off Switching

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Graphene monoxide bilayer as a high performance on/off switching media for nanoelectronics Jungwook Woo, Kyung-Han Yun, and Yong-Chae Chung ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b01772 • Publication Date (Web): 05 Apr 2016 Downloaded from http://pubs.acs.org on April 9, 2016

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ACS Applied Materials & Interfaces

Graphene monoxide bilayer as a high performance on/off switching media for nanoelectronics Jungwook Woo, Kyung-Han Yun, Yong-Chae Chung* Department of Materials Science and Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul, 04763, Republic of Korea *Email address: [email protected] Abstract The geometries and electronic characteristics of the graphene monoxide (GMO) bilayer are predicted via density functional theory (DFT) calculations. All the possible sequences of the GMO bilayer show the typical interlayer bonding characteristics of two dimensional bilayer systems with a weak van der Waals interaction. The band gap energies of the GMO bilayers are predicted to be adequate for electronic device application, indicating slightly smaller energy gaps (0.418 ̶ 0.448 eV) compared to the energy gap of the monolayer (0.536 eV). Above all, in light of the band gap engineering, the band gap of the GMO bilayer responds to the external electric field sensitively. As a result, a semiconductor-metal transition occurs at a small critical electric field (EC=0.22 ̶ 0.30 V/Å). It is therefore confirmed that the GMO bilayer is a strong candidate for nanoelectronics.

Keyword: graphene monoxide, giant Stark effect, band gap, electric field, first-principles calculation 1

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Introduction Band gap engineering of two dimensional (2D) materials is considered to be a key technique and an essential part of nanoelectronics, both experimentally1-6 and theoretically.726

As a method of tuning the band gap, the external electric field effect has been studied by

many research groups for decades.3-26 In particular, for some 2D bilayer systems, it is reported that the band gap change is sensitive to an external electric field perpendicular to the basal plane, which is a phenomenon well known as the giant Stark effect (GSE).7-13 The band gap opening of the graphene3-5, 14-17, silicene, and germanene18 and the semiconductor to metal transition (SMT) of the 2D bilayers including transition metal dichalcogenides (TMDs)10-12,1922

and phosphorene2,6,23-24 have been reported based on GSE. Graphene monoxide (GMO), which has been recently discovered and reported based on

electron diffraction observations during in situ thermal reduction of graphene oxide (GO) multilayers27, has attracted research interest due to its suitable electronic properties for electronic device applications. The predicted band gap energy of GMO is in a moderate range (0.5 ̶ 0.9 eV)27,28 , and higher carrier mobility is expected due to the lower effective masses (m*Le/me=0.112 ̶ 0.132, m*Lh/me=0.185 ̶ 0.225) than silicon or graphene nanoribbons (GNRs).28 Moreover, in light of band gap engineering, due to the unique geometrical aspect of GMO where the two carbon atoms in the graphene unitcell are connected by two oxygen atoms form double epoxide bonding,27,28 its band gap is found to be sensitive to the changed lattice angle of epoxide by strain.28 Therefore, GMO has attracted more research interest in band gap engineering. Interestingly, although the GMO multilayer has also been observed in the thermal reduction of multilayer GO27, research topics have been confined to the properties of the GMO monolayer except for the GMO multilayer. As the thinnest multilayer, the GMO 2


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bilayer could be a strong candidate for nanoelectronic device applications together with other 2D materials. However, the structural information and the corresponding electronic structures of the GMO bilayer are still unexplored. Therefore, systematic studies of the GMO bilayer are needed to apply it to nanoelectronics. In this study, the structure of the GMO bilayer is suggested by matching the high symmetric sites of the unitcell. By means of density functional theory (DFT) computations, the interlayer bonding characteristics of different bilayer structures are analyzed by comparing the charge distribution and interlayer binding energies. The band gap properties of the GMO bilayers are compared with the GMO monolayer in terms of band splitting. The band splitting phenomena of the conduction band minimum (CBM) and the valence band maximum (VBM) is discussed via band structure analysis. The band gap modulation of the GMO bilayer by electric field is studied in terms of the orbital degeneracy and band splitting.

