Buffer-eliminated, charge-neutral epitaxial graphene on oxidized 4H-SiC (0001) surface

Graphene, a natural two-dimensional honeycomb lattice of sp² hybridized carbon, shows extraordinary electronic properties with potential applications in various fields.^1–3 These ideal properties of graphene may degrade during its growth process.^4,5 Growth techniques must be advanced to achieve high-quality graphene while meeting other requirements such as capability for large scale production, easy transferrability, etc. Epitaxial growth of graphene by thermal decomposition of SiC is one of the promising approaches in this regard.^6,7

Epitaxial graphene (EG) on the Si-face (i.e., (0001) surface) of 4H-SiC is preferred over that on its C-face (i.e., (⁠$0001¯$⁠) surface) because the growth of EG on the Si-face can be controlled. During the thermal annealing process, Si-face of 4H-SiC undergoes a $3×3$ R Cos 30° (R3) followed by a $63×63$ R Cos 30° (6R3) surface reconstruction. Sublimation of Si atoms results in a formation of honeycomb array of C atoms on the 6R3 surface of 4H-SiC. It has been found that the first C layer formed on top of the Si-face of 4H-SiC is chemically bound to the substrate and does not show graphenic properties. This chemically bound honeycomb array of C atoms (which is called the buffer layer) is followed by a monolayer graphene. In fact, formation of monolayer graphene followed by a buffer layer on the Si-face of 4H-SiC is reported in numerous works.^8,9 The presence of a buffer layer is not desired for device applications as it reduces the electron mobility of EG.⁸ EG on the Si-face of 4H-SiC is intrinsically electron doped, thus high electric fields are required to achieve charge neutral graphene.¹⁰ 

Various approaches such as atomic intercalation and surface passivation have been considered to achieve buffer-eliminated, charge-neutral EG.^10–14 Oxidized interfaces are the most natural way of decoupling the buffer layer from substrate, yet this approach has only recently been implemented for engineering the electronic properties of the 4H-SiC/EG system. Based on the results from first principles Density Functional Theory (DFT) calculations, we show that oxidation of the interface results in buffer-eliminated, charge-neutral EG on the Si-face of 4H-SiC.

We considered two types of oxidized interfaces: 4H-SiC/silicate/EG and 4H-SiC/silicon oxy-nitride/EG. Our calculations are based on the atomistic model proposed for the oxidized Si-face of 4H-SiC from experimental surface studies,^15–17 which is similar to that is used for modeling EG on bare Si-face of 4H-SiC.¹⁸ A schematic of the basic calculation cell (which is called the R3 model) is shown in Figure 1, where a 2 × 2 honeycomb array of C atoms is placed on top of $3×3$ R Cos 30° 4H-SiC (0001) super cell. In this model, two out of three Si surface atoms are chemically bound to two C atoms in the buffer layer.^18,19 The first honeycomb network of C atoms (buffer layer) on the Si-face of 4H-SiC does not show graphene like properties because it is chemically bound to the substrate. The honeycomb network of C atoms followed by the buffer layer shows graphenic properties. The 4H-SiC/EG interface is characterized by dangling electrons that stem from the unbound Si atoms on the substrate. Monolayer graphene (second honeycomb array of C atoms) on the Si-face of 4H-SiC is electron-doped, thus high electric fields are required to achieve charge neutral graphene.²⁰ First principles calculations based on the R3 model provide a correct explanation for the experimentally observed properties of the 4H-SiC/EG system.^18,19 In the current study, we extended the same model to understand the effect of interface oxidation on EG.

All calculations were performed using the first principles DFT, which is implemented in the Quantum Espresso package.²¹ Initial atomic configurations for oxidized interfaces (explained in Sections II A and II B) are modeled as they are proposed by Starke et al.¹⁶ and Tochihara and Shirasawa¹⁷ At least 8 Å vacuum space was used to separate the structure from its periodic image. Local density approximation (which has shown to work well for layered structures²²) and Hartwigsen-Goedecker-Hutter norm-conserving pseudopotentials²³ were used for the exchange and correlation functional with 45 Ry energy cutoff for the plane wave basis expansion. A $12×12×1$ Monkhorst Pack grid was used to sample the Brillouin zone for the systems. All the structures were optimized until the interatomic forces are less than 0.025 eV/Å.

