Assessing the graphene and SiC(111) interface: Surface equilibria and the(3×3)-3C-SiC(111) reconstruction

Lydia Nemec,1 Florian Lazarevic,1, ∗ Patrick Rinke,1 Matthias Scheffler,1 and Volker Blum2, 1

1Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195, Berlin, Germany2Department of Mechanical Engineering and Material Science, Duke University, NC 27708 USA

(Dated: August 14, 2014)

We address the stability of the surface phases that occur on the C-side of 3C-SiC(111) at theonset of graphene formation. In this growth range, experimental reports reveal a coexistence ofseveral surface phases. By constructing an ab initio surface phase diagram using a van der Waalscorrected density functional, we show that this coexistence can be explained by a Si-rich model forthe unknown (3×3) reconstruction, the known (2×2)C adatom phase, and the graphene covered(2×2)C phase. The surface energies of these three phases cross at the chemical potential limit ofgraphite.

For practical applications of graphene based electron-ics, wafer-size high-quality graphene films are needed.Graphene grown on silicon carbide (SiC) is one ofthe most promising material combinations for futuregraphene applications.[1–5]

On SiC, graphene growth is achieved by thermal de-composition of the substrate.[6, 7] The electronic prop-erties of few-layer graphene films grown on the C-side ofthe polar 3C-SiC(111) surface are similar to those of anisolated monolayer graphene film with very high electronmobilities.[8–10] However, controlling the layer thicknessof the graphene films remains a challenge.[11] While somegroups report the successful growth of large-scale mono-layer graphene [12, 13], other reports suggest that thepure monolayer growth regime is difficult to achieve onthe C face of SiC. [11] This is very different from the Siside, where nearly perfect, monolayer graphene films canbe grown over large areas.[1, 4] Investigating the relativephase stability of the competing surface phases in thethermodynamic range of graphitisation is an importantstep for a better understanding of graphene growth.

For epitaxial graphene films on the Si-side of 3C-SiC(111), we have recently shown by ab initio atom-istic thermodynamics that individual phases, the (6

√3×

6√

3)-R30◦ zero layer and monolayer graphene (ZLG andMLG) can form as near equilibrium phases under certainexternal conditions (represented by the C and Si chem-ical potentials that are controlled by temperature andbackground gas pressure in experiment).[14] What is nota priori clear is whether on the C face of SiC, graphenefilms can also be thermodynamically stable. To addressthis question, atomistic models are required for the dif-ferent competing phases, in particular for the C rich con-ditions close to the graphitization regime.

We here present first-principles evidence that the for-mation of monolayer graphene films on the C face is hin-dered by stable Si rich phases. To shed light on the phasemixture at the graphitisation limit, we use a possiblemodel of the unknown (3×3) reconstruction. The cen-tral feature of this model is a capping layer of Si atoms,

minimizing dangling bonds in the same way as the knownSi-rich (3×3) phase on the Si face of SiC.[15, 16]

On the C-side, a series of different surface structureshave been observed during annealing.[6, 17–25] Graphenegrowth starts either with a Si rich (2×2) phase in an Sirich environment[19, 20] or with an oxidic (

√3 ×√

3)reconstruction.[19, 26] In the absence of a Si back-ground like disilane, a (1×1) phase is observed, whichexhibits the periodicity of bulk SiC underneath a disor-dered oxidic layer.[17] Continued heating leads to a (3×3)phase. Using qualitative low-energy electron diffraction(LEED), Bernhardt et al. [20] showed that the (3×3)reconstructions originating from different starting struc-tures and environments are equivalent.[20] Further an-nealing leads to a (2×2) Si ad-atom phase, referred to as(2×2)C (notation taken from [20]). Just before grapheneforms on the surface, a coexistence of the two surfacephases, the (3×3) as well as the (2×2)C, is observed.[20, 27] In addition, different groups reported strongexperimental evidence that both reconstructions persistunderneath the graphene films with the (3×3) phasegradually fading, but never disappearing.[24, 25, 27–32]While the atomic structure of the (2×2)C reconstructionwas resolved by quantitative LEED [21], the (3×3) re-construction and the graphene/ SiC interface remain apuzzle. Over the last two decades, several structuralmodels have been suggested for the (3×3) phase on theC face.[18, 19, 25, 33] We here summarise the exper-imentally observed characteristics of the (3×3) recon-struction. The stoichiometry of the surface reconstruc-tion was found to be Si-rich by Auger electron spec-troscopy (AES).[18, 20] The corresponding filled stateSTM image is consistent with three adatoms residing atthe same height [25, 33] and scanning tunnelling spec-troscopy shows a semiconducting surface with a band gapof 1.5 eV.[23]