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Calculation method DFT calculations were implemented using the Vienna Ab-initio Simulation Package (VASP) 29

code. Projector-augmented waves (PAW)30 were used to describe the ion cores, and the

exchange-correlation interactions were expressed with a generalized gradient approximation (GGA)31,32 in the form of the Perdew, Burke, and Ernzerhof (PBE) functional.33 All of the self-consistent loops were iterated until the total energy difference of the systems between the adjacent iterating steps became less than 10-9 eV. The calculations were performed with a Gamma-point centered 12 × 12 × 1 k-point generated by the Monkhorst-Pack scheme.34 To avoid interaction between the adjacent periodic images, a simulation model was placed in a vacuum spacing of 35Å in a normal direction to the GMO sheets. The Hellmann-Feynman force on each atom was less than 0.01 eV/Å. Ionic relaxation was executed using the conjugate gradient method. The electronic structure was calculated using the Gaussiansmearing method with a width of 0.01 eV. The van der Waals interactions were taken into account through a dispersion correction as proposed by Grimme35 and with the BeckeJohnson damping (DFT-D3 (BJ) method).36 The perpendicular electric field to the basal plane of the bilayer GMO was applied without a symmetric constraint to avoid incorrect rendering of the electric field.11 The lattice parameters of GMO (a0=3.12Å, α=130˚) were obtained through lattice parameter optimization.

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Results and discussion

Figure 1. (a) Primitive cell of GMO with the lattice vectors (a and b). C and O are the on-top sites of the carbon atoms (gray atoms) and oxygen atoms (red atoms), respectively. The bridge and the hollow site are br and hol, respectively. (b)-(e) Top and side views for the possible four structure of the GMO bilayer. Dashed lines indicate the superimpositions between the sites of the upper and lower layer. The structural optimization for all the bilayer structures was carried out based on the GMO monolayer to confirm the energetically stable GMO bilayer structures. GMO is a graphenebased quasi-hexagonal unit cell with a 1:1 oxygen/carbon ratio27,28 with double epoxide bonding, which connects two carbon atoms (Figure 1(a)). Among various structures of stoichiometric graphene oxide (C:O = 1:1) suggested,37,38 GMO with double epoxide is considered due to experimental observation using infrared microspectroscopy27. As shown in Figure 1(a), the primitive cell of GMO consists of vectors, a and b, with an angle of α=130º. The double epoxides are in the center of the primitive cell connecting two carbon atoms. 5



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Hence, two carbon atoms in the basal plane of GMO are positioned at the points (0.326a, 0.674b) and (0.674a, 0.326b), slightly displaced from the basis of the graphene primitive cell ((0.333a, 0.667b) and (0.667a, 0.333b)).39 As shown in Figure 1 (b)-(e), four possible structures of the GMO bilayer were classified by matching the high symmetric sites of each layer (hollow, bridge, O, and C site). In the case of the hol-hol structure, there is no slide of the upper layer along the directions of a and b. As a result, all the high symmetric sites are entirely superimposed (Figure 1(b)). The other configurations were attained by sliding one of the two layers (upper layer) relative to the other layer (lower layer) along the directions of a and b. The hol-O structures can be obtained by sliding the upper layer by 0.500a and 0.500b causing the hollow and bridge sites of the upper layer to be superimposed on the oxygen on the top and bridge sites of the lower layer, respectively (Figure 1(c)). In the case of the hol-C structure, the upper layer slides by 0.326a and 0.674b and thereby the hollow sites of the upper layer are positioned at the carbon on the top sites of the lower layer (Figure 1(d)). In the case of the hol-br, the upper layer slides by 0.500b and the hollow sites of the upper layer are on the bridge sites of the lower layer (Figure 1(e))

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Figure 2. Differential charge density of the GMO bilayer ((a) the hol-hol, (b) hol-O, (c) hol-C and (d) hol-br) relative to the GMO monolayer. The yellow and green isosurfaces correspond to the accumulation and depletion region in the values of 3.5 × 10-4 e/Å3, respectively. The red and gray atoms represent the carbon and oxygen atoms, respectively. In Table 1, the interlayer distances, binding energies, band gap, shift of the energy band of all four of the GMO bilayers are given. Here, the interlayer distances are measured based on the center of the carbon atoms of each layer of the bilayer (Figure 1(a)). The GMO bilayers are divided into two groups in terms of the interlayer distance. The hol-hol and hol-O have the larger interlayer distance (5.24 Å and 5.15 Å), and the hol-C and hol-br have the smaller interlayer distance (4.61 Å and 4.60 Å) (Table 1). Similar to cases of h-BN25 and MoS211, the large difference (~ 0.6 Å) in interlayer distance of GMO bilayers could be caused by the columbic repulsive interaction of oxygen atoms. Moreover, in cases not only of D3 scheme, 7



