Conversion of the stacking orientation of bilayer graphene due to \break the interaction of BN-dopants
Nzar Rauf Abdullah, Hunar Omar Rashid, Chi-Shung Tang, Andrei Manolescu, Vidar Gudmundsson
CConversion of the stacking orientation of bilayer graphene due tothe interaction of BN-dopants
Nzar Rauf Abdullah a,b , Hunar Omar Rashid a , Chi-Shung Tang c , Andrei Manolescu d , Vidar Gudmundsson e a Division of Computational Nanoscience, Physics Department, College of Science, University of Sulaimani, Sulaimani 46001, KurdistanRegion, Iraq b Computer Engineering Department, College of Engineering, Komar University of Science and Technology, Sulaimani 46001, KurdistanRegion, Iraq c Department of Mechanical Engineering, National United University, 1, Lienda, Miaoli 36003, Taiwan d Reykjavik University, Department of Engineering, Menntavegur 1, IS-102 Reykjavik, Iceland e Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
Abstract
A conversion of AA- to AB-stacking bilayer graphene (BLG) due to interlayer interaction is demonstrated. Two typesof interlayer interactions, an attractive and a repulsive, between the Boron and Nitrogen dopant atoms in BLG arefound. In the presence of the attractive interaction, an AA-stacking of BN-codoped BLG is formed with a less stablestructure leading to weak mechanical properties of the system. Low values of the Young modulus, the ultimate strengthand stress, and the fracture strength are observed comparing to a pure BLG. In addition, the attractive interactioninduces a small bandgap that deteriorates the thermal and optical properties of the system. In contrast, in the presenceof a repulsive interaction between the B and N atoms, the AA-stacking is converted to a AB-stacking with a more stablestructure. Improved mechanical properties such as higher Young modulus, the ultimate strength and stress, fracturestrength are obtained comparing to the AA-stacked BN-codoped BLG. Furthermore, a larger bandgap of the AB-stackedbilayer enhances the thermal and the optical characteristics of the system.
Keywords:
Thermoelectric, Bilayer graphene, DFT, Electronic structure, Optical properties, and Stress-strain curve
1. Introduction
Graphene has been considered as a promising materialfor applications in the fields of sensors, photonics, and elec-tronic devices because of its excellent characteristics suchas optical transparency, low density, high carrier mobility,and chemical stability [1, 2, 3, 4]. Combining two lay-ers of graphene in a specific configuration called bilayergraphene is also a high-potential material with possibleapplications in electronics and optics [5, 6, 7, 8]. It hasbeen experimentally shown that BLG has a number ofremarkable characteristics such as outstanding electrical,mechanical and chemical performance leading to a greatflexible transparent electrodes used in touch-screen devices[9], high-switching ratio digital transistors [10], and effi-cient infrared detectors [11]. Stiffness and flexibility prop-erties of BLG make it a great candidate for fuel cells and amaterial for use in structural composite applications [12].The aforementioned properties of BLG can be improvedby tuning the interaction between the graphene layers, orthe van der Waals interactions appearing between the lay-ers [13, 14]. The DFT-D technique, dispersion-correcteddensity functional theory, has been used to describe the
