Band gap opening of bilayer graphene by graphene oxide support doping †

The zero-band-gap features of monolayer and bilayer graphene (SLG and BG) limit their applications in logic circuits and photonic devices. Replacing adsorptions of foreign atoms or organic molecules, coupling of BG with derivatives of graphene provides a promising way to modify the electronic properties of BG. In this work, based on ﬁ rst-principles calculations, a sizeable bandgap is created in BG as it is supported on the highly stable graphene oxides (GOs). This result totally di ﬀ ers from the remaining semimetallic behavior of SLG supported on GOs revealed by previous works. The opened band gap can reach values as large as 245 – 261 meV, which depend on the structure of GOs substrates, including the oxidation species and their atomic arrangement. The e ﬀ ective p-type doping in BG is induced as GO substrates mainly contain the presence of single epoxides. More importantly, the high carrier mobility and large Fermi velocity in supported BG can be maintained due to the weak interaction with GOs. The band gap opening is attributed to the charge transfers between GOs and its neighboring graphene layer, which leads to a signi ﬁ cant chemical potential di ﬀ erence between bilayer graphene. Thus, the present work provides a scienti ﬁ c basis for the development of high-performance graphene-based nanodevices.


Introduction
][21][22][23][24][25][26][27] However, all these strategies drastically reduce the carrier mobility of graphene or only open a nite band gap due to the destruction of the honeycomb structure and high requirement for the quality of substrate.
][30][31] Although the opened band gap in BG can reach 0.25 eV, a large external voltage is required to be applied to both the top and bottoms gates, thus making this approach impractical. 319][40][41][42] Unfortunately, some disadvantages induced by these methods are found, such as structural conformation, defects, and clustering of dopants.
The clustering from doping atoms can be avoided by molecular adsorbates due to the repulsion of the charged molecules between each other.4][45] For example, rst-principles theoretical calculations 43 have revealed that adsorption of tetra-uorotetracyanoquinodimethane (F4-TCNQ) on one side surface of graphene can open the band gap in BG and achieve charge transfers, inducing p-type doping effect.However, chemical doping of BG with organic molecules easily generates highly degenerate semiconducting properties, which moves the Fermi level within the valence band or the conduction band, causing problems in switching device applications.
The stability of organic molecules adsorbed BG systems is very important for the graphene-based nanoelectronic device, because they are mostly environmentally unstable.Very recently, our theoretical works 46 reported that replacing the adsorbed organic molecules, the functionalized hexagonal boron nitride (h-BN) substrates with hydrogen and uorine atoms can lead to n-or p-type doping of graphene, and even open the band gap in graphene.According to this idea, Hu et al. 47 proposed a promising way to open a large band gap in BG by sandwiching it between surface functionalized h-BN with H and F atoms.It is reported that BG can have energy gaps ranging from 0.35 eV to 0.55 eV.However, the challenge for such device realization may be comes from the difficult preparation of these functionalized hexagonal boron nitride experimentally.Thus, searching for an effective method for opening band gap in BG still remains challenging.
9][50] Owing to the presence of the rich oxygen-containing functional groups, combining the GOs with other twodimensional nanomaterials provides an effective route for fabricating the hybrid structures with novel physical and chemical properties. 51,52Recently, the experiment works combining with DFT calculations 53 revealed that aer mild O 2 plasma treatment on SLG and BG, the sufficiently oxidized SLG shows the semiconducting properties, while the oxidized BLG maintains its semimetallic behavior even at high oxygen level.][56] Motivated by these contributions, we investigated the effect of GOs substrates on the electronic properties of bilayer graphene using DFT calculations.The results revealed that in contrast to the metallic properties of SLG/GOs revealed by the experimental reports, 53 the BG supported on GOs are semiconductors with sizeable band gap.