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but also of other vdW correction scheme, there are large differences in interlayer distance of GMO bilayers (Figure S1). Corresponding to the trend of the interlayer distance, the binding energies of the hol-C and hol-br are larger value than the hol-hol and hol-O by 30-40 meV/unitcell (Table 1). The binding energy was calculated as follows:

‫ܧ‬௕ = ‫ܧ‬௕௜௟௔௬௘௥ − 2‫ܧ‬௠௢௡௢௟௔௬௘௥ , where the Ebilayer and Emonolayer represent the energy of the GMO bilayer and isolated GMO monolayer, respectively. Although four bilayers indicate different binding energies, all the GMO bilayers are predicted to form interlayer-bonds due to the weak van der Waals interaction. As a result of forming the bilayers, the charge redistributions in the region between the two layers are observed (Figure 2, S2 and S3). Here, the differential charge density (∆ρ) was derived as

∆ρ=ߩ௕௜௟௔௬௘௥ − ൫ߩ௨௣௣௘௥ + ߩ௟௢௪௘௥ ൯, where ρbilayer, ρupper and ρlower represent the charge densities of the GMO bilayer and upper and lower monolayer GMO, respectively. In the GMO monolayer, the electrons are accumulated around the oxygen atom, of which the electronegativity is higher than the carbon atom.28 As demonstrated in Figure 2, when two GMO monolayers form bilayers in different stacking orders, the differential charge densities show different aspects for the four GMO bilayer structures (Figure 2(a)-(d)). In the hol-hol and hol-O (Figure 2(a) and (b)), the accumulation region around the oxygen in the upper and lower layers are facing each other. However, in the hol-C and hol-br structures (Figure 2(c) and (d)), the oxygen region of each layer crosses the depletion region around the carbon atoms of the opposite layer. In Figure 2, 8


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due to the smaller interlayer distance of the hol-C and hol-br, the differential charge density of the hol-C and hol-br structures indicates that more electrons accumulate in the region between the upper and lower layers than the cases of the hol-hol and hol-O. In terms of the electronic properties, the band gap energies of all four of the GMO bilayers show slightly reduced values (0.418-0.448 eV) compared to the band gap energy of the GMO monolayer (0.536 eV) (Table 1). The reduction of the band gap is caused by the energy level shift of the conduction band minimum (CBM) relative to the CBM energy level of the GMO monolayer, whereas the energy level shift of the valence band maximum (VBM) is relatively small. As shown in Figure S4, CBM and VBM are mainly contributed by the pz and py orbitals, respectively. That is, the energy level related to the vacuum level of the pz orbital shifts closer to the Fermi level than the energy level related to the vacuum level of the py orbital. Also, the energy decreasing gap of the CBM of the hol-C and hol-br structures, of which the interlayer interaction is stronger than the interactions of the hol-hol and hol-O structures, is larger than the gap of the hol-hol and hol-O. Because the pz orbitals are perpendicular to the basal plane and are placed around the surface terminated oxygen atoms, the pz orbitals are more interactive than the py orbitals when each layer binds to each other one. These results infer that band gap reduction is mainly derived from the CBM decrease to the Fermi level by interaction of the pz orbitals between the two layers due to the unique geometrical property of GMO.

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Figure 3. The band gap as a function of the external electric field for the GMO bilayers. The dashed lines are fitted to the linear part of the band gap curve. The magnitudes of the slopes (SL) of the linear band gap changes are indicated. Because the band gap energies of all four possible GMO bilayers are in an adequate range for electronic device application, the band gap changing aspects of all the four GMO bilayers are tested as a function of the external electric field perpendicular to the basal plane. When applying the electric field to the GMO bilayers, the force induced by charge redistribution does not influence the atomic position of GMO bilayers because the resulting force for the all cases are under force criteria (Figure S5 and S6). In addition, due to canceling of the spontaneous polarization caused by the inversion symmetry of the GMO bilayer, the band gap change shows the same trend regardless of the direction of the electric field (+z or–z). Therefore, the band gaps are plotted with the electric field in the +z direction only as shown in Figure 3. Following Ramasubramaniam et al.,10 the slopes of the band gap changing curve (SL) for the linear region can be calculated as ݀‫ܧ‬௚ = −݁ܵ௅ ݀‫ܧ‬ where e, Eg, and E are the electron charge, band gap energy, and external electric field strength, respectively. The SL values for the hol-hol and hol-O are calculated to be 2.30 Å and 10


