Electronic Properties of Homo- and Heterobilayer Graphyne: The Idea

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Electronic Properties of Homo and Hetero Bilayer Graphyne: The Idea of a Nanocapacitor Barnali Bhattacharya, Utpal Sarkar, and Nicola Seriani J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07092 • Publication Date (Web): 02 Nov 2016 Downloaded from http://pubs.acs.org on November 8, 2016

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The Journal of Physical Chemistry

Electronic Properties of Homo and Hetero Bilayer Graphyne: The Idea of a Nanocapacitor Barnali Bhattacharya1, Utpal Sarkar 1* and Nicola Seriani 2* 1

Department of Physics, Assam University, Silchar-788011, INDIA

2

The Abdus Salam ICTP, Trieste, Italy

*

To whom correspondence should be addressed. E-mail [email protected] (Utpal

Sarkar), [email protected] (Nicola Seriani)

ACS Paragon Plus Environment

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ABSTRACT

We have investigated the capacitive behavior of bilayer graphyne and its boron nitride derivatives by first-principles simulations based on density functional theory, including van der Waals interactions. Our predicted energy and charge storing capacity are greater than those predicted for nanocapacitors based on graphene and hexagonal boron nitride. In the most stable configuration, the two layers are stacked on top of each other, just as in bulk graphyne. The stacking arrangement has a strong effect on the electronic properties of the system: the stable stacking configurations for the graphyne systems are semiconductors with direct band gaps of 0.38 eV and 0.50 eV respectively. Substitutional boron–nitrogen doping provides a way to tune the band gap of the system. The band gap generally increases in presence of the dopants, but the value of the band gap depends on the substitution sites. This suggests that controlled boron nitride doping of graphyne could be a useful and flexible method to build nanoscale electronic and optoelectronic devices.


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INTRODUCTION Electronics is facing great challenges as the size of typical devices shrink down to few nanometers in size, at a level where the precise atomic structure of the device and quantum effects play a fundamental role. Therefore the search for novel materials and new approaches to nanoscale electronics is being run extensively. In this context, low-dimensional carbon-based layered materials attracted considerable attention. 1-4 Due to the flexibility of carbon in forming allotropes and the wide range of possible applications, tremendous efforts have been devoted to the discovery and study of new possible carbon allotropes during the past few decades.2-4 Newly synthesized important members of the carbon family include zero–dimensional fullerene,2 quasi– one–dimensional carbon nanotubes,3 two–dimensional graphene.4 In particular, bilayer and fewlayer graphene have already been studied at large scale, including assemblies of graphene with hexagonal boron nitride (h-BN)5-7 or with SiC8 or with Phosphorene.9 These systems exhibit some outstanding electronic, optical and mechanical properties, including capacitive behavior. 1014

It is assumed that these carbon allotropes and carbon-based molecules with their tunable

properties can potentially become building blocks in next-generation electronic and optoelectronic devices, thereby increasing the interest in new carbon allotropes. Baughman et al. in 198715 proposed one such 2D carbon allotrope built from graphene where acetylenic linkages (–C≡C–) are present in the unit cell, instead of the double bond (C=C) as in graphene. Depending on the various arrangements of acetylenic linkages and percentage of the inserted acetylenic linkages (–C≡C–), graphyne is mainly divided into three categories– α graphyne, β graphyne and γ graphyne. The α graphyne is the most symmetrical one and resembles graphene. It can be obtained from graphene by replacing every C-C bond of graphene with acetylenic linkages (–C≡C–), thus 100% acetylenic groups are present in the α graphyne. Whereas in β