Email address: [email protected] (Nzar RaufAbdullah) interlayer interaction energy of BLG with high accuracy[15]. It has been found that the interlayer electron mo-tion is affected by the atomic orientation of the two layers[16, 17]. The atomic orientation controls the strength ofthe interlayer van der Waals bonding. The interlayer elec-tron interaction is influenced by the stacking configurationof the BLG leading to interesting physical properties. Forinstance, a moir´e pattern has been observed due to theinteraction between the layers for twisted BLG [18] withextraordinary optical properties found [19, 20, 21]. Fur-thermore, a relatively weak strength of interlayer interac-tion, and low energetic cost of relative translation of thelayers, has been seen for AA-stacking BLG [22]. Com-pared with other stacking structures, AA- and twisted-stacking, very strong coupling exists between the two lay-ers of AB-stacked BLG, which has the lowest energy andthe most stable structure among the different orienta-tions [23]. Strong coupling between the layers improvesand leads to numerous physically interesting properties inBLG. In recent experimental work, the stacking orienta-tion of BLG is investigated and it is found that the orienta-tion of BLG could be changed from weak stacking couplingto AB strong stacking coupling. In addition, a reductionin the interlayer distance is considered in a high-pressureenvironment to detect orientation changes [24]. We there-fore, believe that the stacking configuration of BLG is still
Preprint submitted to Elsevier January 5, 2021 a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n hallenging and further work is needed to clearly the situ-ation.In the present paper, we try to control the distance andinterlayer interactions of AA-stacked BLG by boron (B)and Nitrogen (N) dopant atoms. We will show how theAA-stacking with a weak interlayer interaction can be con-verted into a AB-stacking with a strong interlayer inter-action by doping of B and N atoms in the BLG. Moreprecisely, the conversion of AA- to AB-stacked BLG willbe achieved by controlling the dimer positions of the B andN atoms in the hexagonal structure of the graphene [25].In addition, the electronic, mechanical, thermal, and op-tical properties of the system will be shown for both AA-and AB-stacked BLG, and one can see significant improve-ment of the physical properties of the AB-stacked BLG inour study [26, 27].In Sec. 2 the BLG structure is briefly over-viewed. InSec. 3 the main achieved results are analyzed. In Sec. 4the conclusion of the results is presented.
2. Computational technique
We assume a pure BLG and BN-doped BLG with dif-ferent B and N atom configurations. The density func-tional theory (DFT) techniques based on the local densityapproximation (LDA) implemented in Quantum espressopackage have been used to study physical properties ofour models [28, 29]. A periodic boundary conditions areapplied to a 5 .
65 ˚A × .
44 ˚A ×
20 ˚A model cell of pureBLG. The Brillouin zone is sampled with k -point gridsfrom 10 × × × ×
1, and the basis set is planewaves with a maximum kinetic energy of 680-1360 eV [30].The spacing of the real space grid used to calculate theHartree, the exchange and the correlation contribution ofthe total energy 1360 eV. The van der Waals interaction isincluded in the exchange (XC) functional, and the struc-tures are relaxed until the forces on each atom were lessthan 0.001 eV/˚A.The XCrySDen is used to visualize all the structures[31, 32]. In addition, the Boltzmann transport propertiessoftware package (BoltzTraP) is employed to study thethermal properies of the systems [33]. The BoltzTraP codeuses a mesh of band energies and has an interface to theQE package. The optical characteristics of the systemsare obtained by the QE code. Optical calculations areperformed using a 100 × × .
3. Results
Pristine BLG and BN-codoped BLG are shown in Fig.1, with the B (red) atom fixed at a para-position in the toplayer, and the N (blue) atom is doped in the bottom layerat a para-position corresponding to the B atom (BLG-1),the meta-position (BLG-2), the ortho-position (BLG-3),and a para-position at a site opposite to the B atom (BLG-4). The position of the B and N atoms together forms different isomers which are called a para-isomer for BLG-1, a meta-isomer for BLG-2, an ortho-isomer for BLG-3,and a para-isomer for BLG-4.
