Graphene layers on Si-face and C-face surfaces and interaction with Si and C atoms in layer controlled graphene growth on SiC substrates

Abstract

It is important to understand the interface and interaction between graphene layers and SiC surfaces as well as the interaction of key intermediate Si and C atoms with these surfaces and interfaces in epitaxial graphene growth on SiC substrates. In this study, we used the DFT-D2 method, which includes critical long-range van der Waals forces in graphene–SiC interaction, to study interface and interaction between mono-, bi-, and trilayer graphene and Si-face and C-face of SiC substrates as well as single Si and C atom interactions with these surfaces and interfaces. Our results show that the interface, which includes the bottom layer of graphene and top layer of SiC, has a major reconstruction due to the strong interaction of C–Si or C–C covalent bonds. The interaction energy of graphene bottom layer with the C-face is significantly lower than that with the Si-face, although there are stronger C–C covalent bonds and shorter interlayer distances at the graphene–C-face than that at the graphene–Si-face. In contrast, the interaction energy of second layer with bottom layer of graphene on the C-face is obviously higher than that on the Si-face. In particular, the top two layers almost float on the bottom layer of trilayer graphene on the Si-face. Furthermore, the bottom layer on Si-face with a metallic surface is more chemically active than that on the C-face with a semiconducting surface. Compared with the interaction of Si and C atoms with these surfaces and interfaces, the results show that Si atom has a stronger interaction with both bare Si-face and C-face than the C atom. Moreover, the interactions of Si and C atoms with bare Si-face are stronger than that with bare C-face. More importantly, once SiC surfaces are covered by a first carbon layer, C atom prefers to stay at the interface between the existing carbon layer and Si-face or C-face rather than on the surface of the existing carbon layer. In contrast, Si atom only prefers to stay on the surface of the existing carbon layer, and not on the interface. The difference in Si and C atoms on this issue may result in the epitaxial growth of new carbon islands or layers at the interface between the existing carbon layer and Si-face or C-face. All these findings provide insight into the controlled growth of epitaxial graphene on SiC substrates and the design of graphene–SiC based electronic devices.

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Introduction

Epitaxial graphene growth on silicon carbide (SiC) substrates with high-quality and well-controlled thickness (or number of layers) has attracted great interest and is intensively researched because it not only can be compatible with current semiconductor technology (patterning via lithography) but also can offer the possibility of large-scale fabrication.^1–11 Many efforts have been devoted to achieving epitaxial graphene growth by the thermal decomposition of 4H- or 6H-SiC crystals in ultrahigh vacuum or under Ar atmospheric pressure conditions, in which Si atoms are sublimated preferentially and the carbon atoms that are left behind spontaneously self-assemble into graphene layers.^11–24 Experimental studies have shown that graphene can be grown on both the Si-terminated (0001) face (Si-face) and C-terminated (0001̄) face (C-face) of SiC substrates.^{2,3,19,23,25–27} However, the growth features and consequent structures are significantly different for graphene grown on Si-face and C-face surfaces. The Si-face usually leads to the growth of homogeneous graphene films with a controlled number of layers, whereas the C-face tends to grow either less homogeneous multilayer graphene films with rotational stacking or carbon nanotubes.^{2,3,8,28–36} In addition, for the Si-face, a complex buffer layer with periodic structure is thought to exist in the interface between the graphene layer and SiC surface, which strongly bonds with the Si-face, whereas the interfacial structure of graphene with the C-face is fairly different from that of the Si-face.^17,37–43 Controversially, some studies have revealed that new graphene layers do grow from the interface between the buffer layer and SiC surface.^{3,21,22,39,44–48} However, it has also been proposed that new graphene layers would grow on the buffer layers, not directly on the SiC surface.⁴⁹ Furthermore, during the growth process of epitaxial graphene by the thermal decomposition method, atomic Si and C are also key intermediates, which interact with the SiC surfaces and interface between the existing graphene layer and SiC substrate. These issues strongly depend on the interface and interaction between graphene layers and SiC surfaces as well as the interaction of Si and C atoms with these surfaces and interfaces. Thus, to achieve the precisely controlled growth of high-quality graphene with specific layers, it is significantly important to obtain a more explicit understanding of the interfacial structures and interaction among Si/C atoms, graphene layers and SiC surfaces. Besides, this is also very useful for designing high performance graphene–SiC based electronic and optoelectronic devices.