Starke et al. proposed a model for a Si₂O₃ (silicate) adlayer on SiC based on their experimental investigation.^15,16 The model has an R3 periodic super cell. Two out of three surface Si atoms in the R3 cell are bound to a Si₂O₃ layer via linear Si-O-Si bridge bonds, while the Lonely (unbound) Si atom sits in the middle of the honeycomb pattern made of Si-O-Si bonds. Effectively, a single Si₂O₃ unit is bound to SiC via 2 O atoms, thus this structure is named as the Si₂O₅ model.¹⁷ Figures 2(b) and 2(c) depict the atomic configuration of the Si₂O₅ structure on the Si-face of 4H-SiC. The bare Si₂O₅ structure was optimized using DFT, yielding Si-O-Si bond angle (shown as α in Figure 2(b)) of 138° and Si-O bond length (marked in the Figure 2(b)) of 1.63 Å which agree with the values obtained by Bernhardt et al. and Lu et al. in their experimental and theoretical investigations.^15,24 Electronic band structure for oxidized Si-face of 4H-SiC is shown in Figure 2(a). The surface state, which lies close to the Fermi level, stems from the Lonely Si atoms as it is depicted by the electronic orbital isosurface in Figure 2(b). The top view of the silicate/Si-face of 4H-SiC is shown in Figure 2(c).

Even though formation of a silicate layer on 4H-SiC is a natural reconstruction of the SiC/EG interface; only a little has been done to explore its potential as a path to engineer electronic bands of EG on SiC. Takahashi et al. reported a possible band gap opening upon oxygen adsorption in EG on SiC.²⁵ Mathieu et al. reported that oxidation reduces the intrinsic electron doping of EG on SiC due to the partial saturation of Si dangling bonds.²⁶ Recently, there have been several reports to confirm that oxidation decouples the buffer layer from graphene.^8,9,27 Oida et al. observed a 3 Å thick oxide layer under the buffer layer.²⁸ 

In this work, starting from the 4H-SiC/silicate model, we provide what is, to our knowledge, the first theoretical calculation to explain the electronic and structural properties of the 4H-SiC/Si₂O₅/EG system. A 2 × 2 graphene supercell is placed on the top of the oxidized R3 cell of the Si-face of 4H-SiC (silicate), and the geometry is optimized. In the optimized configuration, the graphene layer sits 3.3 Å away from the silicate surface. The resultant graphene layer is decoupled from the substrate and electronically neutral as it is shown in the electronic band structure (Figure 3(a)), which is in agreement with recent experimental observations.⁸ Also, it is important to note that there is a 3 Å thick oxide layer underneath the graphene layer, which is consistent with the experimental observation made by Oida et al.²⁸ Figure 3(b) shows the electron band structure for 2 C layers on SiC/Si₂O₅ surface, which shows bilayer graphene properties. In contrast, a buffer layer followed by a n-doped graphene layer is formed on the bare SiC surface.^18,19

Similar to the EG on bare 4H-SiC,¹⁹ there is a surface state, which stems from a dangling electron on the Lonely Si atom on the oxidized 4H-SiC surface (Figures 2 and 3). Existence of Lonely electrons at the interface suggests a route for further engineering EG on oxidized SiC, which is similar to the case of EG on bare SiC.¹⁹ To demonstrate this point, we considered the passivation of the Lonely atom with hydrogen, oxygen, and nitrogen, the most natural passivating agents for this system. Figure 4 shows the electron band structure of three cases, EG on oxidized 4H-SiC with Lonely atom passivated with (a) H, (b) O, and (c) N. Passivation of dangling electrons significantly changes the electronic density of EG on oxidized 4H-SiC (Figure 4). In the case of H-passivation (Figure 4(a)), the graphene shows n-type behavior because graphene attracts charge from the passivated H-atom. The charge density plot (top panel of Figure 4(a)) shows that the charge is lost from the passivated H-atom. The opposite effect (i.e., p-type behavior) is observed in the case of oxygen and nitrogen passivation as shown in Figures 4(b) and 4(c). The top panels of Figures 4(b) and 4(c) show the electrons being transferred towards the passivated O and N atoms, resulting in p-type graphene. Depending on the dopant type, EG becomes n-type or p-type, while its Dirac behavior is preserved.

