First-principles prediction of graphene/SnO₂ heterostructure as a promising candidate for FET

Abstract

Very recently, graphene/SnO₂ heterostructures (G/SnO₂ HTSs) were successfully synthesized experimentally. Motivated by this work, the adhesion and electronic properties of G/SnO₂ HTSs have been studied by using first-principles calculations. It is found that the graphene interacts overall with the SnO₂ monolayer with a binding energy of −67–−70 meV per carbon atom, suggesting a weak van der Waals interaction between graphene and the SnO₂ substrate. Although the global band gap is zero, a sizable band gap of 10.2–12.6 meV at the Dirac point is obtained in all G/SnO₂ HTSs, mainly determined by the distortion of isolated graphene peeled from the SnO₂ monolayer, independent of the SnO₂ substrate. When the bilayer graphene is deposited on the SnO₂ substrate, however, a global gap of 100 meV is formed at the Fermi level, which is large enough for the gap opening at room temperature. Interestingly, the characteristics of the Dirac cone with a nearly linear band dispersion relation of graphene can be preserved, accompanied by a small electron effective mass, and thus higher carrier mobility is expected. These finds provide a better understanding of the interfacial properties of G/SnO₂ HTSs and will help to design high-performance FETs in nanoelectronics.

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I. Introduction

Graphene, a two-dimensional (2D) hexagon carbon network, has been attracting much attention since it was synthesized in 2004,¹ and thus much effort has been devoted to its fundamental physics and the exploration of the possibility of application in electronic devices.^2–6 The unique behavior revealed in graphene is that the π and π* bands derived from the C-p_z orbital disperse linearly to cross the Fermi level (E_F), and the electrons behave as massless Dirac fermions due to the equivalent two carbon sublattices.^2,7 Hence, graphene is expected to be used in the next-generation nanoscale electronic devices such as high-performance field effect transistors (FETs) operating at room temperature.^8,9 However, the lack of band gap make it currently unsuitable for nanoelectronics, and thus opening and tailoring a band gap in graphene becomes one of the most important and urgent research topics.

To achieve graphene-based electronics devices, many approaches, such as cut 2D graphene into finite-sized 1D nanoribbons,¹⁰ hydrogenation,¹¹ uniaxial strain,¹² and molecule doping,¹³ have been suggested to open an energy gap in graphene. The main disadvantage of these methods is that the carrier mobility and on-state current are greatly reduced because the destruction of honeycomb network introduces scattering centers, and enhances the carrier effective mass. Thus, the development of a reliable technique to create a finite gap without degrading the linear band dispersion character of graphene remains challenging. Recently, it is reported that the graphene/substrate HTSs^14–19 is easier to synthesize in experiments than the aforementioned functionalized approaches. Especially, if the graphene/substrate interaction is weak, many intrinsic properties of monolayer graphene can be kept. Inspired by this result, more and more works have been performed to pursue an energy-gap without destroying the intrinsic properties of graphene.^17–19 Despite these achievements, the search for ideal substrates is still underway.

More recently, Miao²⁰ reported the geometric stability and lithium storage performance in new constructed G/SnO₂ HTSs. They predict the stable interface formed by C–O covalent bonds, which makes G/SnO₂ HTSs more conductive than SnO₂. Paek²¹ reported enhanced cyclic performance and lithium storage capacity of G/SnO₂ electrodes with 3D delaminated flexible structure. According to the TEM analysis, the graphene are homogeneously distributed on the loosely packed SnO₂ substrate in such a way that the nanoporous structure with a large amount of void spaces could be prepared. However, the electronic properties of G/SnO₂ HTSs have not been investigated up to date. Motivated by this experiment, we explore the energetics and electronic properties of G/SnO₂ HTSs and freestanding distorted graphene (FDG) peeled from SnO₂ substrate, as well as bilayer graphene (BLG) deposited on SnO₂ monolayer by using first-principles calculations. It is unexpected that, different from the previous reported G/semiconductor HTSs,^14–20 no energy-gap opening is obtained in the G/SnO₂ HTSs. However, the FDG peeled from G/SnO₂ HTSs opens a sizeable energy gap (10.2–12.3 meV) with the linear characteristic of graphene at the Dirac point. When the bilayer graphene is deposited on SnO₂ substrate, we also find a global gap of 100 meV at the Fermi level, larger than k_BT (26 meV) at room temperature, suggesting potential applications in graphene-based FET.