The interfacial structures and interaction between graphene layers and SiC surface have been intensively studied with experimental and theoretical studies. Experimental results indicate that the first carbon layer is a graphene-like lattice, but without distinct graphene electronic properties.^{14,30,37,50,51} Several recent studies have shown that the distance is 2 Å from the first carbon layer to the Si-face.^27,37 Nevertheless, a few other studies revealed that the first carbon layer is a corrugated layer, in which 75% carbon atoms of the first carbon layer are at a distance of 2.4 Å and the other 25% carbon atoms are 2.1 Å above the topmost Si layer.^52,53 Moreover, several theoretical calculations have also been applied to study the interfacial structures of the graphene layers on SiC surfaces. They focused on the effect of interfacial structures on its electronic properties. Furthermore, the common method used in these theoretical studies is the local density approximation (LDA) or general gradient approximation (GGA) methods.^54,55 However, it is well known that the LDA method overestimates the weakly bound van der Waals (vdW) interactions, while the GGA method underestimates such interactions.⁵⁶ In general, neither the LDA nor GGA methods would be reliable for understanding interfacial structures and interactions of graphene–SiC surfaces because they are known to poorly describe vdW forces.

In this study, we chose the semi-empirical DFT-D2 Grimme's method, which includes long-range vdW forces, to study the interfacial structure and interaction between graphene layers and SiC surfaces.^57,58 On this basis, we further investigated the key intermediates of the interactions of Si and C atoms with the bare Si-face, C-face, and the Si-face and C-face covered with the first carbon layer.

Computational methods

All the computations were performed using the Vienna Ab initio simulation package (VASP), which is based on the density functional theory.^59,60 The exchange–correlation interaction used the general gradient approximation (GGA) formulated by Perdew–Burke–Ernzerhof (PBE).⁶⁰ Long-range dispersion corrections have been taken into consideration within the DFT-D2 method.^61,62 Electron interactions have been described with projector augmented wave (PAW) pseudo potentials. The plane-wave basis set energy cutoff has been restricted to 400 eV, and an 11 × 11 × 1 k-point mesh has been used for the interaction of the Brillouin-zone. The electronic self-consistency criterion has been set to 10⁻⁶ eV. Mulliken charge has been calculated using the DMol³ package.^63,64

The periodic slab model has been adopted in graphene–SiC systems, which is known to be a theoretically good prototype for the experimental surface.⁶⁵ The unit cell was constructed using 6 silicon–carbon bilayers and monolayer, or bilayer, or trilayer graphene. These various graphene layers were placed on the Si-face or C-face in graphene–SiC systems, which include at least 12 Å vacuum intervals to avoid interaction with their own images. To optimize the graphene–SiC systems, the graphene lattice constants were elastically adjusted to the SiC lattice with 8% mismatch. The periodic slab model was adopted in adsorption systems of single Si/C atoms to avoid interaction with their own images. All graphene layers and the top four SiC bilayers were relaxed during optimization. The other two SiC bilayers in the bottom were fixed at their bulk lattice positions.

The interaction energy per unit cell between graphene layers is calculated by ΔE_g = (N × E_mono − E_bi/tri)/N, where N is the number of graphene layers. There are 8C atoms in each unit cell. E_mono and E_bi/tri are the total energies of freestanding monolayer and bi- or trilayer graphene per unit cell, respectively. The interaction energy per unit cell of graphene on SiC surfaces is calculated by ΔE_g–SiC = E_g + E_SiC − E_g–SiC, where E_g, E_SiC and E_g–SiC are the total energy of freestanding graphene after elastic adjustment, SiC and graphene–SiC systems per unit cell, respectively.