Figure 1: Pristine BLG (a) and BN-codoped BLG (b-d) where theC, B, and N atoms are green, red, and blue colored, respectively, theB(N) atom is doped in top(bottom) layer. The B atoms is fixed ata para-position in the top layers of all structures, but the N atomis doped in a para-position at a site corresponding to the B atomin BLG-1, a meta-position in BLG-2, ortho-position in BLG-3, andpara-position at a site opposite to the B atom in BLG-4 in the bot-thom layer. d indicates the interlayer distances. The structural parameters calculated for BLG and BN-codoped BLG are presented in Tab. 1. The calculation ofthe structural parameters indicate that in the presence ofthe B and N atoms the average bond lengths of C-C, C-B,and C-N are slightly changed for all BN-codoped BLGs.This is due to the larger and the smaller atomic radiusof the B and the N atoms, respectively, compared to theatomic radii of a C atom [34]. Furthermore, the averagelattice parameters of the BN-codoped structures are in-creased compared to the pure BLG indicating a super-cellexpansion of the BN-codoped BLG. It is found that theC-C bond length, the lattice parameters, and the inter-2 able 1: The average bond lengths of C-C, C-B, and C-N, lattice parameters, a , interlayer distance, d , interlayer interaction energy, E in , anddistance between B and N atoms, d BN , for BLG and BN-codoped BLG structures. The unit of all parameters except ∆ E is ˚A. Structure C-C C-B C-N a d ∆ E (eV) d BN BLG 1.42 —– —– 2.44 3.59 —– —BLG-1 1.413 1.46 1.417 2.468 3.21 -3.25 3.21BLG-2 1.418 1.458 1.419 2.471 2.94 2.45 4.11BLG-3 1.415 1.458 1.419 2.471 2.96 2.39 4.1BLG-4 1.416 1.458 1.418 2.465 3.35 -4.35 4.4layer spacing of our pure BLG are consistent with previousstudies [35, 36]. The C-B and C-N bond lengths and lat-tice parameters of BN-codoped BLG agree very well withAlattas and Schwingenschl¨ogl [37].
The key point of this work is the interlayer interactiondue to the B and N doped atoms. There are several detailsthat should be considered to analyse the components orthe sources of the interlayer interactions in BLG. We takeinto account the van der Waals interactions which intro-duce a non-bonding potential between the layers of BLG.The Van der Waals interaction is a dipole-dipole interac-tion that can dominate other interactions if the distancebetween dipoles is around and beyound 4-5 ˚A [38, 39, 40].This type of interaction does not play a key role in oursystems as the distance between the layer does not reachthat limit (see Tab. 1). Other types of interactions domi-nate over the weak dipole-dipole interaction in our system.More important is the interaction that arises due to thesp bonding between the two layers of the BLG. This typeof interaction is best studied by incrementally moving twoatoms with the same planar coordinates (one in the upperlayer and the other one in the lower layer) to the sp bonddistance which is about 1 .
54 ˚A and allow the structure torelax [41]. Again, we do not expect this type of interac-tion to be important as our models have larger interlayerdistance. The third type of interaction is a nonbondinginteraction between the layers of a BLG that could be ei-ther a repulsive or attractive [42]. This type of interactionis effective if the interlayer distance is around 2-4 ˚A. Weassume this type of interaction to play an important rolebetween the layers, and the interaction energy between twodopant atoms in a structure is given by [43]∆ E = E − E + 2 × E (1)where E , E and E are the total energies of the systemswith zero, one, and two dopant atoms, respectively. Theobtained interaction energies of all BN-codoped systemsare presented in Tab. 1. It has been shown that the in-teraction energy in BN-codoped graphene varies inverselywith the distance between the B and N atoms because ofthe nature of the Coulombic electrostatic interaction, andthe interaction strength is almost zero when the separa-tion distance is greater than or equal to 4 . E can have a negative or a positive sign indi-cating that the interaction between the B and N atoms isattractive or repulsive, respectively.At first the sight, one can see the interaction betweenthe B and the N atoms leading to an attractive betweenthe layers of BLG-1, as the interaction energy is negativewhen both the B and N atoms sit on the same isomer posi-tion, para-position, but in different layers. Consequently,the ’Coulomb electrostatic potential’ between the B andN atoms is directly along the π -bond directions on thesame line perpendicular to both the B and N atoms. TheCoulomb electrostatic force only affects the interlayer spac-ing in the z -direction and does not influence the atomicpositions of both layers in the xy -plane. In this case, theAA-stacking behavior of BLG-1 is unchanged. The samescenario can be applied to BLG-4 when the B and N atomssit in opposite para-positions. The separation between theB and N atom is large here, 4 . . LG BLG-1 BLG-2 BLG-3 BLG-4
Figure 2: Dispersion energy or electronic band structure of pure BLG (a), and BN-codoped BLG (b-e) are shown. The Fermi energy is setto zero. the effective interaction of the two dopant atoms formingan effective interaction [43]. The distance between the Band N atoms after full relaxation in BLG-2 (BLG-3) is4 .