Computational details
All rst-principles calculations were performed within the framework of the plane-wave pseudopotential densityfunctional theory (DFT) implemented in CASTEP code. 57The Perdew-Burke-Ernzerhof (PBE) 58 functional including the van der Waals (vdW) correction proposed by Grimme 59 (referred as PBE + D, where D stands for dispersion) was adopted.The ultraso pseudopotentials 60 for the ion-electron interactions and a kinetic energy cutoff of 350 eV in the plane-wave expansion were used.The two-dimensional (2D) periodic boundary conditions are considered along the growth directions of graphene layer.A vacuum layer of 10 Å is set in the z-direction to avoid the interaction between the periodic images.The 2D Brillouin zone was sampled by 7 Â 7 Â 1 k-points within the Monkhorst-Pack scheme.In geometry optimization, the whole conguration was allowed to relax until all of the force components on any atom were less than 0.01 eV ÅÀ1 .The convergence criterion for energy was chosed as 10 À5 eV.Test calculations (see Table S1 in ESI †) showed that increasing the sampling space has less impact on the charge transfers between GOs and BG.
In the computational model, we apply supercell of 2 Â 2 graphene unit cells consisting of 8 carbon atoms to simulate deposition of BG on GOs substrate.The optimized lattice constant of graphene is 2.46 Å, and the distance between two adjacent graphene layers is evaluated to be 3.35 Å, in excellent agreement with experimental values.The A-B stacking BG is mainly considered due to its higher stability than other patterns.
2][63][64][65][66][67][68][69][70][71][72][73][74][75][76] It is commonly accepted that the oxygen functional groups on the graphene basal plane exist in the form of the hydroxyl and epoxy groups.Some other oxygen functional groups are found, such as veand sixmembered ring lactols. 71More importantly, the recent X-ray photoelectron spectroscopy (XPS) measurements 53 showed that aer O 2 plasma treatment, the epoxy and hydroxyl groups are mainly introduced on the basal plane of oxidated BG.Based on the theoretical calculations, various atomic congurations of GOs including disordered and ordered models were proposed.It is found that epoxy and hydroxyl groups tend to aggregate on graphene plane. 66,72In particular, the band gaps of GOs are well tuned in wide energy range by controlling the oxygen concentration and the atomic arrangement of oxygen groups. 66,72,74,76n our models, therefore, GOs support includes adsorption of the hydroxyl and epoxy groups.We mostly used the model structures of graphite oxide proposed by previous DFT results 75 and by XPS measurements 53 to simulate GOs support of BG, which are energetically favorable and close to the experimental datas.In these models, the oxidation level and atomic arrangement of the oxygen groups as well as combination of the hydroxyl and epoxy groups were considered.The lattice constant of BG/ GOs nanocomposite is set to that of pristine BG.We used BG/ GO-mO-nOH-i to represent the hybrid structure between BG and different GOs, in which the m and n dene the number of the epoxy and hydroxy groups, respectively, and i marks the atomic conguration of GOs with the same oxygen groups.
To evaluate the stability of hybrid structure between BG and GOs support, the adsorption energies are calculated by: E a ¼ E BG + E GOs À E BG/GOs , where E BG , E GOs , and E BG/GOs are the total energies of graphene bilayer, GOs, and the hybrid BG/GOs structure, respectively.