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graphyne, acetylenic groups are inserted into two-thirds of C-C bonds of graphene and in γ graphyne, only one-third of C-C bonds of graphene contain acetylenic groups. Due to the structural similarity, the band structure of α graphyne is very similar to graphene, containing the same type of Dirac cone, only the pseudospin in α graphyne has the opposite direction to that in graphene.16 The presence of Dirac cones are also observed in β graphyne, but it is not like graphene.16 A previous study16-22 by some of the authors shows that monolayer γ-graphyne is a direct band gap semiconductor and its band gap is tunable under different circumstances. Due to the tunable band gap property graphyne can be used in building p-n junction. In addition, graphyne has high stability in comparison to graphene. Since gamma graphyne is the lowest energy member among the three types of graphyne and semiconductor with a small band gap, we focus our study on γ- graphyne. Graphyne induce a rich variety of optical, electronic and elastic properties17-20,23-24 due to presence of triple bonds. Recently, substructures of γ- graphyne have been fabricated as low-dimensional nanostructures.25-29 Moreover, another family member of the γ-graphyne family, with di-acetylenic linkages, graphydine, has been synthesized in the form of large-area-multilayer films,30 flakes,31 nanotubes, 32 and nanowires.33 Much less attention has been devoted to the graphyne bilayer. In fact, theoretical investigations exist only for bilayers of graphydine,34 for α - and β -graphyne,35-37 showing the possibility to tune the band gap by doping with boron nitride and on external electric field. Moreover, a subtle dependence of the gap on position and concentration of the dopants is also discussed. The band gap modulation of α and β graphyne due to applied strain and electric field35-38 highlights the possibility of using them in electronic and electro-mechanical devices. Till today all the reported study of bilayer graphyne (α graphyne, β graphyne and graphdiyne) explored the electronic structure and properties under different stacking modes,37 external electric field,35 strain38 and


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substitutional doping.36 The electronic properties of three dimensional forms of graphyne39 and lithium decorated multilayer graphyne as a Li ion battery anode40 are reported also. It seems that bilayer systems offer a wide range of possibilities to control the gap, including acting on the stacking of the bilayer. But, to the best of our knowledge, the band gap tailoring of γ- graphyne due to combined effect of systematic BN doping and external electric field has not been explored so far. Moreover, the application of bilayer graphyne as a charge storage medium and its possible use as nanocapacitor is still unrevealed. Through this study, in particular, we are interested in the possibility to tune γ-graphyne bilayer properties in order to employ it as a nanocapacitor. To nullify the major drawbacks of the conventional capacitor such as comparatively heavy weight, slow response time due to the motion of ions in electrochemical reactions and to meet the up growing demand for lightweight, recyclable, efficient, and high-capacity energy storage capacitor the researcher are testing the capacitive behavior of nanoscale material and designed nanoscale nanocapacitor. Nanoscale capacitors have been recently shown to display very interesting functional behavior, such as faster charge storing and releasing capacity, higher amounts of charge delivering capability at higher power rates, longer life with short load,41-46 that might be relevant for practical applications. Other carbon allotropes have already been investigated for this purpose. Carbon nanotube based capacitors44,45,47 was proven to be highly efficient for energy storage in connection with photovoltaic devices. Graphene has been proposed as ideal nanocapacitor material48-51 and has recently shown high capacitance per unit area. Recent calculations of periodic hetero-layer systems seem to confirm this potential, especially for graphene–silicene bilayers13 and graphene-h-BN bilayers.10-12 In this paper, we have investigated graphyne-based bilayers by first-principles simulations to assess their properties in view of a possible employment as nanocapacitors. We have considered


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the effects of different stacking modes and of doping through boron nitride. Our approach is based on the charge redistribution at the interface of bilayer graphyne because of the externally or intrinsically induced interfacial electric field that mimics the mechanism of a parallel plate capacitor. In the next section, the details of the employed computational techniques are reported. First, the results on the relation between stacking and electronic structure are reported; then, the effects of BN doping are presented, and finally the capacitive behavior of this system is investigated. A summary concludes the article. COMPUTATIONAL DETAILS We have done density functional theory (DFT) calculations with Perdew-Zunger (LDA) functional to describe exchange and correlation. Van der Waals interactions were included by using the second version of the van der Waals density functional (vdW-DF2) theory proposed by Lee et al.52 All atomic coordinates are fully relaxed using the conjugate gradient algorithm, until the forces on each atom are equal to or less than 1× 10−9 Ry/au and the energy difference between the consecutive scf steps is less than 1 × 10−9 Ry. 10 k-points have been chosen along the periodic direction of unit cell and 4 k-points are chosen along the vacuum direction. The vacuum was set to 15 Å to avoid the interactions between periodically repeated images of the bilayer system. Structure optimizations have been carried out with the Quantum-ESPRESSO 5.1.2 package,53 which employs a plane-wave basis set to describe wavefunctions. A cutoff of 65 Ry and 520 Ry have been employed, respectively for the wavefunctions and for the charge density. The smearing scheme by Marzari and Vanderbilt has been used for orbital occupations.54-55 The scalar relativistic ultrasoft pseudopotential [version ‘2.0.1’] with non-linear core correction has been employed in the calculation. Capacitor properties such as dipole