II. Computational method and details

All calculations are performed by means of the Vienna ab initio Simulation Package (VASP).^22,23 The electron–ion interactions were represented by the projector augmented wave (PAW) potentials.²⁴ To treat exchange–correlation interaction of electrons, we chose the Perdew–Burke–Ernzerhof (PBE) functional within the generalized-gradient approximation (GGA).²⁵ To properly take into account the van der Waals (vdW) interactions in the layered structures, the DFT-D2 method^26,27 was used throughout all the calculations. The plane-wave basis set cutoff is 400 eV. The convergence thresholds for energy and force are 10⁻⁵ eV and 0.01 eV Å⁻¹, respectively.

To simulate G/SnO₂ HTSs, we considered an O-terminated surface of SnO₂ possessing a triangular lattice of O atoms at the topmost layer. The interface of G/SnO₂ HTSs are simulated using a supercell model in which graphene is put on surface of SnO₂ monolayer, and a vacuum layer of 15 Å is used in the direction normal to SnO₂ monolayer. We imposed a commensurability condition between graphene and SnO₂, where a 4 × 4 lateral periodicity of graphene and 3 × 3 lateral periodicity of the SnO₂ monolayer are employed, as shown in Fig. 1. The small lattice mismatch between graphene and SnO₂ substrate is 2.5%.

Fig. 1 Side and top views of the three patterns of G/SnO₂ HTSs: (a) TO, (b) TS, and (c) B; as well as (d) FDG of pattern B. The blue, red and green balls represent C, O and Sn atoms, respectively.

III. Results and discussions

In this work, we consider three representative patterns of graphene on SnO₂ substrate: (i) a C atom of graphene on top of one of the Sn atoms (TS) (Fig. 1(a)); (ii) a C atom of graphene on top of one of the O atoms (TO) (Fig. 1(b)); (iii) a C atom of graphene on top of bridge site between Sn and O atoms (B) (Fig. 1(c)). After structural relaxations, we find that the graphene keeps its original planar and hexagonal atomic network, while maintaining the interlayer spacing of ∼3.0 Å (Table 1), when bonded to the SnO₂ monolayer. Notice that the interlayer spacing is much larger than the sum of covalent radii of C and oxygen atoms, suggesting that the interfacial C–O lengths of G/SnO₂ HTSs are beyond the bonding range. In addition, we also find that the corrugation of the graphene layer is ∼0.07 Å, close to that in G/MoS₂ (ref. 16) and G/SiC HTSs.²⁸

Table 1 The calculated distance between graphene and SnO₂ monolayer, and the binding energy (meV per C atom) of graphene on different adsorption sites with DFT and DFT-D2, respectively

Patterns	DFT (without vdW)		DFT-D2 (with vdW)
	d (Å)	Eb (meV)	d (Å)	Eb (meV)
TO	3.59	−11.67	3.07	−67.23
TS	3.61	−11.34	3.07	−67.22
B	3.67	−16.56	3.11	−70.42

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To quantitatively characterize the interface interactions, the binding energy (E_b) between the graphene and SnO₂ monolayer is calculated as