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2.07 Å, respectively and the SL values for the hol-C and hol-br are 1.64 Å equally (Table 2). According to previous work,10-11 when an external electric field is applied, the electrostatic potential energy difference between each layer is larger for the bilayers with a larger interlayer distance and thereby the rate of the band gap reduction, SL, is larger than the bilayers with a smaller interlayer distance. In the cases of the GMO bilayers similar to a previous study,11 because the interlayer distances of hol-hol and hol-O are larger than the interlayer distances of hol-C and hol-br, the rates of the band gap reductions are larger for the bilayers of the hol-hol and hol-O compared to the hol-C and hol-br with smaller interlayer distances. If the GMO bilayers has the same interlayer distance (Figure S7), the rates of band gap reduction are almost same. Furthermore, in the band gap calculation based on the several hybrid function (Figure S8), the SL value of hol-hol (2.37 ̶ 2.4 Å) is similar to PBE functional result (2.30 Å) within 3 ̶ 4 % error. Considering the critical electric field (EC), where the semiconductor-metal transition (SMT) appears due to the higher rates of band gap reduction of the hol-hol and hol-O, the SMTs for the hol-hol and hol-O are expected to occur at smaller EC than the hol-C and hol-br (Table 2). Furthermore, compared with the semiconducting 2D bilayers such as MoS211 and phosphorene24, which have attracted considerable attention for electronics application, GMO bilayers are considered to be advantageous for electronics applications, indicating even higher SL and lower EC. In particular, although the h-BN bilayer25 is well known as an insulating-metal transition with a high rate of band gap reduction (SL ≈ 6.67 Å), EC is reported to be relatively high (EC ≈ 0.6 V/Å) due to its intrinsic wide band gap. Therefore, technical bottle necks still remain in applying the h-BN bilayer to nanoelectronics such as field effect transistors. On the other hand, even though the band gap reduction rate of the GMO bilayer is 11



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smaller than the rate of the h-BN bilayer, a smaller Ec (0.22 ̶ 0.3 V/Å) is expected for GMO bilayers. Therefore, GMO bilayers are considered to be useful material for application to nanoelectronic devices.

Figure 4. The band structures and the partial density of states (PDOS) (a) without and (b) with electric field (0.2 V/Å) for the GMO bilayers (the hol-hol and hol-C). The color bar indicates the degree of the contributions of each band to the upper (blue) or lower (red) layers. CBM+1 and VBM-1 indicate the sub-bands of CBM and VBM, respectively. In terms of the electronic structures of the GMO bilayer, it was observed that CBM is divided into two bands of CBM and CBM +1 separately by the interlayer interaction of the GMO bilayers (Figure 4(a) and Figure S9 (a)). Because of the similarity in electronic structures for bilayer structures with a similar interlayer distance, only the band structures of 12


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the hol-hol and hol-C were compared in Figure 4 (The figures for the hol-O and hol-br are included in Figure S9). In Figure 4(a), the VBM is also split into VBM and VBM+1, and the energy difference between VBM and VBM+1 is smaller compared to the band split energy of CBM and CBM+1. The band gap modulation of the 2D bilayer by the external electric field arises from the well-known Stark effect7-13, which has been studied and discussed in previous studies on hBN25 or MoS2 bilayers11. An external electric field results in a potential energy difference between the two layers. As a result, the energy bands belonging to each layer are separated from each other, and the band splitting energy of CBM and VBM increase with the increase in the electric field strength. Spontaneously, the energy level of CBM and VBM increases and decreases towards the Fermi level, respectively. Hence, the band gap reduces to the zero gap with the increase in the electric field strength. In the partial density of states (PDOS) of the GMO bilayers in Figure 4, the pz orbitals of the upper and lower layers contribute CBM and CBM+1 equally. When an electric field is applied to the GMO bilayer, the energy bands belonging to the upper and lower layers are observed to be separated from each other with the downshifts of the energy level of both the pz and py orbitals of the upper layer. As a result, the CBM level composed of the pz orbital of the upper layer at the Γ point reduces towards the Fermi level. At the same time, the VBM level composed of the py orbital of the lower layer increases towards the Fermi level at the X point. The band splitting phenomena caused by the Stark effect is observed for all four GMO bilayer structures. The pz and py orbitals belonging to CBM and VBM become degenerate, and thereby the CBM and VBM are localized on the upper layer and lower layer, respectively (PDOS in Figure 4(a) and (b)). When the external electric fields of the hol-hol and hol-C reach the critical electric fields (EC,hol-hol=0.22 V/Å and 13



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EC,hol-C=0.3 V/Å), both the energy levels of CBM and VBM touch the Fermi level indirectly. Therefore, all four GMO bilayers indicate metallic properties.