Structures and stabilities of BG/GOs
The semiconducting property of GOs and its high stability make this materials a good candidate for BG support.The considered GOs substrates contain single the epoxy and hydroxyl groups and both them.When several oxygen functional groups are adsorbed on GOs surface, the effect of atomic arrangements of these groups are considered.Fig. 1 shows the adsorption congurations of BG/GOs.Table 1 presents the corresponding adsorption energies and distance between support and BG.
According to different initial position of oxygen groups on substrate relative to bottom graphene layer, we also investigated other stacking patterns of BG/GOs as shown in Fig. S1 in the ESI.† For example, in the case of GO-2O support, the two epoxy groups include three possible congurations with respect to the bottom graphene layer: two oxygen atoms are almost placed beneath the carbon atoms (Fig. 1d), directly below the bridge site of C-C bond (Fig. S1a †), and below the hollow site (Fig. S1b †).Similarly, for the GO-2OH-2, one oxygen from OH points to the carbon atom and the second oxygen to the hollow site (Fig. 1b and S1c †), or the two oxygen are directly below the carbon atoms (Fig. S1d †).The atomic congurations for other stacking are shown in Fig. S1e-h.† Table S2 in the ESI † presents the corresponding adsorption energy and distance for other BG/GOs structures.Comparing with Tables 1 and S2, † it is found that the stacking conguration of BG/GOs from Fig. 1, whose epoxides and/or H atom from the hydroxyl group are close to the hollow site of neighboring graphene layer, is the ground state among all considered stacking patterns due to the less repulsion or has similar adsorption energy with other patterns, and the largest energy  difference between all stacking order for each substrate is less than 7 meV per carbon atom.Thus, we mainly focused on the BG/GOs systems with the ground state in the following.Aer geometry relaxation, the distance between BG has no distinct change before and aer GOs interaction except for the BG/GO-2O structure.The BG remain the character of basal plane, without breaking the geometric structure of pristine graphene sheet (see Fig. 1).As seen in Table 1, the interlayer spacing between GOs and the bottom graphene layer is in the range of 2.47-3.08Å, depending on the structure of substrates, which are smaller than that of organic moleculars adsorbed BG. 43,44 The sp 2 to sp 3 hybridization change of carbon networks of GOs and the atomic arrangement of adsorbed oxygen group determine the interlayer spacing.In generally, as shown in Fig. 1e-j, in the presence of both epoxy and hydroxyl groups, the H atom from the hydroxyl group of GOs is more close to the graphene layer than the epoxide.The small distance between GOs and graphene layer plays important role in the charge transfer between them.The Mulliken population analysis (see Table 1) show that there are signicant charge transfers from GOs to bottom graphene layer.
Total energy calculations show that the adsorptions of BG on all GOs substrates are energetically favorable with adsorption Fig. 2 Band structures of BG/GOs only containing single hydroxyl and epoxy groups.The Fermi level is set to 0. The corresponding geometry structures are shown in Fig. 1a-d.
Fig. 3 Band structures of BG/GOs containing both the hydroxyl and epoxy groups.The Fermi level is set to 0. The corresponding geometry structures are shown in Fig. 1e-j.
energies of À208 to À328 meV (corresponding to À26 to À44 meV per carbon atom of graphene layer).Obviously, the coupling of BG with GOs is sensitive to the substrate structures, including the atomic arrangement of oxygen groups as well as oxidation species (see Table 1).The interlayer coupling strength of BG/GOs is comparable to the adsorption of graphene on functionalized h-BN with uorine and/or hydrogen revealed by the recent reports. 46,47Therefore, the larger interlayer spacing and small adsorption energy indicate the dominant weak interaction between BG and GOs.

Electronic structures of BG/GOs
In the following, we investigated the effect of GOs support on the electronic properties of BG.Fig. 2 and 3 present the band structures of BG/GOs.Table 1 also gives the corresponding band gap in BG.When GOs substrates mainly include the hydroxyl groups, the opened band gap in BG is small with 31 meV for GO-2OH-1 (Fig. 2a) and 79 meV for GO-2OH-2 (Fig. 2b).The other stacking orders for BG/GO-2OH-2 also remain the small band gap (see Fig. S2a and b †).However, when BG is supported on GOs with single epoxy group, the band gaps in BG are increased to 200 meV for GO-2O (Fig. 2d) and 220 meV for GO-O (Fig. 2c).Furthermore, the band structures show that the mainly linear energy dispersion of the pristine graphene around K point is preserved.The semiconducting BG/GOs are totally different from O 2 plasma-treated BG by previous works, 53 in which oxidized BG are metallic.
From Fig. 2c and d, one can clearly nd that the Fermi level of BG/GOs nanocomposite is shied downward, lower than the valence band maximum, indicating the p-type doping of BG.Such doping is also conrmed by the charge transfer from GOs to bottom graphene layer (À0.04 e for GO-O and À0.02 e for GO-2O shown in Table 1).This can be understood by the higher electronegativity of oxygen than the carbon atom of bottom graphene layer.Such the hole doping and band gap opening are also occurred on other systems for interaction of graphene with electron-withdrawing organic groups 44,45 or B-doped graphene. 35he band gap value and p-type doping effect in BG induced by GO-2O are independent of the stacking patterns (see Fig. S2c  and d †).We also considered other atomic arrangement of two Table 2 Summary of calculated results for BG/GOs: deformation potential constant (E 1 ), 2D elastic modulus (C), effective mass (m*) and mobility (m) for election, heavy and light hole at 300 K.The vacuum level was set to zero for reference.Note that only x direction is considered