11 (4 . In order to understand the physical properties of BN-codoped BLG, such as thermal and optical characteris-tics, we need to present the dispersion energy of the struc-tures. In Fig. 2, the dispersion energy or the electronicband structures of pure BLG (a), and BN-codoped BLG(b-e) are displayed. In Fig. 2(a) the dispersion of pureBLG has multiple linear dispersion bands forming π , π and π ∗ , π ∗ that touch at the K-point of the first Brillouinzone. So, the intersection of the conduction and valencebands is located symmetrically near the K-point. The lin-ear dispersion bands are mainly due to the electronic in-terlayer coupling that is suppressed by the Pauli repulsionbetween the graphene layers [46]. The linear dispersion ofthe AA-stacked BLG has been experimentally confirmed[47].The computed electronic band structures of BLG-1,BLG-2, and BLG-3, based on LDA calculation, showa semiconducting property with an indirect bandgap ofBLG-1, and a direct bandgap of the BLG-2 and BLG-3structures. The band structure of BLG-4 exhibits a met-alic behavior as the lowest conduction band crosses theFermi energy near the Γ-point. The origin of bandgapopening comes from the redistribution of surface chargedue to the B and N atoms that breaks the local symmetryof the BLG. The redistribution of the charge density ofthe BN-codoped BLG gives rise to the separation of thevalence band and conduction band at the Dirac point. TheB atoms lead to band shift below the Fermi level, and theN atoms above the Fermi level, such that the counterbal-ance of both creates a gap at the Fermi level. Furthermore,the electrostatic Coulomb dipole interaction between theB and N atoms is also important in breaking the symmetryof BLG and thus to the band gap opening [44]. A narrow-ing of the bandgap in BLG is also induced by interlayer interaction [48]. The computed bandgaps of the BLG-1,BLG-2, and BLG-3 are 0 . . .
515 eV, re-spectivily. It is interesting to see that the bandgaps ofthe BLG-2 and BLG-3 with the repulsive interaction be-tween the B and N atoms are relatively larger than thoseof the BLG-1 and BLG-4 with the attractive interactionbetween the B and N atoms. It has been confirmed thatthe repulsive interaction between the layers forms a directand large bandgap, while an attractive interaction inducesan indirect and small bandgap in both the AA- and theAB-stacked BLG with B and N dopant atoms [49]. Our re-sults for the band dispersion and the bandgaps agree verywell with recent results for BN-codoped BLG in which theBLG is doped with one B atom in one layer and one Natom in the other [37].The computed partial density of states (PDOS) of pureBLG and BN-codoped BLG are presented in Fig. 3. It isclearly seen that the maximum of the valence band and theminimum of the conduction band for pure-BLG are totallyformed by the four p z π -bands around the Fermi energy.Furthermore, the s and p x,y contribute to the lower part ofthe valence band and upper part of the conduction bandas is expected for pure BLG [50, 51]. Figure 3: Partial density of states (PDOS) of pure BLG (a), andBN-codoped BLG (b-e) are shown. The Fermi energy is set to zero.
