (2013) 1512e1519 1517

Fig. 5. Charge density difference for graphene adsorbed on Si(111) 2 � 1 surface in (a). Charge density difference graphene adsorbed on C-decorated Si(111) 2 � 2 surfaces withconcentration of 1/4 ML, 1/2 ML, 3/4 ML, and 4/4 ML are shown in (b), (c), (d), and (e), respectively. Charge density difference graphene adsorbed on C-decorated Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surface with concentration of 1/3 ML, 2/3 ML, 3/3 ML are show in (f), (g), and (h), respectively. Green area and red area represent electron gathered area and loss area, respectively.(Isovalues ¼ 0.0002 e/�A). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

J. Liu et al. / Current Applied Physics 13 (2013) 1512e15191518

However, in the complex systems consisting of graphene andthe reconstructed Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surfaces, the Dirac cones aremoved below the Fermi level when the concentration of thedecorated carbon atoms is 1/3 ML and 3/3 ML, the Dirac cones aremoved above the Fermi levels when the surface is decorated bycarbon atoms with concentration of 2/3 ML. The electronic prop-erties of graphene are preserved perfectly (zero band gap semi-conductor) when the graphene is absorbed on the Si(111)

ffiffiffi

3p

�ffiffiffi

3p

decorated by carbon atoms with concentration of 1/3 ML, Fig. 4(e).The complex systems consisting of graphene and the Si(111)ffiffiffi

3p

�ffiffiffi

3p

surfaces decorated by carbon atoms with concentration of2/3 and 3/3 ML show relatively strong interactions between gra-phene and the substrate; the graphene behaves as semiconductorswith obvious band gaps of 0.399 eV and 0.264 eV, respectively. Wealso compute the band structures of the graphenes peeled from thecomplex systems and find that there are similar band gaps as thoseof the graphenes adsorbed on the substrates. Such results indicatethat the substrates induce the structure distortions of graphene asmentioned above and then produce the opening of the band gap.From Fig. 4(g) and (h) we can see that in these two systems thereare different doping effects of substrates on adsorbed graphenes.The graphene adsorbed on the Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surface loses andgains electrons when the concentrations of the decorating carbonatoms are 2/3 and 3/3 ML, respectively. Such doping mannerdependence on the carbon decorated concentration can be clearlyshown in their charge difference density that will be discussedbelow.

To better understand the doping manners of the substrates ongraphene, we analysis the charge transfers between graphene andthe substrates through studying their charge difference densitydefined as:

r ¼ rgrapheneþsub � rgraphene � rsub; (3)

where rgrapheneþsub is the charge density of the graphene/substratecomplex system, rsub and rgraphene are the charge density of isolated

graphene and substrate in the same supercell and positions as inthe complex systems, respectively. The charge difference density ofthese complex systems can provide us qualitative informationabout the charge transfers between graphene and substrate. Theresults as shown in Fig. 5 indicate that in the complex systemsconsisting of graphene and the Si(111) 2 � 1 surface, graphenetransfer part of charges to the substrate which can be regarded as ahole doping of graphene, leading a shift of the Dirac cone in theband structure of graphene above the Fermi level, which agreewiththe results of the band structures. In the complex systems con-sisting of the graphene and reconstructed Si(111) 2 � 2 surface, thegraphene also transfer part of charges to the substrates, which isindependent of the concentrations of the decorating carbon atoms.In these systems the graphenes are hole-doped and their Diraccones are consequently moved above the Fermi level. In the com-plex systems consisting of graphene and the Si(111)

ffiffiffi

3p

�ffiffiffi

3p

sur-faces, the charge transfer is dependent on the concentrations of thedecorating carbon atom.When the decorating carbon atoms are 1/3and 3/3 ML, the substrate transfers electrons to the adsorbed gra-phene so that the graphene is electron-doped and their Dirac coneslocate below the Fermi level. When the concentration of thedecorating carbon atoms is 2/3 ML, the graphene transfers elec-trons to the substrate which results in its Dirac cone above theFermi level.

4. Conclusion

We have investigated the electronic structures of grapheneadsorbed on clean or C-decorated Si(111) surface. Two surface re-constructions of 2 � 2 and

ffiffiffi

3p

�ffiffiffi

3p

have been considered to bedecorated by carbon atoms with different concentration. The mostfavorable carbon decorated configurations for the Si(111) 2 � 2 andSi(111)

ffiffiffi

3p

�ffiffiffi

3p

surfaces are the concentrations of decorated car-bon with 1/2 and 2/3 ML, respectively. We find that grapheneadsorbed on ideal clean Si(111) surface induces a 2 � 1

J. Liu et al. / Current Applied Physics 13 (2013) 1512e1519 1519

reconstruction while its characteristics of the electronic dispersionpreserves very well. Graphene adsorbed on the carbon decoratedSi(111) 2� 2 surface opens aweak gap in its band structures, whichis slightly dependent on the concentration of decorating carbonatoms. For the Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surface, adsorbed graphene pre-serves their electronic properties well when the concentration ofthe decorating carbon atom is 1/3 ML, but open band gaps of0.399 eV and 0.264 eV when the carbon concentrations are 2/3 and1 ML, respectively. Our results indicate that the carbon decoratedSi(111) 2 � 2 and Si(111)

ffiffiffi

3p

�ffiffiffi

3p

surfaces are promising substratefor graphene which preserves the excellent electronic structure ofgraphene.

Acknowledgments

This work is supported by the Program for New CenturyExcellent Talents in University (Grant No. NCET-10-0169), the Sci-entific Research Fund of Hunan Provincial Education Department(Grant No. 10K065), the National Natural Science Foundation ofChina (Grant No. 10874143), and the Hunan Provincial InnovationFoundation for Postgraduate (Grant No. CX2012B273).

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.cap.2013.05.012.

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