E_b = E(G/SnO₂) − E(G) − E(SnO₂), (1)

where E(G/SnO₂), E(G), and E(SnO₂) are energies of G/SnO₂ HTSs, isolated graphene and SnO₂ monolayer, respectively. Fig. 2 displays the E_b per C atom with respect to the spacing between graphene and SnO₂ for TS, TO, B patterns, respectively. At the optimized interlayer spacing, the E_b in three patterns is about −67–−70 meV (Table 1, demonstrating that the E_b is not sensitive to the adsorption patterns. These can be understood through a comparison with the adsorption of graphene on HfO₂ surfaces.²⁹ In the case of HfO₂ substrate (−112 meV per C), it is found that the absorption of graphene is caused mainly by the hybridization between the C-π and O-2p states with Hf-d character. By contrast, the present results suggest the graphene is bound to SnO₂ via the weakly vdW mechanism. Since the energy of pattern B is lowed by about 3 meV than that in patterns TO and TS, we only consider pattern B in the following.

Fig. 2 Binding energy (E_b) per C atom in G/SnO₂ HTSs for the three patterns TO, TS, and B, respectively, as a function of the spacing between the graphene and SnO₂ monolayer. The insert is the enlarged plot near the equilibrium lattice of G/SnO₂ HTSs.

To check the validity of vdW interactions to G/SnO₂ HTSs, We also calculated the interlayer distance dependence of the E_b per C atom of G/SnO₂ HTSs using PBE approximation, as shown in Table 1. A comparison study shows that the variational trends and equilibrium interlayer spacings given by PBE + vdW and PBE approaches are different significantly for all stacking patterns. The resulting interlayer spacing are ∼3.6 Å for TS, TO, and B patterns without vdW interactions, and the corresponding E_b are ∼−11–−16 meV. Obviously, there is a significant difference between the results with and without inclusion of the vdW interactions, indicating that the vdW interaction is extremely important for accurately describing the geometric structure of the G/SnO₂ HTSs.

To explore whether the electronic structures of graphene can be affected by SnO₂ substrate, we examine the band structures of the G/SnO₂ HTSs, as shown in Fig. 3(a)–(c). As a comparison, the band structures of free-standing graphene and SnO₂ monolayer are shown in Fig. 3(d) and (e), respectively. For the SnO₂ monolayer, E_g = 2.75 eV, consistent with the previous results.³⁰ Due to the relatively weak interaction between graphene and SnO₂ monolayer, a size band gas of 13.4 meV, 15.8 meV, and 17.2 meV for patterns TO, TS, B, respectively, are obtained. However, the hybridized graphene π and π* bands with oxygen atoms significantly cross E_F and thus unexpected metallic behavior appears for G/SnO₂ HTSs, in contradiction to the previous results reported for G/semiconductor HTSs.^14–19 The possible reason can be attributed to the interlayer-induced self-doping phenomenon, as found in G/BC₃ HTSs,³¹ which significantly reduces the gap for the whole band structure and renders graphene n or p-type metallic behaviors. In fact, these results are in good agreement with experimental observations, in which G/SnO₂ HTSs has a higher electric conductivity.^20,21

Fig. 3 Band structures of the G/SnO₂ HTSs for patterns (a) TO, (b) TS, (c) B, (d) SnO₂ monolayer, and (e) free-standing graphene. (f) Is PDOS of pattern TO in the ground state.

To further explain this unexpected phenomenon, we display the partial density of states (PDOSs), as shown in Fig. 3(f). One can see that the E_F cross the Sn-5s and O-2p states at the conduction band minimum (CBM), as well as C-2p states at the valance band maximum (VBM). This is because that the C-2p states of graphene lose some electrons, making E_F shift down clearly, while the CBM from Sn-5s and O-2p hybridized states make the E_F move up correspondingly due to the electrons transfer from graphene to SnO₂ monolayer. Also, further Bader charge analysis indicates that the charge density is redistributed by forming electron-rich and hole-rich regions between graphene and the SnO₂ monolayer, as shown in Fig. 4(a) According to π-electron tight-binding (TB) model³² of bipartite lattices, the dispersion relation near E_F can be expressed as^33,34