GOs
Carrier type adsorbed epoxides on substrate (see Fig. S3 †), the large band gaps are still obtained, while the doped gap states by GOs are found.
As shown in Fig. 3, the coexistence of the epoxide and hydroxyl groups on GOs support can further increases the band gap in BG to 245-261 meV.More importantly, the band structures of these BG/GOs around the Fermi level are very similar to that of pristine BG, indicating no breaking the intrinsic electronic properties of graphene.It is also noticeable that the band gap strongly depends on the atomic arrangement of these oxygen groups on substrate.For example, the band gap of BG supported on GO-2O-2OH-2 or GO-2O-4OH-2 is 261 (Fig. 3d) and 230 meV (Fig. 3f), respectively, whereas this value is lower as the corresponding GOs structure is transformed into other one (89 meV for GO-2O-2OH-1 shown in Fig. 3c and 74 meV GO-2O-4OH-1 in Fig. 3e).
In addition, in the presence of both the epoxide and hydroxyl groups on support, the similar band gap values in BG are found for the other stacking pattern (see Fig. S4 †), implying that these systems should be robust and suitable for the real applications.This results are totally different from those previously reported for the BN/BLG/BN system, in which the electronic properties are sensitive to the stacking order. 77The semiconducting BG/ GOs are further conrmed by the total density of states (DOS) (see Fig. 4).The projected DOS (PDOS) of BG also suggest that the interaction of GOs substrates not only induces a band gap in BG, and but also maintains the intrinsic electronic properties of pristine graphene.Thus, irrespective of the oxygen density in the GOs substrates, the supported BG is always semiconductor.
The effect of oxidation species of substrates on the electronic properties of BG has a signicant difference.Different from only the single epoxides, adsorptions of both the epoxide and hydroxyl groups on substrates lead to less or no doping effect in BG except for GO-O-2OH-1 (see Fig. 3 and S4 †).This results may be due to the formation of electron-hole separated domain in bottom graphene layer, in which some carbon atoms have positive charges transferred from GOs and some other carbon have negative charges.In contrast, the GO-O-2OH-1 support leads to the signicant net charge transfer because no or less negative charges are transferred from the H atom to carbon atom of graphene due to the larger distance between GO and bottom layer (3.1 Å), compared to other supports (see Table 1).From the PDOS of BG, the downshi of the Fermi level relative to pristine BG suggest the p-type doping by GOs substrate only for adsorption of single epoxy group (see Fig. 4a-c), whereas less doping of BG is found as the GOs contain both the epoxide and hydroxyl groups (Fig. 4d-f).
For the current practical applications of graphene-related nanoelectronics, higher carrier mobility and linear band dispersion are two very important aspects.Thus, we calculated the electron (m * e ) and hole (m * h ) effective mass of the conduction band minimum (CBM) and valence band maximum (VBM) of BG/GOs by m* ¼ h -2 v 2 EðkÞ vk 2