Results and discussion

Fig. 1a shows the optimized geometric structures of free mono-, bi-(AA and AB), trilayer (ABA and ABC) graphene with different stacking sequences. Each unit cell includes two C atoms in each graphene layer (as the blue dashed line in Fig. 1a). Fig. 1b shows the optimized geometric structures of monolayer graphene adsorbed on the Si-face and C-face. Each unit cell includes eight C atoms in each graphene layer (four graphene unit cells) and three C and three Si atoms in each SiC bilayer, respectively. The C–C bond length in the freestanding graphene layer is 1.42 Å, while the C–C bond length is stretched to 1.54 Å in graphene–SiC systems (as listed in Table 1). The elastic stretching energy would amount to 0.69 eV per unit-cell.

Fig. 1 (a) Optimized geometric structures of mono-, bi-(AA and AB) and tri-layer (ABA and ABC) graphene. (b) The side and top views of monolayer graphene adsorbed on Si-face and C-face. Green, gray and yellow spheres represent graphene C atoms, C and Si atoms in the SiC substrate, respectively. The unit cell is highlighted by blue solid or dashed lines.

Table 1 Optimized geometric structure parameters of free mono-, bi-(AA and AB), tri-layer (ABA and ABC) graphene, and these graphene layers adsorbed on the Si-face and C-faces. b is the C–C bond length in graphene. d₁₂ and d₂₃ are the interlayer distances between the bottom and second layers and the second and third layers in graphene structures, respectively. d_g–SiC are the distances from the bottom layer of graphene to the Si-face or C-face. All the values are given in angstroms (Å)

System		Stacking
		Monolayer	Bilayers		Trilayer
			AB	AA	ABA	ABC
Graphene	b	1.42	1.42	1.42	1.42	1.42
	d23	—	—	—	3.28	3.23
	d12	—	3.24	3.49	3.28	3.24
G/Si-face	b	1.54	1.54	1.54	1.54	1.54
	d23	—	—	—	3.35	3.36
	d12	—	3.25/3.55	3.48/3.77	3.24/3.54	3.24/3.54
	dg–SiC	2.00/2.64	2.00/2.62	2.00/2.61	2.00/2.62	2.00/2.62
G/C-face	b	1.54	1.54	1.54	1.54	1.54
	d23	—	—	—	3.40	3.35
	d12	—	3.33/3.71	3.51/3.89	3.34/3.72	3.34/3.72
	dg–SiC	1.64/2.48	1.64/2.47	1.64/2.47	1.64/2.47	1.64/2.48

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The side view of Fig. 1b shows that for both Si-face and C-face, the graphene bottom layer and substrate top layer become significantly distorted because there are strong covalent bonds at the interface. On the Si-face, there are two lower C atoms at the diagonal of the graphene hexagonal ring (labeled as position A), bonding with two higher Si atoms on the Si-face surface by strong Si–C chemical bonds such that the bond lengths are 2.00 Å. However, the other higher C atoms of the graphene hexagonal ring (labeled as position B) have slightly longer separation distances (2.30 Å) compared to the Si-face surface, and the other one lower Si atom at the unit cell corner still remains an unsaturated dangling bond. The adsorption energy of monolayer graphene on the Si-face is 2.60 eV per unit-cell. Compared to the Si-face, it is noted that the distance from monolayer graphene to the C-face is closer. Two lower C atoms at position A bond to two higher C atoms on the C-face surface by strong C–C covalent bonds, such that the bond length is only 1.64 Å. The graphene bonding atoms migrate 0.38 Å downwards the substrate surface, whereas the substrate surface bonding atoms move 0.46 Å upwards from the graphene. The graphene–C-face layers have major distortion as compared to the graphene–Si-face layers. Furthermore, it is a well known fact that the C–C bond is stronger than the Si–C bond. However, the adsorption energy of monolayer graphene on the C-face is only 1.81 eV, which is significantly lower than that on the Si-face by 0.79 eV per unit-cell. A recent study⁶⁶ reported that the chemisorption energy between graphene and a substrate is dominated by the interplay of bonding energy, Pauli repulsion and van der Waals interactions, which depend differently on the graphene-substrate distance. Furthermore, the Pauli repulsion grows rapidly as the graphene–substrate distance decreases below 2.00 Å. In this case, the Pauli repulsion at a graphene–C-face distance of ∼1.64 Å is stronger than that at a graphene–Si-face distance of ∼2.00 Å. Relatively strong C–C bonding between graphene and C-face surface is counteracted partially by the stronger Pauli repulsion of graphene–C-face. Thus, the adsorption energy of monolayer graphene on the C-face is lower than that on the Si-face surface. This result indicates that the adsorption energy of graphene layers on a substrate surface decreases rapidly as the graphene–substrate distance decreases below 2.00 Å.