here, k is the wave vector relative to the K point, v_f is the Fermi velocity, and Δ is the onsite energy difference between two sublattices. For free-standing graphene, the onsite energies of A and B sublattices are identical (Δ = 0), and thus results in the Dirac-like linear dispersion relation. When graphene is deposited on SnO₂ substrate, the symmetry-breaking substrate potential is introduced, and thus the inversion symmetry of graphene is broken by making Δ ≠ 0, giving rise to a nonzero band gap, E_g = 2Δ. As is shown in Fig. 4(a) and (b), the charge transfer from graphene to SnO₂ monolayer and non-uniformity of electron charges disrupt the degeneracy of the π and π* bands at K point, resulting in the band gap opening.

Fig. 4 (a) The differential charge density (0.005 e Å⁻³) of pattern B. Here, the yellow (cyan) indicates the charge accumulation (depletion). (b) Plane-averaged electron density difference, Δρ(z) for pattern B. The q is the charge transfer calculated by integrating Δρ(z) over the full z range. The yellow and cyan areas represent electron accumulation and depletion, respectively.

It is the weakly interaction between graphene and SnO₂ monolayer that FDG can be easily peel from G/SnO₂ HTSs, as shown in Fig. 1(d). The structure of FDG is the same as that of G/SnO₂ HTSs except that the substrate is removed to distill the effect of the structure distortion on the band structure. The equivalence of the two carbon sublattices inside FDG lattice basically remains unaffected because of the slightly corrugation of carbon atoms, so the geometric structure of the FDG is almost the same as the silicene or germanene.^35,36 Fig. 5 further displays the band structures of the FDG in patterns TO, TS, B, respectively. Interestingly, one can see that the π and π* bands repulse each other, forming a direct band gap at the K points. The calculated band gap is about 10.2, 12.3, and 10.6 meV for patterns TO, TS, B, respectively. These gap values are comparable to those obtained for graphene on hydroxylated (0001) surfaces of SiO₂,³⁷ smaller than that of hexagonal BN surface,³⁸ indicating that the transport properties of FDG decreases slightly compared with the pristine graphene.^37,38 Remarkably, the curvature of the band dispersion around the Dirac point of FDG is almost linear, suggesting that the carrier effective mass and, consequently, the high carrier mobility are hardly influenced by SnO₂ substrate. It indicates that the on–off current ratio in logical devices made of G/SnO₂ HTSs would be largely improved. Since the presence of a finite E_g without degrading the electronic properties of graphene is highly expected, SnO₂ is a suitable choice as a substrate for graphene-related electronic devices.

Fig. 5 Band structures of the FDG in patterns (a) TO, (b) TS, (c) B, respectively. The insert is the enlarged band gap at the Fermi level. The Fermi level points to zero energy.

Now, we turn to the bilayer graphene (BLG) on SnO₂ surface. The stacking patterns are simulated by adding another graphene monolayer on patterns TO, TS, and B of G/SnO₂ HTSs, which are still defined as patterns BTO, BTS, and BB, respectively. In all the cases, the BLG is arranged in two different ways, i.e., AA and AB (Bernal stacking order). After structural relaxation, we find that the AB stacking order of graphene is more stable energetically than AA order and thus we only considering pattern AB in the following, as shown in Fig. 5(a–c). The optimized interlayer spacing between BLG and SnO₂ interface preserves about 3.6 Å, consistent with monolayer graphene on SnO₂ surface. The relaxed interlayer spacing between graphene sheets is found to be larger than the typical length of C–C bond (1.42 Å) in monolayer graphene, suggesting that the bonds in BLG are absent in all the hybrid structures.

Fig. 6 displays the electronic band structures of BLG on SnO₂ substrate in the ground state AB. It can be seen that around the Fermi level, the band structures of G/SnO₂ HTSs have the characteristic graphene feature of linear dispersions, i.e., the merits of Dirac system, such as the high Fermi velocity and large carrier mobility, may be well retained in the G/SnO₂ HTSs. More importantly, these stacking patterns exhibit the semiconducting character with an energy-gap of 110 meV, larger than k_BT (26 meV) at room temperature, differ from the previous report on BLG on semiconductors (Fig. 7).