À1
, respectively, where ħ is the reduced Planck constant, k is the wave vector, and E(k) is the energy dispersion relation with respect to the wave vector k.As shown in Table 1, no remarkable increase of effective mass of charge carrier of BG is found aer band gap opening.The  calculated m * h (or m * e ) of BG for BG/GOs nanocomposites with large band gap are only 1.11-2.07(1.65-2.8)times larger than that of freestanding BG.This indicates that in addition to opening a sizeable band gap, the BG of BG/GOs may maintain the high carrier mobility, which provide a potential application in high speed electric devices.
We calculated the carrier mobility (m) of selected BG/GOs systems using the deformation potential (DP) theory proposed by Bardeen and Shockley. 78Such method is extensively used to predict the carrier mobility of 2D materials, such as Si-based pentagonal monolayer. 79Based on the effective mass approximation, the mobility can be estimated as follows: , where e is the electron charge, m* is the carrier effective mass, E 1 is dened as DE ¼ E 1 (Dl/l 0 ), in which DE is the energy shi of band edge with respect to lattice dilation Dl/l 0 , and S 0 is the elastic modulus of the 2D system activated by the applied strain d, where E is the total energy and S 0 is the area of the system.As shown in Table 2, the predicted acoustic-phonon-limited carrier mobility for electron is 0.19-0.29 Â 10 5 cm 2 V À1 s À1 , while the hole mobility can reach 2.38 Â 10 5 cm 2 V À1 s À1 .The small deformational potential and small effective mass for GO-O-2OH-2 support are the main reason for high carrier mobility.
To further examine the carrier mobility near the Dirac cone, we evaluate the Fermi velocity.Using the p-electron tightbinding approximation, the effective mass of carriers of BG/ GOs near the Dirac point can be calculated as m* z E g /2y F 2 .
Clearly, the Fermi velocity y F is larger with m* smaller, which means higher carrier mobility with appropriate band gap E g on the BG/GOs nanocomposites.Table 3 presents the Fermi velocity of carrier of VBM and CBM of BG/GOs with larger band gap.The calculated results show that the Fermi velocity of BG remains large values of 5.1-8.0Â 10 5 m s À1 , which has the same order of monolayer graphene (9.5 Â 10 5 m s À1 ). 80Previous experimental reports 48 also revealed that the Fermi velocity in epoxidized BG prepared by O 2 plasma treatment is remarkably comparable with that of pristine monolayer graphene.The GOs models contain the high oxygen concentration larger than 0.25 as discussion above, which may present some restriction in wide applications of graphene-based nanoelectronics.To reduce the oxidation level of graphene, we also used supercell of 4 Â 4 graphene consisting of 32 carbon atoms to simulate BG/GOs nanocomposites.Only three GOs supports are considered: adsorption of one epoxide, two epoxides, and two epoxides and two hydroxyl groups, which correspond to 0.062, 0.125, and 0.187 oxygen concentration, respectively.Fig. S5a-f † present the geometry structures and the corresponding band structures.The calculated results show that the GOs support with low oxygen concentration still open a signicant band gap in BG.However, the opened band gap by low oxygen concentration is smaller than that by the corresponding GOs with high oxygen level.This may be due to the less charge transfers between BG and GOs for the former.
From the discussion as above, it is found that the band gap opening of BG by support can be obtained in a wide oxygen concentration of GO.The GO support including the presence of both the epoxides and hydroxyl groups, which are closer to the samples prepared experimentally, can induce larger band gap in BG, compared to other GO structures.Thus, such method for using GO support to open the band gap of BG can be easily realized in experiment.