When bi- and tri-layer graphene are adsorbed on Si-face and C-face, Table 1 shows that their interlayer distances from the bottom layer to the substrate surface (d_g–SiC) are similar to that of monolayer graphene on the Si-face and C-face. For the Si-face, the interlayer distances from the bottom to the second layer of graphene (d₁₂) are comparable to those of freestanding graphene structures. However, the interlayer distances from the second to third layer of graphene (d₂₃) are slightly longer than those of freestanding graphene structures by 0.07 Å for ABA and 0.13 Å for ABC stacking. As illustrated in Table 2, the interaction energies decrease with the increase of graphene layers: monolayer (2.60 eV per unit-cell) > bilayer (2.58 for AA and 2.56 for AB eV per unit-cell) > trilayer (2.44 eV per unit-cell). However, similar to graphene layers on the Si-face, the interlayer distances of d₁₂ on the C-face are comparable to those of freestanding graphene structures. The interlayer distances of d₂₃ on the C-face are slightly longer than those of freestanding graphene structures, which are 0.12 Å for ABA and ABC. The interaction energies of the graphene layers on the C-face are obviously weaker than those on the Si-face. Their adsorption energies also decrease with the increase of graphene layers: monolayer (1.81 eV per unit-cell) > bilayer (1.74 for AA and 1.72 for AB eV per unit-cell) > trilayer (1.58 eV per unit-cell). Besides, the adsorption energies are not significantly different between AA and AB stacking and between ABA and ABC stacking on the Si-face or C-face.

Table 2 The interaction energy of graphene layers with and without SiC surfaces. ΔE_g–SiC is the interaction energy of the graphene layers on SiC surfaces. ΔE_g is the interaction energy between freestanding graphene layers. ΔE_g12 and ΔE_g23 are the interaction energies between the bottom and second layers and between the second and third layers in graphene–SiC systems, respectively. All the values are given in eV per unit-cell

System		Stacking
		Monolayer	Bilayers		Trilayers
			AA	AB	ABA	ABC
Graphene	ΔEg	—	0.22	0.30	0.62	0.62
G/Si-face	ΔEg23	—	—	—	0.19	0.19
	ΔEg12	—	0.15	0.20	0.09	0.09
	ΔEg–SiC	2.60	2.58	2.56	2.44	2.44
G/C-face	ΔEg23	—	—	—	0.20	0.20
	ΔEg12	—	0.21	0.27	0.17	0.17
	ΔEg–SiC	1.81	1.74	1.72	1.58	1.58