Fig. 6 Side and top views of the three patterns of BLG/SnO₂ HTSs: (a and d) TO, (b and e) TS, and (c and f) B. The blue, red and green balls represent C, O and Sn atoms, respectively.

Fig. 7 Band structures for BLG/SnO₂ HTSs in patterns (a) BTO, (b) BTS, (c) BB, respectively. The insert is the enlarged band gap at the Fermi level.

In generally, to realize the practical applications of G/SnO₂ HTSs in FET, higher carrier mobility and linear band dispersion are very essential. So we investigate the electron effective mass (m*) at Dirac point of G/SnO₂ HTSs. As have mentioned before, the G/SnO₂ HTSs preserve the linear band dispersion relation of graphene. According to the graphene dispersion relationship, the m^*_e and m^*_h can be expressed as^39–41

where k is wave vector and v_f is Fermi velocity. Table 2 present the calculated fitting value of v_f for all G/SnO₂ HTSs. Fortunately, it can be seen that all the stacking patterns obtain a considerable v_f value (∼0.81 × 10⁶ m s⁻¹), which is comparable to that of FSG (1.0 × 10⁶ m s⁻¹). Furthermore, we also investigate the calculated m^*_e and m^*_h along Γ–K and K–M directions of all the stacking patterns, as shown in Table 2. It can be observed that the m^*_e and m^*_h at VBM and CBM for G/SnO₂ HTSs are very small, which is still more superior to others graphene-based nanoelectronics. This indicates that the G/SnO₂ HTSs may have a higher carrier mobility which is necessary in the application of FETs. The large value of v_f and the less m* is indispensable for the design of application and this can be analyzed qualitatively by the interaction between graphene and SnO₂ substrate. Similar results are also found for BLG/SnO₂ HTSs. As a consequence, an ideal FET with the high carrier mobility and certain band gap on G/SnO₂ HTSs based nanoelctronics can be expected.

Table 2 The calculated effective masses of electrons and holes, the maximum Fermi velocity (v_f) for all stacking patterns of G/SnO₂ HTSs

Patterns	Effective mass	Γ–K	Γ–M	vf (max)
TO	m^*e	6.78 × 10^−19	6.14 × 10^−19	0.80 × 10^6
	m^*h	6.98 × 10^−19	6.78 × 10^−19
TS	m^*e	6.58 × 10^−19	6.32 × 10^−19	0.80 × 10^6
	m^*h	6.97 × 10^−19	6.43 × 10^−19
B	m^*e	6.42 × 10^−19	6.38 × 10^−19	0.81 × 10^6
	m^*h	6.99 × 10^−19	6.56 × 10^−19

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IV. Conclusions

In summary, our first-principles study indicates that the graphene can grows on SnO₂ substrates with a binding energy of about −67–−70 meV per C atom, irrespective of the adsorption patterns, suggesting vdW interaction between graphene and SnO₂ monolayer. Different from the conventional G/semiconductor HTSs, the Dirac cone of the G/SnO₂ HTSs appears yet, but the metallic character of HTSs is obtained. However, the FDG peeled from G/SnO₂ HTSs exhibit semiconducting behavior with a sizeable band gaps of 10.2–12.6 meV at K point. When the bilayer graphene is deposited on SnO₂ substrate, however, a global gap of 100 meV is formed at the Fermi level. Also, the nearly linear band dispersion character of graphene can be preserved in all graphene and bilayer graphene on SnO₂ substrate, and thus high carrier mobility of graphene is expected. Our finds provide a better understanding of the interfacial properties of G/SnO₂ HTSs and help to design the high-performance FET in nanoelectronics.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 11274143, 11434006, 61172028, and 11304121), and Research Fund for the Doctoral Program of University of Jinan (Grant no. XBS1433).

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