Figure 5. Band energy splitting of (a) CBM and (b) VBM as a function of the applied electric field. The CBM (VBM) splitting is defined as the difference in the energy between CBM (VBM) and CBM+1 (VBM-1) indicated in Figure 4. Furthermore, as shown in Figure 5(a) and (b), the curves of the band splitting energies as a function of the electric field for four GMO bilayers showed different aspects for CBM or VBM. While the VBM splitting energy linearly increases with the increase in the electric field strength (Figure 5(a)), the CBM splitting energy increases non-linearly in the small electric field range. In particular, the rate of the CBM and VBM splitting with the increasing electric field is dependent, not on the different stacking orders, but the interlayer distances. That is to say, the band splitting energies of the hol-hol and hol-O structure with larger 14


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interlayer distances are larger than the splitting gap of the hol-C and hol-br. As discussed above, this is because the electrostatic potential difference is larger for the structures with the larger interlayer distances (the hol-hol and hol-O), and thus the band splitting energy changes more intensively than the structures with the smaller interlayer distances (the hol-C and holbr).

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Conclusion The geometric and electronic properties of all the possible GMO bilayer structures were predicted, and the feasibility of the GMO bilayers for the field effect transistor was investigated via DFT calculations. The four GMO bilayer structures were classified by stacking order. In terms of the band gap properties, the band gaps of the four GMO bilayers (0.418 ̶ 0.448 eV) were slightly reduced compared with the GMO monolayer (0.536 eV). When the external electric field is applied, it is observed that the band gap of the GMO bilayer decreases with the increase in the external electric field. The larger the interlayer distance, the larger the electrostatic potential difference between the two layers. As a result, the rate of the band gap reduction is predicted to be fast for GMO bilayers with a large interlayer distance. Nevertheless, for all four GMO bilayers, the critical electric fields are predicted to be much smaller (EC=0.22 ̶ 0.3 V/Å) than any other bilayers, and thereby the GMO bilayers show the possibility to be utilized for field effect transistors. In light of the energy efficiency, due to the relatively small EC of the GMO bilayer compared to other 2D bilayers, the GMO bilayer can be considered as a potential candidate for nanoelectronics.

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Supporting Information Supporting Information Available: The energies versus interlayer distance, differential charge densities for the same interlayer distance, the partial density of states (PDOS) of the GMO monolayer and bilayers, the planar-averaged differential charge density and electric field induced by charge redistribution, the band gaps as a function of electric field for the same interlayer distance, The band gap as a function of electric field using hybrid functionals and the band structure and PDOS of the GMO bilayers (the hol-O and hol-br). This material is available free of charge via the Internet at http://pubs.acs.org

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Acknowledgment This research was supported by the Basic Science Research Program through the National Research

Foundation

of

Korea

(NRF)

funded

by

the

(2013R1A1A2A10064432).

18


Ministry

of

Education

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Table 1 Interlayer distance indicated in Figure 1, binding energy, band gap, and the CBM and VBM level shift of the four possible GMO bilayers. The CBM and VBM level shift is the difference in the CBM and VBM level of the monolayer based on the vacuum level, respectively. Structure

hol-hol

hol-O

hol-C

hol-br

Monolayer

Interlayer distance (Å)

5.24

5.15

4.61

4.60

-

Binding energy (meV/unit cell)

-47.29

-51.72

-82.86

-81.60

-

Band gap (eV)

0.448

0.440

0.418

0.441

0.536

CBM shift (eV)

0.080

0.084

0.103

0.101

-

VBM shift (eV)

0.007

0.012

0.015

-0.005

-

Table 2 Slope of the linear band gap change (SL) and the critical electric field of the GMO bilayers and several 2D bilayer materials (MoS2, h-BN, and phosphorene). The values of the particular stacking sequence indicate that the most sensitive change in the band gap were selected and cited from references. Structure

hol-hol

hol-O

hol-C

hol-br

MoS212

Phosphorene15

h-BN16

SL (Å)

2.30

2.07

1.64

1.64

~ 1.6

~ 0.5

~ 6.67

EC (V/Å)

0.22

0.23

0.3

0.3

~ 1.0

> 0.5

~ 0.6

24


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Graphical Abstract

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