Mechanisms for opening band gap of BG by GOs support
Previous works 43,44,47 revealed that the charge transfer plays an important role in band gap opening in BG.Huang et al. 81 systematically discussed charge and energy transfer in plasmonic photocatalytic composites.The charge transfer can induce the built-in electric eld in BG when the graphene layer is placed at external environment with organic moleculars and substrate.Alternatively, the symmetry breaking realized by asymmetric chemical doping in BG also can open the band gap. 35,36Therefore, to investigate the mechanism for band gap opening, we rst calculate the charge density difference of BG/ GOs for selected systems as shown in Fig. 5a-c.The charge density difference is constructed by Dr ¼ r BG/GOs À r BG À r GOs , where r BG/GOs , r BG , and r GOs represent the total charge densities of hybrid systems BG/GOs, free bilayer graphene, and free GOs, respectively.
From Fig. 5a-c, it clearly shows that the charge densities of BG are redistributed aer GOs interaction.The oxygen atoms from all GOs always accumulates electrons transferred from bottom graphene layer, while the carbon atoms of bottom graphene layer can lose and/or accumulate electrons, depending on the structure of GOs substrate.This results lead to coexistence of electron-rich and hole-rich regions on the bottom graphene layer.The charge transfer in the interface of BG/GO-2O-4OH-1 (Fig. 5a) is slightly more apparent, compared to other two GOs (Fig. 5b and c) due to the shorter interlayer spacing for the former.According to the charge density difference and the corresponding band gap (74 meV for GO-2O-4OH- 1, 230 meV for GO-2O-4OH-2, and 245 meV for GO-O-2OH-2), it is difficult to nd any positive correlation between the opened band gap value in BG and the charge transfers.
The charge transfers from GOs to its neighboring graphene layer break the symmetry balance of two graphene layers, leading to band gap opening.Thus, we analysed the partial charge densities of VBM and CBM of pristine BG and BG/GO-2O-4OH-2.As shown in Fig. 5d, for the pristine BG, the carbon atoms from two graphene layers have equivalent contribution to the Dirac point (DP).However, when BG is supported on GOs, the electronic states of CBM and VBM are contributed by two different graphene layer: the former mainly comes from the p z orbitals of carbon atoms of the upper graphene layer (Fig. 5e), while the latter be from the bottom layer (Fig. 5f).
To further insight into the charge transfer, we plots the planar averaged charge density difference along the z direction perpendicular to the bilayer graphene for selected systems as shown in Fig. 6.The positive and negative values represent the electron accumulation and depletion, respectively.It is clear that besides the interlayer regions between GOs and bottom graphene layer, the interface between BG appears two signicant peaks: one located at about 8 Å in z direction corresponds to the electron accumulation, the other at about 9.5 Å belongs to the electron depletion.Based on these data and the band gaps as shown in Table 1, it seems to be that the larger the electron accumulation and depletion in these two peaks, the larger the band gap one can obtain.Therefore, the value of band gap in BG is well correlated to the charge transfers from the interface between upper and bottom graphene layers.
The remarkable charge transfers can induce the formation of an effective electronic eld in BG.The magnitude of built-in electric eld depends on the structure of GOs substrate, determining the band gap value in BG.As reported in previous reports, 82 increasing the chemical difference between two degenerated bands at the Fermi level is a very important factor for opening the energy gap in the graphene systems.To illuminate this correlation, we calculated the electrostatic potential of selected BG/GOs systems.As shown in Fig. 7, the effective electronic eld of BG/GO-2O-2OH-2 (Fig. 7b) and GO-2O-4OH-2 (Fig. 7d) is more distinct, compared to the GO-2O-2OH-1 (Fig. 7a) and GO-2O-4OH-1 (Fig. 7c) substrates.We use the difference in core-level electrostatic potential (corresponding to two highest points in potential of each BG/GOs nanocomposite) to represent the chemical difference.These values are 2.52 (Fig. 6a), 7.96 (Fig. 6b), 2.34 (Fig. 6c), and 5.22 eV (Fig. 6d), Fig. 7 The xy-averaged electrostatic potential of BG/GOs nanocomposites as a function of position in the z-direction.The vertical dashed lines denote the central location of atomic layer of the BG and carbon atoms of GOs.The potential difference between graphene bilayer is marked with the blue number.
implying a positive correlation with the band gaps of 89, 261, 74, and 230 meV.Thus, we obtain a promising way to open a sizeable band gap in BG but retain its intrinsic electronic properties using the highly stable GOs as substrate.

Conclusions
In summary, we performed rst-principles calculations to study the electronic properties of BG adsorbed on GOs substrates.Our results show that in contrast to the metallic properties of oxidated BG, the highly stable GOs support can open the band gap in BG, whose values are determined by controlling the structures of GOs.The coexistence of the epoxy and hydroxyl groups on GOs can further increase the band gap in BG to 260 meV.The effective p-type doping of BG is realized as the GOs substrates only contain single epoxides.More importantly, the high m e value in supported BG can be largely maintained.The band gap opening in BG may be attributed to the charge transfers from GOs to bottom graphene layer, which produces a signicant chemical difference between two graphene layers.Thus, BG supported on highly stable GOs may present a new way for fabricating high-performance graphene-based nanodevices.

Fig. 1
Fig. 1 Side and top view of optimized structures of BG/GOs and the corresponding band gap E g (in meV).The yellow balls represent the bottom graphene layer.

Fig. 6
Fig.6The profile of the planar averaged charge density difference for the BG/GOs hybrids as a function of position in the z-direction.The vertical dashed lines denote the central location of atomic layer of the BG and carbon atoms of GOs.

Table 3
The calculated Fermi velocity (m s À1 ) for the VBM and CBM of selected BG/GOs with larger band gap