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moment (D), excess charge (Q), energy stored by the capacitor (E c) and capacitance (C) have been calculated using the SIESTA 3.2 code.56 Here, a further self-consistent calculation has been done for the optimized geometry with an electric field. SIESTA code works with atomic orbital (AO) basis sets while in Quantum-ESPRESSO plane wave basis set is used. For the same exchange-correlation functional, the unoccupied states in the band diagram can be reproduced better using well-converged plane-wave (PW) basis set than the AO basis sets.57 Thus, the plane wave basis set is a better choice for optimizing and electronic properties calculation of periodic system, and so we have carried out optimization and electronic properties calculation of bilayer system in Quantum-ESPRESSO suit. For capacitive properties calculation, we have used SIESTA code since it directly provides the electric dipole moment for a finite electric field. The interplanar binding energy or adhesion energy of a bilayer has been calculated as (1) (2) where

and

are the total energy of the bilayer system and of the monolayer

respectively. The formation energy of a BN doped hetero-bilayer has been calculated as-

(3)

=

where

and

are the total energies of BN doped bilayer graphyne and the perfect bilayer

graphyne. The number m is the number of CC pairs that are substituted by the BN pairs in the


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unit cell. μC–C and μB–N are the energies per unit cell of graphene and h-BN monolayer respectively. RESULTS AND DISCUSSION First, the stacking of the bilayer has been investigated. There are three main types of stacking arrangements, shown in Figure 1; two of them, namely AA and AB, resemble those of graphene. In the AA stacking, the two layers are orientationally identical and lie exactly on top of each other. In the AB stacking the two layers are orientationally mismatched. In addition, one more stacking mode is expected in bilayer graphyne, namely A⍺Aβ, where the hexagonal hollow of one layer is stacked on the triangular void of the other layer.

Figure 1. Optimized geometries with unit cell of: (a) AA stacked graphyne; (b) AB stacked graphyne; (c) A⍺Aβ stacked graphyne Structural parameters and binding energies of bilayer graphynes are presented in Table 1 and Table 2. ‘Table 1’ represents pristine bilayer graphyne while ‘Table 2’ represents BN doped bilayer graphyne. All bilayers are more stable than the monolayer, with the A⍺Aβ structure having the largest binding energy. This is the same stacking found to be stable in bulk graphyne


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and bulk graphdiyne.39,58 For all systems the inclusion of van der Waals corrections is crucial for a correct description of the interlayer interactions (see the Supporting Information Table S1 for a comparison). In fact, the interlayer distance increases when vdW interactions are included. This counterintuitive result is in agreement with what found in other layered systems.59-62 Table 1. Calculated lattice constant (a); interlayer distance (d), binding energy (BE), and energy band gap with van der Waals (vdW) correction of bilayer graphyne with different stacking modes.