For the graphene/SiC interfaces on the C-side two verydifferent scenarios have been invoked. a) The first carbonlayer is strongly bound to the substrate.[11, 35, 36] In thisscenario, the Si sublimation rate during graphene growth

2

ac

eb

d

Incre

asin

g sta

bility a

t C rich

limit (G

rap

hite

)

d) (3x3) Li-Tsong

b) (2x2)c

e) (3x3) Si Hoster

c) (3x3) Kulakov

a) (3x3) Si Twist

h) (3x3) Hoster

g) (3x3) Deretzis

f) (3x3) Hiebel

g

h

f1x1

PBE+vdW

FIG. 1. Comparison of the surface energies relative to thebulk terminated (1×1) phase as a function of the C chemicalpotential within the allowed ranges (given by diamond Si,graphite C and for completeness diamond C, respectively).The shaded areas indicate chemical potential values outsidethe strict thermodynamic stability limits. Included in thesurface energy diagram are structure models as proposed forthe C face [(b)[21] (d)[19], (e) and (h)[18], (f)[25], (g)[33]] andmodels adapted from the Si face [(a)[15] and (c)[34]]. In theright panel the different models for the (3×3) reconstructionsof the 3C-SiC(111) are ordered by their surface energies inthe graphite C limit of the chemical potential with increasingstability from top to bottom.

on the C face is controlled by either working in an inertgas atmosphere [1], by using a confined geometry [31], orby providing an external Si gas phase [7, 36] for exam-ple disilane background gas. It is not clear, however, ifthe different groups observe the same structures. Basedon their LEED data, Srivastava et al. [36] proposed a(√

43×√

43)-R±7.6◦ SiC substrate with a (8×8) car-

bon mesh rotated by 7.6◦ with respect to the substrate(’√

43-R7.6◦’).[36] The detailed atomic structure of thisinterface is not known.[37] b) For samples prepared underUHV conditions, the first carbon layer is weakly boundto the substrate and shows the characteristic behavior ofthe π-band at the K-point of the Brillouine zone. Herean inhomogeneous interface is present since the (3×3)as well as a (2×2)C reconstruction is observed under-neath the graphene layers.[24, 29, 30] A recent study ongraphene grown by molecular beam epitaxy (MBE) onthe C-side exhibited the same structural characteristicsas graphene grown by high-temperature annealing.[32]This is a strong indication that indeed the (2×2)C as wellas the (3×3) reconstruction prevails below the graphenefilms.

To our knowledge, the different (3×3) models sug-gested in the literature and likewise the remaining phasesincluding the graphene/SiC interfaces have not yet beenplaced in the context of a surface phase diagram. Weemploy density-functional theory (DFT) using the FHI-aims all-electron code [38, 39] exploiting the massively

parallel ELPA eigensolver library.[40, 41] We use thevan der Waals (vdW) corrected [42] Perdew-Burke-Enzerhof (PBE) generalised gradient approximation[43](PBE+vdW) and the Heyd-Scuseria-Ernzerhof hybridfunctional (HSE06+vdW) [42, 44] for the exchange corre-lation functional. If not stated otherwise the calculationsare non-spin-polarised, the technical parameters and bulklattice constants are listed in the supplemental material(SM)[45]. All surface structures are calculated using aslab of six SiC bilayers. The bottom silicon atoms arehydrogen terminated. The top three SiC bilayers andall adatoms or planes above are fully relaxed (residualenergy gradients: 8 · 10−3 eV/A or below).