Introducing nitrogen into the 4H-SiC/EG system as a way of decoupling the buffer layer and achieving charge neutrality in EG has received recent interest.^29–32 Wang et al. reported that thermal annealing of the SiC system in the presence of NH₃ leads to nitrogen intercalation at the SiC/EG interface.²⁹ Masuda et al. reported that the formation of a silicon nitride (Si₂N₃) structure at the interface of SiC/EG reduces the interface carrier scattering, improving the carrier mobility of EG.³³ Various groups have recently considered depositing silicon nitride at the SiC/EG interface to achieve charge neutrality in EG^34,35 intercalates. Recently, Wehrfritz et al. reported that SiN at the SiC/EG interface introduces electron doping; however, growth conditions can be controlled to achieve a charge neutral Dirac point in the 4H-SiC/SiN/EG system.²⁰ Based on their DFT-based investigation, Caffrey et al. reported that the first honeycomb layer of C atoms is chemically bound to the Si₂N₃ layer on SiC, thus it does not show graphene-like properties. That is, the buffer layer remains when Si₂N₃ is present at the interface. Caffrey et al. then reported that, in the presence of N on a bare SiC surface, nitrogen is attached to the substrate; thus buffer layer decouples from SiC.³⁶ 

In this paper, we show for the first time that the buffer layer decouples from substrate in the presence of a silicon oxy-nitride layer, rendering the resultant graphene layer electronically neutral. Our calculation starts with the bare silicon oxy-nitride layer formed on the Si-face of 4H-SiC. Tochihara and Shirasawa reported the formation of SiON at the Si-face of 4H-SiC when SiC/SiO₂ is annealed with excess nitrogen, and the atomic structure of this interface was determined by Low Energy Electron Diffraction (LEED) analysis.¹⁷ This model, which has the R3 periodicity consists of hetero double layer structure, silicon nitride (Si₂N₃) and silicate (Si₂O₃) layers connected via Si-O-Si bridge bonds.

The optimized silicon oxy-nitride layer on the Si-face of 4H-SiC along with its electronic band structure is shown in Figure 5. The bond angles and bond lengths in the optimized structure are shown in Table I, along with those values reported by Devynck et al. from their DFT calculations.³⁷ Most importantly, unlike the silicate interface discussed in Section II A, the SiON interface is free of dangling electrons making it ideal for buffer-eliminated, charge-neutral EG on the 4H-SiC substrate.

Atomic configuration of the SiC/SiON/EG interface consists of a 2 × 2 graphene supercell placed on top of the optimized SiC/SiON surface with R3 periodicity. The structure is fully optimized within the DFT. The electron band structure of SiC/SiON/EG (shown in Figure 6(b)) clearly shows the electronically neutral Dirac point. The first honeycomb array of C atoms on the 4H-SiC/SiON shows graphene properties, confirming that the presence of SiON at the interface completely eliminates the buffer layer. For a comparison, we show the electron band structure for EG at the SiC/Si₂N₃ interface (Figure 6(a)), which is in agreement with the work done by Caffrey et al.³⁶ Slight charge transfer out of graphene is observed when Si₂N₃ forms at the interface. The first honeycomb array of C atoms is chemically bound to the interface, which is not desirable for device applications. In contrast, electronically neutral, buffer-eliminated EG is formed on the SiC/SiON surface. Two honeycomb arrays of C atoms on the interface clearly show graphene bilayer properties as shown in Figure 6(c).

Based on the first principle DFT calculations, we showed that the graphene layer is stable on the surface for both 4H-SiC/silicate and 4H-SiC/silicon oxy-nitride. It was found that the buffer layer is decoupled from the substrate on both these surfaces and the resultant EG is electronically neutral. The interface is free of dangling electrons for the SiC/silicon oxy-nitride/EG system, while there are unbound electrons at the 4H-SiC/silicate/EG interface. Existence of dangling electrons provides a route for further engineering EG on 4H-SiC, while dangling electron free interfaces assure the charge neutrality. Most importantly, our calculations disclose that charge-neutral buffer-eliminated EG on 4H-SiC, which is desired for its device applications, is possible upon interface oxidation.

The authors thank computer facilities from the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. Computer facilities and financial support from Southern Illinois University Carbondale are acknowledged.