The atomic structure of the favorite graphene/α-SiO2
(0001) interface configuration with the distance between the graphene and SiO2
= 2.820 Å, is shown in Figure , which is named as structure A; d0
is in the van der Waals distance range, but it is smaller than the interlayer distance of graphite of 3.4 Å. From the figure, the surface reconstruction occurred after the relaxation which a covalent bond forms between the two O atoms on the particular Si atom to eliminate the dangling bonds. The related structure parameters are given in Table . As shown in the table, a bond length expansion between the surface or interface atoms is found with l0bulk
, where l0
denotes Si-O bond length, and the subscripts bulk, clean, and A denote bulk SiO2
, clean SiO2
slab, and structure A, respectively. The result l0bulk
= 1.596 Å is consistent with the reported result of 1.61 Å [20
] while the extension of Si-O bonds at the surface or interface is found. We consider that the extension is caused by the one Si-O broken bond on the substrate surface or at the interface. In addition, the weak interaction between the graphene and the SiO2
surface slightly reduces the l0
at the interface compared with that on the surface.
Atomic structure parameters of bulk SiO2, clean SiO2(0001) surface, and graphene/SiO2(0001) interface
In addition, Table also shows the distance between the first and second Si layers [d1] and the Si-O-Si bond angle [α1] in different structures; d1bulk >d1clean >d1A and α1bulk >α1clean >α1A are found. In light of Figure , d1 is affected by both l0 and α1. The former brings out d1bulk <d1clean, and the latter leads to d1bulk >d1clean. Therefore, the effect of α1 on d1 is stronger than that of l0. Comparing structure A with the clean SiO2 surface slab, both l0 and α1 lead to the decrease of d1, where d1 and l0 of structure A shrink to about 4%.
Quantitative experimental data for the interaction strength of graphene/substrate interface is very limited. The first principle calculations showed that the binding energy of graphene on a Si-terminated SiO2
surface is around 20 meV/C atom with interface distance d0
= 3.29 Å and that on a hydrogen passivation O-terminated SiO2
surface is 0.13 eV/C atom with d0
= 2.58 Å [20
]. In addition, the interlayer binding energy in graphite was reported to be 50 to 60 meV [28
]. In the system of structure A, the binding energy calculated between graphene and the SiO2 substrate is about 77 meV/C atom, which is larger than that in graphite and also in the graphene on Si-terminated SiO2
surface, but it is smaller than that on the hydrogen-passivated O-terminated SiO2
surface. Note that d0
in structure A is 2.820 Å, which is smaller than 3.14 Å in graphite and graphene laid on the Si-terminated SiO2
surface, but it is larger than that on hydrogen-passivated O-terminated SiO2
surface. It is known that the binding energy is inversely proportional to d0
. The system of graphene on hydrogen-passivated O-terminated SiO2
surface has the smallest d0
and the strongest binding energy. A previous study implied that the C-C bond is weakened through the strengthening of bonds to the substrate [29
]. A similar phenomenon is found in structure A where the C-C bond length of graphene is 1.430 Å, which is longer than the 1.420 Å in graphite. Thus, the adsorption of graphene on SiO2
with structure A is stronger than that between the bulk graphite layers as shown previously.
On the other hand, in order to understand the effect of substrate on the graphene electrical properties, the band structure for three different systems in Figure , namely free graphene monolayer, clean SiO2(0001) slab, and graphene/SiO2 interface, are represented in Figure . The band structure of free graphene monolayer is calculated on a periodic structure where the graphene monolayer is separated by the same vacuum distance as that for the graphene/SiO2 slabs. This band structure shows the crossing of π and π* bands at the K point and also at the Fermi level, which agrees with a well-known result that graphene is semimetallic with a 0 bandgap. The band structure of the interface shows that the bands of graphene layer are open with a 0.13-eV gap at the K point. It is interesting to note that the Fermi level is lowered with the amount of transferred charges. Thus, the charge should be transferred from graphene to the substrate in structure A. As a consequence of the charge transfer, the SiO2 substrate induces p-type doping in the graphene. Except for these variations, the band structure of interface is almost identical with the sum of band structure of the free graphene monolayer and SiO2 slab, as shown in Figure .
Calculated band structures for graphene monolayer (a), clean α-SiO2(0001) slab, (b) and graphene/α-SiO2 interface (c). The dash line at 0 value denotes the Fermi level.
The charge transfer and atomic charge can be obtained using the Mulliken analysis; it is shown in Table . Mulliken analysis is performed using a projection of the plane wave states onto a localized basis with the technique described by Sanchez-Portal et al. [30
]. Subsequently, the resulting projected states are performed using the Mulliken formalism [31
]. This technique has been widely used to analyze the electronic structures performed with linear combinations of atomic orbital basis sets. As shown in Table , all C atoms of graphene are positively charged in structure A, and the graphene transfers 0.144 e
to the SiO2
substrate where e
denotes one electron charge. This is consistent with the result of the band structure where the p
-type-doped graphene induced by the substrate is found.
Charge transfer and atomic charge obtained by Mulliken analysis
In addition, the electron charges of O4 and O8 atoms at the SiO2 surface are -0.448 and -0.424 e, respectively, for structure A. Those in the clean SiO2(0001) slab are -0.396 and -0.293 e, and in bulk SiO2 are both -0.781 e. On the other hand, the charges of Si15, which binds with O4 and O8, are 1.681, 1.510, and 1.562 e in structure A, clean SiO2 slab, and bulk SiO2, respectively. It is known that the bond strength is in proportion with the multiplication absolute value of changes of the O and Si atoms. Therefore, the interaction between O4 and Si15, and O8 and Si15 are the strongest in bulk SiO2, followed by that in structure A, and the weakest was that in the SiO2 slab. These also agree with the results in Table where the Si-O l0 at the surface or interface is l0bulk <l0A <l0clean.