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Subsequently, we compared the interaction energy between graphene layers with and without the SiC substrate. As listed in Table 2, the interaction energies between the graphene layers on the SiC surface is significantly lower than that of freestanding graphene layers. For bilayer graphene, the interaction energies follow the order ΔE_g12/Si-face (0.15 eV per unit-cell) < ΔE_g12/C-face (0.21 eV per unit-cell) ≈ ΔE_g (0.22 eV per unit-cell) for AA stacking and ΔE_g12/Si-face (0.20 eV per unit-cell) < ΔE_g12/C-face (0.27 eV per unit-cell) < ΔE_g (0.30 eV per unit-cell) for AB stacking. In addition, the interaction energies of AB stacking are higher than that of AA stacking, which are 0.05, 0.06, and 0.08 eV per unit-cell on the Si-face, C-face, and without substrate, respectively. These energy results suggest that AB stacking is more stable than AA stacking on both SiC surfaces. For trilayer graphene, the interaction energies follow the order ΔE_g12/Si-face (0.09 eV per unit-cell) < ΔE_g12/C-face (0.17 eV per unit-cell) < ΔE_g (0.31 eV per unit-cell) for both ABA and ABC stacking, and ΔE_g23/Si-face (0.19 eV per unit-cell) ≈ ΔE_g23/C-face (0.20 eV per unit-cell) < ΔE_g (0.31 eV per unit-cell) for both ABA and ABC stacking. More interestingly, the adsorption energy between the bottom and second layers decrease rapidly (about 0.10 eV for both ABA and ABC on the Si- and C-face) due to the attraction of the third layer for the second layer. In particular, the interaction energy between the bottom and second layers, E_g12, is only 0.09 eV per unit-cell, which is significantly lower than that between the second and third layer, ΔE_g23, by 0.19 eV per unit-cell for both ABA and ABC stacking in graphene–Si-face systems. This result suggests that the top two graphene layers only float on the bottom layer bonded on the Si-face, which is favorable for new graphene layer growth from the interface. It should be noted that, in the graphene–SiC systems, the lattice constants of all the graphene layers were elastically adjusted to the SiC lattice with 8% mismatch. Actually, because of the weak interaction between the bottom and second layers, it is possible that the lattice constants of the top layers in the graphene–SiC systems is almost identical to that of freestanding graphene. This mismatch of lattice structure between the top layers and bottom layer induces a substantial variation in the interaction energy. Thus, we further compared the interaction energy of graphene layers at different lattice constants. The results show that the mismatch of lattice structure between the top layers and bottom layer in our calculations is thought to have minor effects on our conclusions.

Charge transfer

The structural and interaction energy results in Tables 1 and 2 show that the bottom layer of graphene structures could form strong chemical bonds with the Si-face or C-face, while the bottom, second, and third graphene layers bond with each other by weak van der Waals forces. This can be further validated by analyzing the charge density distribution at the interfaces in graphene–Si-face and graphene–C-face systems. To better illustrate the charge distribution at interfaces, the charge density difference of mono- and bilayer graphene on the Si-face and C-face are plotted in Fig. 2. The charge density difference refers to the variance between the total charge density of graphene–Si-face or graphene–C-face systems and the sum of the charge density of the separated graphene structures and SiC substrate with the Si-face or C-face. The geometric structures of separated graphene structures and Si-face or C-face were kept the same as those in graphene–Si-face and graphene–C-face systems. The green regions in Fig. 2 represent the accumulation of electronic charges, while the red regions indicate the depletion of electronic charges.

Fig. 2 Charge density difference plots of mono- and bi-layer graphene absorbed on the Si-face and C-face. The positive and negative charges are shown in red and green on charge density isosurface, respectively.

Fig. 2a shows that there is major charge transfer and electronic polarization between monolayer graphene and Si-face surface. The side view in Fig. 2a further confirms that there are strong polar C–Si covalent bonds between monolayer graphene and Si-face. The Si atoms directly donate electrons to the C atoms at position A. The top view in Fig. 2a shows that on monolayer graphene, electrons are localized significantly at the C atoms at position A. Mulliken charge analysis further shows that the C atoms at position A accumulate −0.43e, while those at position B only deplete around +0.06e. Correspondingly, the Si atoms directly bonding C atoms at position A deplete +1.20e, while other neighboring Si atoms only deplete about +0.97e. Next, for the bilayer graphene shown in Fig. 2c, there is neither significant charge accumulation nor depletion on the top layer of bilayer graphene on the Si-face. The bottom layer of bilayer graphene shows similar charge transfer and electronic polarization as that of the monolayer graphene shown in Fig. 2a.