Stacking

Lattice parameter a Interlayer distance d (Å) Binding energy (eV)

Band gap (eV)

(Å) AA

6.900

3.720

-0.463

0.120

AB

6.900

3.520

-0.558

0.510

A⍺Aβ

6.900

3.510

-0.571

0.380

Figure 2. Band structure and projected density of states (PDOS) of the A⍺Aβ stacked graphyne


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The electronic band diagram of bilayer graphyne is very similar to that of monolayer graphyne.16-20 The valence band maximum (VBM) and conduction band minimum (CBM) are located at the M point of the Brillouin zone, making the bilayer a small-gap semiconductor. The band structure of the stable A⍺Aβ configuration is shown in Figure 2 (a), and displays a gap of 0.38 eV. In the other configurations, the band structure is very similar (see Supporting Information Figure S1). Each band of the monolayer is split in two bands differing by a small energy, due to the interlayer interaction. The projected density of states of bilayer graphyne is depicted in Figure 2 (b). The contributions of each layer to the total DOS is exactly equal at any energy. The states near the gap, including HOMO and LUMO, are mainly due to the pz orbitals of carbon irrespective of the stacking arrangement (see Supporting Information Figure S2). The density of states (DOS) and projected density of states (PDOS) of monolayer graphyne [Supporting Information Figure S3] and most stable bilayer graphyne show that the contribution of px+py is comparatively larger in a certain energy range of VB and CB for bilayer graphyne compare to monolayer graphyne. Although near the Fermi level (depicted as dotted line in Figure S3) only the pz orbital contributed to DOS for both mono layer and bilayer graphyne and the noticeable contribution of px+py starts at -1.710 eV at VB and 3.202 eV at CB. For monolayer graphyne, throughout the considered energy range, contribution of pz orbital is larger than px+py orbital. Only in the energy range -2.262 to -2.720 eV and 4.500 to 4.700 eV, the contribution of px+py orbital is comparable with pz orbital. But for bilayer graphyne, in the energy range -1.900 to -3.100 eV and 3.400 to 4.700 eV the contribution of px+py orbital is greater than pz orbital. BN doping:


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Co-doping by boron and nitrogen is a common method to engineer the band gap of carbon systems. Since A⍺Aβ is the stable structure of the pure bilayer, we have investigated BN doping in this structure only. We have considered nine main configurations for the doped bilayer. In three of them, there is one BN unit per layer and the two layers are structurally equivalent (homo-layer structures), while in the other six the two layers are not equivalent (hetero-layer structures). The most stable homo- and hetero-layer structures are presented in Figure 3, while the others are shown in the Supporting Information Figure S4. The structures differ from one another for the position of the BN units, which can be at the chain sites or at the ring sites. Moreover, we have considered the possibility of the full substitution of carbon with BN in one layer, leading to the formation of one layer of h-BN.

Figure 3. Optimized geometry of: (a) most stable hetero layer “pristine + graphyne like BN sheet” (b) most stable homo layer “graphyne like BN sheet + graphyne like BN sheet”


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BN doping induces structural changes in the bilayer, in particular in the interlayer distance and lattice constant. BN doping leads to a decrease in the interlayer distance when BN is present in both layers while BN doping of only one layer leads to an increase in the interlayer distance. Similar to bilayer and trilayer graphdiyne

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and nitrogen doped graphene bilayer63 interlayer

mixing of п orbitals is expected in bilayer graphyne. Our crystal orbital overlap population64 (COOP) calculation shows the existence of covalent-like п-п interaction63 between the layers. It has been predicted from the calculated integrated crystal orbital overlap population (INTCOOP) [supporting information Table S2] that, most of the п-п interactions are bonding nature which plays an important role in determining the interlayer distance.63 In addition to п-п bonding, electrostatic, dispersive and Pauli interactions are also crucial for anchoring the layers at equilibrium distance. The delicate interplay between electrostatic interaction, van der Waals interaction, Pauli repulsion and covalent-like п-п interaction between the layers, actually dictates the equilibrium interlayer distance. One of the possible explanations of increased interlayer distance of the ‘bilayer containing BN at only one layer’ may be the reduction of п-п bonding interaction between the layers compare to pristine bilayer [see Table S2 in the supporting information]. The п-п bonding interaction is negligible for the structure ‘pristine + graphyne like BN sheet’ in which interlayer separation is highest and interlayer binding energy is lowest. The significant reduction of interlayer distance for structures ‘BN at chain + BN at chain’; ‘BN at chain + BN at ring’; ‘BN at ring + BN at ring’; may be lies on the enhancement of п-п bonding interaction between the layers compare to the pristine bilayer. But, the reduction of the interlayer distance for structures ‘graphyne like BN sheet + graphyne like BN sheet’; ‘BN sheet + BN at linear chain site’; ‘BN sheet + BN at linear ring site’ cannot be explained on the basis of п-п bonding interaction only. For the bilayer structures having B-N bond in both layers, due to the