A good indicator for finding the most likely (3×3) re-construction or interface structures is a comparison ofthe respective surface free energies as formulated in theab initio atomistic thermodynamics approach.[46–50] Weneglect vibrational and configurational entropy contribu-tion to the free energy, although in the coexistence regionthey might lead to small shifts. In the limit of sufficientlythick slabs, the surface energy γ of a two-dimensional pe-riodic SiC slab with a C face and a Si face is given as

γSi-face + γC-face =1

A

(Eslab −NSiµSi −NCµC

). (1)

NSi and NC denote the number of Si and C atoms in theslab, respectively, and µSi and µC refer to the chemicalpotential of Si and C. All our surface energies are given ineV per area (A) of a (1×1) SiC unit cell. The letter E de-notes total energies for a given atomic geometry through-out this work. The chemical potential limits are definedby the bulk phases as Ebulk

SiC − EbulkSi ≤ µC ≤ Ebulk

C . Be-cause of the close competition between the diamond andgraphite structure for C [51–53], we include both limitingphases in our analysis.

The surface energies of the (2×2)C surface model bySeubert et al. and the different models for the SiC-(3×3) reconstruction are shown as a function of ∆µC =µC − Ebulk

C in Fig. 1. The structure with the lowest en-ergy for a given ∆µC corresponds to the most stablephase. We here briefly discuss the alternative surfacephases of the SiC C-face (for more details see SM [45]).Hoster, Kulakov, and Bullemer suggested a geometricconfiguration for the (3×3) reconstruction on the basisof STM measurements without specifying the chemicalcomposition.[18] Highest in surface energy is the varia-tion suggested by Hiebel et al. [25] labeled as h, followedby a carbon rich composition suggested by Deretzis andMagna [33] labeled as g. We added a modification withall adatoms chosen to be Si, labeled e. Of all the Hoster-type models that we tested, this is the most stable chem-ical composition. Hiebel et al. suggested a new model,labeled as f. [25] Li and Tsong proposed a tetrahedrallyshaped cluster as reconstruction.[19] They suggested a Siand C rich configuration. We tested both configurationsand included an additional Si tetrahedron (for details see

3

FIG. 2. I: The a) and b) phases from Fig. 1 calculated usingthe HSE06 exchange-correlation functional with fully relaxedstructures and unit cells. II: The geometry of the Si twistmodel and simulated constant current STM images for occu-pied and empty state of the Si twist model (unit cell shownin red). The three points of interest (A, B, C) are markedby arrows and labeled according to Hiebel et al.[25]. III: Thedensity of states for the spin up and spin down states clearlyshows a band gap rendering the surface semiconducting.

SM [45]). Here, we include only the most stable clusterformed by 4 Si atoms, labeled d. The next structure weadded is a model originally proposed as a Si rich structurefor the 6H-SiC(0001)-(3×3) reconstruction by Kulakov,Henn, and Bullemer [34], labeled c. To summarise Fig. 1,all the alternative models we tested are too high in energyat the graphite line to coexist with the (2×2)C adatommodel.

We next show that a conceptual model for the (3×3)reconstruction based on a Si-rich termination performsmuch better at explaining the various surface characteris-tics. To create a plausible termination, we base our modelon the Si twist model, known from the 3C-SiC(111)–(3×3) reconstruction – the Si twist model [15, 16] InFig. 2 (II) its geometry is shown in a side view and fromatop. The top bulk C layer is covered by a Si adlayerforming heterogeneous Si-C bonds. Three Si adatomsform a triangle twisted by 7.7◦ with respect to the topSiC layer. In comparison, the twist angle on the Si side

amounts to 9.3◦. The topmost Si adatom is positionedon top of the triangle. In the surface diagram (Fig. 1),this phase has the lowest energy of all previously pro-posed (3×3) models. Its formation energy crosses thatof the (2×2)C phase just at the C rich limit (graphite)of the chemical potential with a surface energy differenceof 0.47 meV in favor of the Si twist reconstruction. Tocoexist with the (2×2)C phase and to be present at theonset of graphite formation, the (3×3) phase has to crossthe graphite line very close to the crossing point betweenthe graphite line and the (2×2)C phase. The Si twistmodel shown in Fig. 2 satisfies this condition.