Compared to monolayer graphene on the Si-face, there are also major electronic polarizations on monolayer graphene in the graphene–C-face system. However, almost all charge transfer comes from the neighboring graphene C atoms, while there is minor charge transfer between monolayer graphene and the C-face. As illustrated in Fig. 2b, the C atoms at position B donate electrons to the C atoms at position A from their σ-bands, and the C atoms in the C-face only partially share electrons with the C atoms at position A. Mulliken charge analysis shows that on monolayer graphene, the C atoms at position A only have −0.11e, while those at position B deplete around +0.05e. Correspondingly, in the C-face surface, the C atoms directly bonding to the C atoms at position A accumulate −0.98e, while other neighboring C atoms also accumulate about −0.96e. Next, for the bilayer graphene shown in Fig. 2d, the bottom layer shows similar electronic polarization and charge transfer as that of the monolayer graphene shown in Fig. 2b. The top layer of bilayer graphene has neither charge accumulation nor depletion as shown in Fig. 2d.

Partial density of states

The differences of monolayer graphene on the Si-face and C-face in charge transfer and electronic polarization may induce distinct chemical reactivity. To further understand their differences in chemical reactivity, we calculated the band structure and DOS of monolayer graphene on the Si-face and C-face. As shown in Fig. 3a, on the monolayer graphene–Si-face, band structure and DOS analyses reveal that the gap states close to the Fermi energy originate from the monolayer graphene and Si-face, which cross the Fermi level and become partially filled, thus resulting in metallic states. In contrast, on the monolayer graphene–C-face, a direct gap of about 0.50 eV appears in the band structure, which makes the interface semiconducting. The PDOS shows that the valence band maximum and the conduction band minimum are mainly contributed by the C-face substrate, while the monolayer graphene has almost no contribution. These results suggest that the metallic interface states of the monolayer on the Si-face would be much more reactive than the semiconducting interface states of the monolayer on the C-face. Our results are consistent with the experimental report in which the Si-face was in a half-filled metallic state, whereas the C-face was semiconducting.³⁷

Fig. 3 Band structure (left) and density of state (DOS) of monolayer graphene on the (a) Si-face and (b) C-face. The Fermi level is assigned at 0 eV.

Interaction of single Si and C atoms

Atomic Si and C are the critical intermediates interacting with the SiC surfaces and interface between the existing graphene layer and SiC substrate during the growth of epitaxial graphene on SiC substrates. An explicit understanding of the Si and C atoms interaction with these surfaces and interfaces is essential for probing the growth mechanism of epitaxial graphene on SiC substrates. In the abovementioned section, the results show that graphene on the Si-face and C-face has different charge transfer, bonding type, and chemical activity. To directly examine the difference in atomic Si and C interaction with these surfaces and interfaces, in this section we further investigate single Si and C atom interaction with bare Si- and C-faces, and the interface between the Si-face or C-face and first carbon layer. The optimized structures and interaction energies of single Si and C atoms on these surfaces are depicted in Fig. 4 and 5. The interaction energies of a single C or Si atom on these surfaces are defined as ΔE_a = E_C(Si)–SiC/E_{C(Si)–g–SiC} − E_g–SiC − E_C(Si) (E_C(Si)–SiC, E_{C(Si)–g–SiC}, E_g–SiC, and E_C(Si) are the total energies of a fully optimized C/SiC or Si/SiC complex, a fully optimized C/g/SiC or Si/g/SiC complex, a fully optimized g/SiC complex, and a single C or Si atom, respectively).

Fig. 4 Interaction of a single Si atom with bare Si-face (a), bare C-face (b), and Si-face (c) and C-face (d) covered by the first carbon layer. Adjacent linking atoms are highlighted by gray (C atom), and yellow (Si atom) balls. The bond lengths are shown in angstroms and interaction energies are shown in eV.

Fig. 5 Interaction of single C atom (green ball) with bare Si-face (a), C-face (b), and Si-face (c) and C-face (d) covered by the first carbon layer. Adjacent linking atoms are highlighted by gray (C atoms of substrate) and yellow (Si atoms) balls. The bond lengths are shown in angstroms and interaction energies are shown in eV.