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polarity of B-N bond, effective charges are developed in the atomic centres, as a result of which electrostatic interaction develop. Although electrostatic interaction exists but previous studies65-67 show that interlayer binding hardly depends on electrostatic interaction; the van der Waals interaction is mainly responsible for fixing the interlayer distance apart from п-п interaction.62 However, the proper reason of variation of interlayer distance with BN doping at various positions of this type of polar bilayer material is a subject of ongoing research. Table 2. Calculated lattice constant (a), interlayer distance (d), binding energy (BE) and band gap (Eg) of homo layer and hetero layer graphyne derivatives. Systems

BN at linear chain site

Lattice parameter a Interlayer distance d

Binding Energy BE Band gap (eV)

(Å)

(eV)

(Å) 6.970

3.490

-0.558

1.440

7.000

3.460

-0.612

2.660

7.000

3.490

-0.531

3.950

6.930

3.520

-0.517

0.550

+ BN at linear chain site BN at ring site + BN at ring site Graphyne

like

BN

sheet + graphyne like BN sheet Pristine graphyne + BN at the linear chain site


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Pristine graphyne +

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6.950

3.520

-0.503

0.600

6.950

3.530

-0.463

0.590

6.980

3.490

-0.558

1.560

6.980

3.490

-0.531

1.560

7.000

3.470

-0.544

2.800

BN at ring site

Pristine graphyne + graphyne

like

BN

sheet BN at linear chain site + BN at ring site BN sheet + BN at linear chain site

BN sheet + BN at ring site

The in-plane lattice constant is calculated by plotting the total energy as a function of lattice spacing. The total energy with full relaxation of all the atoms, as a function of lattice spacing, is obtained by varying the lattice constant a. We have considered seven equispaced lattice constants. The value of ‘a’ at which the total energy is minimum for this graph is identified as inplane lattice constant. The in-plane lattice constant is minimal for the pristine bilayer and increases through BN doping. We have calculated the binding energy of the bilayer with respect to the monolayer (Table 2). With our convention, a negative value of the binding energy stands for an exothermic binding. In fact, bilayer formation is always exothermic. On the other side, the


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BN doping process is endothermic except two cases having negative formation energies (see Table 3). Among the homo-bilayer structures, the bilayer formed by graphyne-like BN sheets is energetically most favorable as it has the lowest formation energy (-2.068 eV) indicating that it is relatively easy to substitute BN throughout the structure of graphyne bilayer. On the other hand, among the hetero layer structures, bilayer originate due to coupling of pristine graphyne and graphyne like BN sheet is most stable as it has negative formation energy. Table 3. Formation energies of homo and hetero bilayer graphyne derivatives.

Systems

Formation energy (eV) Homo layers

BN at linear chain site + BN at linear chain site

3.497

BN at ring site + BN at ring site

3.687

Graphyne like BN sheet + graphyne like BN sheet

-2.068

Hetero layers Pristine graphyne + BN at the linear chain site

1.796

Pristine graphyne + BN at ring site

1.932

Pristine graphyne + graphyne like BN sheet

-0.939

BN at linear chain site + BN at ring site

3.619

BN sheet + BN at linear chain site

0.721


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BN sheet + BN at ring site

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0.830

The effect of BN doping on electronic structure: The electronic band structures of selected BN-derivatives of bilayer graphyne are shown in Figure 4 and Supporting Information Figure S5. Doping increases the band gap, and the graphyne-like BN bilayer has the largest gap of 3.95 eV. Still, all systems have a direct band gap. In systems with BN doping, the band gap depends on the position of the BN pair.

