Graphene, a single two-dimensional layer of graphite in hexagonal structure, is the starting point for many nanographite devices with promising electrical properties 1. After the theoretical prediction of the peculiar electronic properties of graphene in 1947 by Wallace 2 and the subsequent studies on its magnetic spectrum 34, it took half a century until the graphene could be first experimentally fabricated 1, and its anomalous quantum Hall effect has been measured 567, which encourages numerous works on it now 891011.

However, the instability of a freestanding graphene (it has an intrinsic three-dimensional structure or ripples) 12 leads graphene to be used on devices by laying it on a substrate. For example, the insulating substrates made from silicon dioxide [SiO₂] are widely used as a dielectric medium in electronic devices. The electrical properties of graphene can be modified using electrical gates, substrates, and chemical species such as atoms and molecules 1314. It has been reported that graphene grown on a SiC surface was n-type and was exhibiting a gap of about 0.26 eV 15. A theoretical study on bilayer graphene grown on a SiC surface showed that the first carbon layer formed covalent bonds with SiC and acted as a buffer layer, and the graphene nature properties were recovered by the second carbon layer 1617. For graphene supported by SiO₂, previous works studied the electrical properties of graphene and the doping effect of the SiO₂ substrate 181920212223. They found that graphene was p doped when the graphene was weakly bonded to an O-terminated surface with hydrogen passivation. However, graphene would exhibit a finite bandgap if there is a strong interaction with an O-terminated surface while n doping took place on a Si-terminated surface with the active dangling bonds 2021. In these works, they considered that graphene would form C-O or C-Si bonds on the interface due to the dangling bonds associated with the absence of hydrogen passivation. However, when graphene is used in an electronic device, the graphene layer is usually deposited on a surface of the SiO₂ substrate where the atomic structure of the surface is usually considered to reconstruct to eliminate the dangling bonds 24. In addition, the atomic force microscopy [AFM] image indicated that the height of a single graphene layer on the SiO₂ substrate is around 4 Å, which is a bit larger than the 3.4 Å of the graphite interlayer distance 25. Therefore, the interaction between graphene and the SiO₂ surface should be a weak van der Waals interaction without the formation of strong covalent bonds.

In this work, we investigate the graphene/α-SiO₂(0001) interface through density functional theory [DFT] calculations with considerations on surface reconstruction of SiO₂. The interfacial atomic structure and the effects of the substrate on corresponding electronic structure of graphene will also be studied.

The atomic structure of the favorite graphene/α-SiO₂(0001) interface configuration with the distance between the graphene and SiO₂ surface, d₀ = 2.820 Å, is shown in Figure 1b, 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 1. As shown in the table, a bond length expansion between the surface or interface atoms is found with l_0bulk < l_0A < l_0clean, 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 l_0bulk = 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.

In addition, Table 1 also shows the distance between the first and second Si layers [d₁] and the Si-O-Si bond angle [α₁] in different structures; d_1bulk > d_1clean > d_1A and α_1bulk > α_1clean > α_1A are found. In light of Figure 1, d₁ is affected by both l₀ and α₁. The former brings out d_1bulk < d_1clean, and the latter leads to d_1bulk > d_1clean. 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 1b, namely free graphene monolayer, clean SiO₂(0001) slab, and graphene/SiO₂ interface, are represented in Figure 2. 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 2a, b.

The charge transfer and atomic charge can be obtained using the Mulliken analysis; it is shown in Table 2. 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 2, 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.

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 1 where the Si-O l₀ at the surface or interface is l_0bulk < l_0A < l_0clean.

In conclusion, DFT calculations were employed to study the graphene/α-SiO₂(0001) interface with an oxygen-terminated SiO₂ surface. After geometry relaxation, a stable structure with a distance between graphene and the SiO₂ surface, d₀ = 2.805 Å, was observed. In addition, the structure reconstruction of the SiO₂ surface took place where the two O atoms binding on a particular Si atom form a covalent bond on the surface to eliminate the surface dangling bonds. Simulation results indicate that the interface interaction is 77 meV/C atom, which indicates that the van der Waals force dominates the interaction. Furthermore, the SiO₂ substrate induces p-type doping in graphene and open a small gap of 0.13 eV at the Dirac point of graphene.

The authors declare that they have no competing interests.

ZA did the calculation and drafted the manuscript. ZW, MJ, and SL co-drafted the manuscript. All authors read and approved the final manuscript.