As illustrated in Fig. 4a and 5a, for a single Si and C atom, there are two stable adsorption sites on a bare Si-face, which include three-fold μ₃-hollow and four-fold μ₄-hollow sites. The Si adsorption energies are 7.77 eV at the μ₃-hollow site and 8.15 eV at the μ₄-hollow site. The C adsorption energies are 7.34 eV at the μ₃-hollow site and 7.71 eV at the μ₄-hollow site. In the case of the bare C-face, the Si atom has only a stable four-fold μ₄-hollow site with an adsorption energy of 6.27 eV. However, the C atom has three stable surface adsorption sites, as illustrated in Fig. 5b. The adsorption energies of the C atom at the bridge-up, three-fold μ₃-hollow, and six-fold μ₆-hollow sites are 5.83, 5.98, and 6.71 eV, respectively. Compared with the interaction of single Si and C atoms on a bare Si-face and C-face, the result of the adsorption energies shows two trends: (1) a single Si atom has stronger interaction with both the Si-face and C-face than the C atom. (2) The interactions of single Si and C atoms with a bare Si-face are stronger than that with a bare C-face.

During the initial stage of SiC thermal decomposition with continual Si atom sublimation, the carbon atoms left behind form covalent bonds among one another. Eventually, the first carbon layer would be formed on the Si-face or C-face. However, once the Si-face or C-face is covered by the first carbon layer, it is necessary to answer the following questions: (1) are there significant differences in single Si and C atom interaction with the covered Si-face and C-face by the first carbon layer? (2) Would Si and C atoms preferably stay on the interface between the existing carbon layer and Si-face/C-face or adsorb on the surface of the existing carbon layer?

As shown in Fig. 4c, for a single Si atom on the Si-face covered by the first carbon layer, there is only one stable surface site (bridge-up) on the first carbon layer with the interaction energy of 2.74 eV. However, we found that there is no stable adsorption site at the interface between the existing carbon layer and Si-face. In the case of the C-face covered by the first carbon layer, as shown in Fig. 4d, the C atom has only one stable surface adsorption site (bridge-up) with an adsorption energy of 2.25 eV and an absorption site (bridge-down) with an adsorption energy of 2.10 eV at the interface between the existing carbon layer and C-face. Interestingly, these interaction energies are lower than that of the Si atom on a bare Si-face or C-face, but higher than that of the Si atom adsorbed on freestanding monolayer graphene at 0.65 eV. This result suggests that sublimated Si atoms preferentially adsorb on the Si-face or C-face before the first carbon layer formation, rather than on top of the growing carbon islands. These surface Si atoms form intermediate metastable Si–C bonds with the edge of the growing carbon islands. Thus, the surface Si atoms may play a role of stabilization as well as catalyst in the growing carbon islands on the SiC surface. Furthermore, the interaction energies of the Si atom on the surface of the existing carbon layer are higher than that of the interface interaction sites for both the Si-face and C-face. This result suggests that, once SiC surfaces are covered by the first carbon layer, Si atoms prefer to stay on the surface of the existing carbon layer, and not at the interface between the existing carbon layer and Si-face or C-face.

For a single C atom on a Si-face covered by the first carbon layer, Fig. 5c shows that there is one stable surface site (bridge-up) on the first carbon layer with the interaction energy of 4.52 eV, and two subsurface sites (μ₃-hollow-down and bridge-down) under the first carbon layer with the interaction energies of 4.60 and 5.89 eV, respectively. In the case of a C-face covered by the first carbon layer as shown in Fig. 5d, the C atom has only one stable surface adsorption site (bridge-up) with an adsorption energy of 4.00 eV and a subsurface absorption site (bridge-down) with an adsorption energy of 4.72 eV. These adsorption energies are lower than that of the C atom on a bare Si-face or C-face, but higher than that of the C atom adsorbed on freestanding monolayer graphene at 1.86 eV. This result suggests that, during the Si atom sublimation stage, C atoms preferentially adsorb on the Si-face or C-face, rather than on top of the existing carbon layer. Thus, it is favorable to grow a flat carbon layer first than to grow multilayer islands on the Si-face–C-face. In contrast to the Si atom, the interaction energies of the C atom at the interface are higher than that of the surface of the existing carbon layer for both the Si-face and C-face. This result suggests that, once SiC surfaces are covered by the first carbon layer, C atoms prefer to stay on the interface between the existing carbon layer and Si-face or C-face, and not on the surface of the existing carbon layer. With the accumulation of C atoms, new carbon islands are formed at the interface between the existing carbon layer and Si-face or C-face, and not on top of the existing carbon layer. This agrees with the experimental findings that underneath the carbon layer of the SiC substrate causes the accumulation of C atoms and a new carbon buffer layer is further formed at the interface between the existing carbon layer and SiC substrate.^3,21,67