Figure 4. Band diagram of structures (a) BN at the linear chain positions of one layer, (b) one layer is graphyne-like BN-sheet and other is pristine, (c) both layers is graphyne-like BN-sheet

Figure 5. DOS and PDOS diagram of (a) BN at the linear chain positions of one layer, (c) one


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layer is graphyne-like BN-sheet and the other is pristine, and (i) each layer is a graphyne-like BN-sheet Also in these systems, as in the pristine bilayer graphyne, the states at the top of the valence band and at the bottom of the conduction band are mainly due to the pz orbitals. Carbon contributes to both valence and conduction bands; nitrogen contributes more to the valence band and boron to the conduction band [see Figure 5 and Supporting Information Figure S6]. Actually, due to the large electronegativity difference between boron and nitrogen, charge is mainly transferred from boron to nitrogen, as confirmed by Hirshfield charge68 and Bader charge69-71 analysis [see the Supporting Information Table S4-S7]. Calculated charge analysis shows that a negative electron cloud resides around the N atom while electron deficiency is observed near the B atom. Thus all kind of B-N bonds acquires some ionic character while all C-C bonds are covalent in nature (Figure 6). The presence of B-N unit in graphyne not only transfer charge between B and N atom but also modify the charge cloud of neighbouring carbon atom. For example, Bader charge analysis shows that, in ‘graphyne with BN at chain’ monolayer of ‘pristine + graphyne with BN at chain’, the negative electron cloud around the nitrogen not only attributed by the transferred electrons from boron but some electrons are also transferred to nitrogen from the adjacent carbon atom. Similarly, a fractional amount of charge is also transferred from boron to adjacent carbon atom. Thus, in case of systems where the dopant BN sits at chain sites, the carbon atom adjacent to nitrogen also loses some charge and acts as a donor while the carbon atom adjacent to boron gains some charge and acts as an acceptor [see the Supporting Information Table S6]. The opposite effect is observed for systems with BN at ring sites [Supporting Information Table S7]. For example in ’graphyne with BN at ring’ of ‘pristine + graphyne with BN at ring’ bilayer, the


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carbon atom adjacent to boron acts as a donor by transferring electron to boron and the carbon atom adjacent to nitrogen behaves as an acceptor by acquiring electron.

Figure 6. Nature of bond in all homo and hetero bilayer structures (a) covalent C-C bond (b) BN bond having ionic character Assessment of potential of graphyne bilayer as a nanocapacitor: Given the great interest in nanocapacitors, 10-13,50-51 in this section we are going to consider the possibility to employ these systems as nanocapacitors. Nanoscale capacitors store energy by accumulating opposite electric charges in two plates separated by a distance. The charge separation is achieved by applying an external electric field. It is therefore natural to consider our bilayer systems as nanocapacitors. To this aim, we have calculated dipole moment, capacitance,


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excess charge stored on each plate and energy stored by the capacitor. The total charge on each plate is obtained from DFT calculations by using the formula =P/d

(4)

where P is the dipole moment and d is the interlayer distance, which acts as separation thickness between two plates of the capacitor. The separation of the two charged plates is kept at the nano scale and the energy stored in the nanocapacitor can be obtained from the energy difference between the total energy under electric field and total energy without field: (5)

If m is the total mass of all atoms in unit cell, then the capacitance per unit mass is expressed by (6) In fact, in the hetero-bilayers considered here, a charge transfer takes place between the two layers, even in absence of an external electric field, resulting in a permanent dipole and in an electrostatic attraction between the two layers. The transferred charge is however quite small, upto 0.03 electronic charges per unit cell, and therefore the effect of this charge on the capacitive behaviour is minor. Still, this results in a difference of electrostatic potential of 0.2 to 0.5 V between the two layers, which might be useful if exploited in electronic devices. On the contrary, in homo-bilayer systems there is no charge transfer without an external electric field. With increasing electric field, the charge storage between two plates increases linearly [see Figure 7 (a) and 8 (a)]. Our calculation shows that for both homo bilayer and hetero bilayer, the charge stored on each plate (Qs) with same electric field is comparatively larger than graphene/hBN/graphene dielectric nanocapacitor with several h-BN layers sandwiched between two