In agreement with the AES experiments our model isSi-rich. We also compared the surface energetics of thecoexisting phases (2×2)C and the Si twist model usingthe higher level HSE06+vdW hybrid functional with fullyrelaxed structures and unit cells, shown in Fig. 2 (I). Ascan be seen, the phase coexistence does not depend onthe chosen functional. However, to distinguish betweena phase coexistence or a close competition between thetwo phases, the inclusion of entropy terms would be thenext step.[54]

We performed a spin-polarised calculation of the elec-tronic structure. In Fig. 2 (III), we show the density ofstates (DOS) for the spin down (in red) and spin up (inblue) channel. While the spin down surface state givesrise to a peak in the band gap above the Fermi-level, thespin up surface state is in resonance with the SiC bulkstates. The DOS clearly demonstrates that the surfaceis semiconducting in agreement with experiment, featur-ing a band gap of 1.12 eV. Thus, the conceptual Si twistmodel - inspired by the Si side - appears to satisfy theexisting experimental constraints well.

Furthermore, our simulated STM images Fig. 2 (II)reproduce the measured height modulation,[25] but theexperimentally observed difference in intensity betweenoccupied and empty state images is not captured by oursimulated images. The disagreement in the STM imagesmight be an indication that a different structure is ob-served in the STM measurements. We started an exhaus-tive structure search [55] to find a surface model that iseven lower in energy than the Si twist model and thatreproduces all experimental observations, including theSTM images. However, if an alternative model were tobe found, its surface energy would have to be close to theSi twist model at the graphite line to still coexist with the(2×2)C phase. As a result, it would very likely coexistwith the Si twist model.

In the following we will use the Si twist model as arepresentative model to shed light on the SiC-grapheneinterface on the C face. In particular, we will make asimple qualitative argument why the C-rich ZLG inter-face, critical towards MLG formation on the Si-face, doesnot form. Figure 3 shows the PBE+vdW surface en-ergies of four different interface structures. The phasediagram also includes the previously discussed (2×2)C

4

c) 6√3-(2x2)c interf.

f) √43-R7.6o interf.

d) 6√3-(3x3) interf.

e) 6√3-R30o interf.

1x1 d

c

e

f

a) (3x3) Si Twist

b) (2x2)c

FIG. 3. Comparison of the surface energies for four differ-ent interface structures of 3C-SiC(111), relative to the bulk-truncated (1×1) phase, as a function of the C chemical poten-tial within the allowed ranges (given by diamond Si, diamondC or graphite C, respectively), using the graphite limit as zeroreference. In addition, the known (2×2)C reconstruction andthe (3×3) Si twist model are shown.

surface phase and the proposed (3×3) Si twist model.As a first step we constructed an interface structure

similar to the ZLG phase known from the Si face - a6√

3-R30◦-interface, labeled e in Fig. 3. This structurecrosses the graphite line 0.46 eV above the crossing pointof the (3×3) Si twist model, rendering it unstable. As asecond structure, we included a purely C based model ofthe√

43-R 7.6◦-interface, labeled f in the surface phasediagram of Fig. 3. In our calculations, this structure iseven higher in energy than the 6

√3-R30◦-interface.

The 6√

3-R30◦- and√

43-R 7.6◦-interface are modelsof a strongly bound interface. Since the Gibbs energy offormation for SiC is quite large (−0.77 eV in exp. [56], −0.56 eV in DFT-PBE+vdW and −0.59 eV in DFT-HSE06+vdW), the formation of SiC bonds is favorable.This explains why the (2×2)C and (3×3) Si twist modelare more stable, because they contain a large number ofSi-C bonds. Conversely, the 6

√3-R30◦- and the

√43-R

7.6◦-interface are made up of energetically less favorableC-C bonds, which increases the surface energy consider-ably.