The intention of this study is to find a general guideline for the layer controlled graphene growth on SiC substrates, and also provide some understanding of the graphene–SiC interface for potential electronic device design. Thus, this study focused on the interaction between graphene layers and Si- and C-face surfaces, and key intermediates of Si and C atoms interaction with the bare Si-face, C-face, and Si-face and C-face covered with one carbon layer. Our results from geometric structure, interaction energy, charge transfer, band structure and DOS analysis further demonstrate that the buffer layer on the Si-face with a metallic surface is distinctly different from that on a C-face with a semiconducting surface, which may induce different growth features and electronic properties. Furthermore, for a bare Si-face and C-face, the Si atom has stronger interaction than the C atom, and the interactions of Si and C atoms with the Si-face are stronger than that with the C-face. For the covered Si-face and C-face, the C atom prefers to stay on the interface between the buffer layer and Si-face or C-face, while the Si atom only prefers to stay on the surface of the buffer layer. These results imply that a new graphene layer would grow from the interface between the buffer layer and Si-face or C-face. Based on the findings from this study, we propose that, to achieve layer controlled growth, it is important to be able to tune the interaction among Si and C atoms, graphene layers, and SiC surfaces during different growth stages. This can be done by controlling the amount of Si and C atom decomposition, and modulating the buffer layer structure and buffer-layer-substrate separation during the thermal decomposition process of SiC, which could be controlled experimentally by the heating temperature, the heating rate, the vacuum pressure, and the composition of the residual gas.

Conclusions

We used the DFT-D2 method to study the interface and interaction between the graphene layers and Si-face and C-face of SiC substrates as well as key intermediate Si and C atoms interaction with these surfaces and interfaces. The results show that the interfacial structures of the graphene bottom layer and SiC top layer have a large reconstruction due to the strong interaction of the covalent bond. The interaction energies strongly depend on the interfacial structures. The interaction energy of the graphene bottom layer with the C-face is significantly lower than that with the Si-face, although there are stronger C–C covalent bonds and shorter interlayer distances at the graphene–C-face than that at the graphene–Si-face. In contrast, the interaction energy of second layer with bottom layer of graphene on the C-face is obviously higher than that on the Si-face. Especially, the top two layers almost float on the bottom layer of trilayer graphene on the Si-face. Charge transfer, DOS and band structure analyses show that the bottom layer on the Si-face with a metallic surface is more chemically active than that on the C-face with a semiconducting surface. Compared with the interaction of single Si and C atoms with these surfaces and interfaces, the results show that a single Si atom has stronger interaction with both bare Si-face and C-face than the C atom. Moreover, the interactions of single Si and C atoms with the bare Si-face are stronger than those with the bare C-face. More importantly, once SiC surfaces are covered by the first carbon layer, the C atom prefers to stay on the interface between the existing carbon layer and Si-face or C-face rather than on the surface of the existing carbon layer. In contrast, Si atom only prefers to stay on the surface of the existing carbon layer, and not on the interface. The results suggest new carbon islands or layers can be easily formed at the interface between the SiC surface and existing carbon layer, and not on top of the existing carbon layer surface. The deeper insights into the interfacial structures and interaction among Si/C atoms, graphene layers and SiC surfaces from this study are expected to guide the layer controlled growth of graphene and the design of graphene–SiC based devices.

Acknowledgements

This study was supported by the National Natural Science Foundations of China (21203094, 21373112, and 11104048) and the Natural Science Foundation of Guangdong Province (S2013010014476).

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