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graphene plates proposed by

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z elik et al.10 In addition, the calculated energy storing capacity

(Ec) [see Figure 7 (b) and 8 (b)] shows the superiority of our proposed homo bilayer and hetero bilayer over other proposed nanocapacitor.10 It indicates that more energy can be stored in our considered periodic bilayer structure in comparison with graphene/h-BN/graphene structure,10 which can be released in the external circuit. The capacitance of homo bilayer systems as a function of increasing electric field is depicted in Figure 7 (c). For electric fields up to ±0.2 V/ , dipole moment [see Supporting Information Figure S7 (a)], stored charge and energy are nearly the same for all homo-bilayer systems. At larger fields, differences start to be evident. We observe dependence of the capacitance from the electric field, with values remaining in the range between 25 and 41 F/g in the whole range of electric fields. At non-zero electric field, the capacitance of the BN doped homo-bilayers remains below that of the pristine graphyne bilayer.

Figure 7. Calculated (a) energy stored (b) charge stored (c) capacitance of homo-bilayer graphyne derivatives in dependence of an external electric field Also in the case of hetero-bilayers, the capacitance is smaller than that of the pristine bilayer graphyne and depends on the electric field. An interesting feature of these bilayers is that the capacitive behaviour is not symmetric with respect to a sign change of the electric field. This is probably due to the charge transfer between the two layers present in absence of an external electric field, which is responsible for a built-in electric field. We assume that this charge


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transfer is also responsible for the fluctuating behaviour of the capacitance in a region around zero electric field, giving rise to a Z shaped fluctuation region. A small electric field may invert the charge transfer, thereby inducing a large change of charge with a small change of energy. This results in a large capacitance at small electric fields, which then decreases again as the reversal of charge transfer is completed.

Figure 8. Calculated (a) energy stored (b) charge stored (c) capacitance of hetero-bilayer graphyne derivatives in dependence of an external electric field These bilayers show an interesting behaviour which can be exploited in nanocapacitors. The value of the capacitance of hetero bilayer systems is lower than the pristine bilayer graphyne [except ‘pristine + graphyne with BN at chain’ with positive electric field], however, our calculated capacitance value is higher than other systems reported in the literature, such as the graphene-h-BN-graphene systems considered in Ref. 10 except the case when only two h-BN layers are sandwiched between graphene layers. Indeed, the graphene-h-BN-graphene was shown to possess a capacitance of 5.6-24.5 F/g, while here we predict values in the range of 2040 F/g, depending on the exact structure and the magnitude of the external electric field. Moreover, the hetero-bilayers display a built-in electric field due to charge transfer between the


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layers, which make the capacitive behaviour asymmetric with respect to the direction of the external electric field, and might be useful on its own for electronic applications.

CONCLUSIONS In summary, structure and electronic properties of bilayer graphyne have been calculated using density functional theory with van der Waals corrections. The highest stability for pristine bilayer systems is found for the A⍺Bβ configuration, while the AA configuration (with the two layers on top of each other) is the most unstable. The stacking arrangement plays a crucial role in determining the gap. The most stable structure, A⍺Bβ, is a semiconductor with a small band gap of 0.38 eV, which is much smaller than the band gap of monolayer graphyne. In contrast, the second most stable structure has a band gap of 0.50 eV, larger than monolayer graphyne. Interestingly, the AA stacked graphyne has a tiny band gap of 0.12 eV. Doping with boron nitride changes the electronic properties so that BN-doped bilayer graphyne becomes a wide band gap semiconductor. Boron and nitrogen doping increases the band gap of the most stable configuration and the increase depends on the BN substitution site. Such properties can make bilayer graphyne a useful and flexible material for applications in electronics, as for field effect transistors and for the creation of heterostructures, if spatially selective doping with a high degree of control can be achieved. Finally, we have investigated the capacitive behavior of the bilayers. They display a high capacitance value, and high energy storage capacity, in comparison to other 2D carbon-based materials. Moreover, the asymmetric behaviour of the capacitance with respect to the sign of the applied bias could also lead to intriguing applications in electronics.