For the weakly bound interface a (2×2) and (3×3)LEED pattern was observed underneath graphene [24,29, 30]. A typical feature of the LEED structure is aring like pattern originating from the rotational disorderof graphene films grown on the C face.[8, 27, 29, 57] Tomodel the interface, we limited our study to a 30◦ rota-tion between the substrate and the graphene film. This

choice was motivated by the LEED study of Hass et al.[8],who showed that graphene sheets on the C face appearmainly with a 30◦ and a ±2.2◦ rotation. A 30◦ rotationhas also be seen in STM measurements for the graphenecovered (2×2) and (3×3) phases [29], from here on called(2×2)G and (3×3)G. We therefore chose a (6

√3× 6

√3)

SiC supercell covered by a (13× 13) graphene cell rotatedby 30◦ with respect to the substrate.

The (2×2)G-interface covers 27 unit cells of the (2×2)Creconstruction (labeled c in Fig. 3). It crosses the (2×2)Creconstruction just to the right of the graphite limit ata chemical potential of 2 meV and a surface energy of−0.69 eV. This finding demonstrates that the observed(2× 2) LEED pattern underneath the graphene layer isindeed consistent with the well known (2×2)C reconstruc-tion. Our model of the graphene covered (3×3) phaseconsist of the same (13×13) graphene supercell, covering12 units of the (3×3) Si twist model (labeled d in Fig. 3).The surface energy difference between (2×2)G- and the(3×3)G-interface amounts to 0.13 eV at the graphite line,favoring the (2×2)G-interface.

To put our results into context, we revisit the growthprocess. In experiment, growth starts with a clean(3×3) reconstruction. The sample is annealed untilthe surface is covered by graphene. At this stage, the(3×3) reconstruction is the dominant phase underneathgraphene.[25] However, a shift from the SiC (3×3) tothe (2×2)C surface reconstruction at the SiC/ grapheneinterface can be stimulated by an additional anneal-ing step at a temperature below graphitisation (950C◦

- 1000C◦) leaving the graphene layer unaffected.[25]Graphene growth starts at a point where bulk SiC de-composes. The interface is determined by the momen-tary stoichiometry at which the sublimation stopped -a coexistences of different phases is observed. The fi-nal annealing step shifts the chemical potential into aregime in which SiC bulk decomposition stops and thegraphene layer does not disintegrate, but the SiC sur-face at the interface moves closer to local equilibrium,in agreement with the phase diagram in Fig. 3, formingan interface structure between the (2×2)C reconstructionand graphene. In our view, the main difference betweenthe Si face and the C face is the fact that Si-terminatedphases are more stable on the C face due to the forma-tion of heterogeneous Si-C bonds. The Si rich phases arethus stable practically up to the graphite line, allowingthe surface to form graphene only at the point wherebulk SiC itself is no longer stable. This makes monolayergraphene growth on the C side more difficult than on theSi face.

In summary, we shed new light on the central aspectsof the thermodynamically stable phases that govern theonset of graphene formation on SiC(111). We show thata Si-rich model, represented by the Si twist model, repro-duces the experimental observations - Si rich and semi-conducting. We also used the (2×2)C and the (3×3)

5

Si twist model as interface structures. We argue thatthe formation of C-face surface monolayer graphene isblocked by Si rich phases in the same chemical poten-tial range in which monolayer graphene formation canbe thermodynamically controlled on the Si face, makingthe growth of homogeneous MLG much more difficult onthe C face.

The authors thank Dr. Fanny Hiebel, Dr. UlrichStarke, and Renaud Puybaret for fruitful discussions dur-ing the preparation of this work. This work was partiallysupported by the DFG collaborative research project 951“HIOS”.

∗ Present address: AQcomputare GmbH, Business UnitMATcalc, Annabergerstr. 240, 09125 Chemnitz, Ger-many

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