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Summarizing, our work predicts pristine and boron nitride doped bilayer graphyne systems to display a variety of properties that could in principle be controlled and tuned at the nanoscale, and should be useful for nanoelectronic applications. ASSOCIATED CONTENT Supporting Information The Supporting Information includes details information of structural parameters (lattice constant, interlayer distance, binding energy (BE), and energy band gap) of pristine graphyne bilayer with different stacking mode including with and without van der Waals correction. It also contains the band structure plot; DOS and PDOS plot and charge analysis of some BN doped graphyne bilayer system. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author Dr. Utpal Sarkar 1, E-mail address: [email protected] (Utpal Sarkar), Tel. +919401542687 Dr. Nicola Seriani 2, E-mail address: [email protected] (Nicola Seriani), Tel. +39 040 2240 279 Notes: The authors declare no competing financial interest. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


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ACKNOWLEDGMENT This research is supported by Assam University, Silchar, India and The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. REFERENCES 1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666-669. 2) Kroto, H. W.; Allaf, A. W.; Balm, S. P. C60: Buckminsterfullerene. Chem. Rev. 1991, 91, 1213-1235. 3) Iijima, S. Helical Microtubules of Graphitic Carbon. Nature 1991, 354, 56-58. 4) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183-191. 5) Moon, P.; Koshino, M. Electronic Properties of Graphene/Hexagonal-Boron-Nitride Moiré Superlattice. Phys. Rev. B 2014, 90, 155406 (1-12). 6) Abergel, D. S. L.; Mucha-Kruczyński, M. Infrared Absorption of Closely Aligned Heterostructures of Monolayer and Bilayer Graphene with Hexagonal Boron Nitride. Phys. Rev. B 2015, 92, 115430 (1-6). 7) Ansari, R.; Malakpour, S.; Ajori, S. Structural and Elastic Properties of Hybrid Bilayer Graphene/h-BN with Different Interlayer Distances Using DFT. Superlattices and Microstructures 2014, 72, 230–237. 8) Cavallucci, T.; Tozzini, V. Multistable Rippling of Graphene on SiC: A Density Functional Theory Study. J. Phys. Chem. C 2016, 120, 7670−7677.


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Table of Contents (TOC)


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Figure 1. Optimized geometries with unit cell of: (a) AA stacked graphyne; (b) AB stacked graphyne; (c) A⍺Aβ stacked graphyne 71x28mm (300 x 300 DPI)


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Figure 2. Band structure and projected density of states of the A⍺Aβ stacked graphyne 177x81mm (300 x 300 DPI)



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Figure 3. Optimized geometry of: (a) most stable hetero layer “pristine + graphyne like BN sheet” 65x23mm (300 x 300 DPI)


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Figure 3. Optimized geometry of: (b) most stable homo layer “graphyne like BN sheet + graphyne like BN sheet” 66x24mm (300 x 300 DPI)



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Figure 4. Band diagram of structures (a) BN at the linear chain positions of one layer, (b) one layer is graphyne-like BN-sheet and other is pristine, (c) both layers is graphyne-like BN-sheet 177x58mm (300 x 300 DPI)


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Figure 5. DOS and PDOS diagram of (a) BN at the linear chain positions of one layer, (c) one layer is graphyne-like BN-sheet and the other is pristine, and (i) each layer is a graphyne-like BN-sheet 177x61mm (300 x 300 DPI)



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Figure 6. Nature of bond in all homo and hetero bilayer structures (a) covalent C-C bond (b) B-N bond having ionic character. 177x138mm (300 x 300 DPI)


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Figure 7. Calculated (a) energy stored (b) charge stored (c) capacitance of homo-bilayer graphyne derivatives in dependence of an external electric field 177x59mm (300 x 300 DPI)



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Figure 8. Calculated (a) energy stored (b) charge stored (c) capacitance of hetero-bilayer graphyne derivatives in dependence of an external electric field 177x62mm (300 x 300 DPI)


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Electronic Properties of Homo- and Heterobilayer Graphyne: The Idea

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