The PDOS of the BN-codoped BLG is analyzed show-ing that in all four cases of a BN-codoped BLG the higher4igzag ArmchairYM (TPa) UTS F-strength F-strain (%) YM (TPa) UTS F-strength F-strain (%)BLG 0.99 99.47 99.47 15.12 0.99 96.06 96.06 12.66BLG-1 0.65 58.55 58.55 12.14 0.65 56.73 56.73 11.24BLG-2 0.856 74.89 70.58 12.45 0.858 77.66 61.73 18.07BLG-3 0.855 77.82 77.82 12.14 0.875 78.04 71.58 13.76BLG-4 0.608 55.67 55.67 12.14 0.622 59.92 59.92 11.24
Table 2: The Young modulus (YM), the ultimate strength (UTS), the fracture strength (F-strength), and the fracture strain (F-strain) forBLG and BN-codoped BLG structures in the zigzag and armchair directions. The unit of UTS and F-stress is GPa. valence bands have a contribution from the p z of the Cand B atoms, and the lower conduction bands are formedby the p z of the C, B and N atoms. We note that the ma-jor contribution to the π -bands comes from the C atoms.More precisely, the contribution of the B and N atomsaround the Fermi energy is slightly higher for the BLG-2and BLG-3, where the a repulsive interaction between theB and N atoms exists. It is also expected that the contri-bution of both the s and p x,y by the B and N atoms areincreased at the lower valence and the upper conductionbands. The DFT calculations can be used to investigate thestress-strain curves of our systems. We apply uniaxialtensile simulations to probe the stress-strain properties.The load is gradually applied to a specific direction of thestructure, the zigzag or armchair directions [52]. Duringa uniaxial tensile loading, the periodic dimension alongthe loading direction is increased step-by-step with a fixedstrain of 0 . .
71 eV which is greater thanthat of C-N (2 .
83 eV) and C-B (2 .
59 eV) [53, 54]. Conse-quently, the structure with a higher number of C–C bondswill be more stable than the others. This is the reason forhigher stress-strain curves of pure the BLG compared tothe BN-codoped BLG.In addition, a structure with the lowest total energywill be the most stable structure [46]. Our DFT calcu-lations of the total energy confirm that the most stablestructures among the BN-codoped BLG are BLG-2 andBLG-3. These two structures have lower total energies than BLG-1 and BLG-4. Therefore, the BLG-2 and BLG-3 structures with repulsive interaction between the B andN atoms have higher stress-strain curves than the BLG-1and BLG-4 structures with an attractive interaction. Thisalso refers to AB-stacked BLG-2 and BLG-3 formed by therepulsive interaction in which the AB-stacked shapes havemore energetically stable structure than AA-stacked one.
Figure 4: Stress-strain curves for pure BLG (golden), BLG-1 (green),BLG-2 (blue), BLG-3 (red), and BLG-4 (purple) in the zigzag (a)and armchair (b) directions.
The values of the ultimate strength (UTS), the Youngmodulus (YM), the fracture strength (F-strength), and thefracture strain (F-strain) can be computed and their valuesfor all structures are presented in Tab. 2. It is known thatthe YM defines the tensile stiffness of a structure. In asmall range of strain of about a few percent (strain < %4),when the tensile strain increases, the stress that the systemexperienced enlarges linearly for the BLG and BN-codopedBLG structures. From the linear regime of the curves, onecan calculate the Young’s moduli, which are basically theinitial slope of the stress–strain curves. The strain-stresscurve of pure BLG reveals the YM to be 0 .
99 TPa for boththe zigzag and armchair directions in good agreement withthe theoretical value of 0 .
96 TPa [55], and the experimen-tal value of 1 . The thermal characteristics of our structures at the lowtemperature ranging from 20 to 160 K are consideredwhere the phonons are inactive [57, 32].
Figure 5: Seebeck coefficient (a), figure of merit ( ZT ), and Lorentznumber ( L ) versus energy for pure BLG (golden), BLG-1 (green),BLG-2 (blue), BLG-3 (red), and BLG-4 (purple). The Fermi energyis set to zero. In such a low temperature range, the electrons deliver the main contribution to the thermal properties. Figure5 presents the Seebeck coefficient, S , (a), the figure ofmerit, ZT , (b), and Lorentz number, L , (c) as a function ofenergy for pure BLG and BN-codoped BLG structures. Agood thermoelectric material should have a a low thermalconductivity, and a high S and electrical conductivity. Thethermoelectric performance of a monolayer and a BLG ispoor because of closed bandgaps, leading to a small S [58,59]. This is also seen for pure BLG shown in Fig. 5(a),where the S has an extremely small value which is almostinvisible in the figure. Similarly, this gives rise to verysmall value of ZT and L for pure BLG as well.Asymmetric peaks in the PDOS close to the highest oc-cupied state shown in Fig. 3, and the opening up of abandgap are expected to increase the S , ZT and L inBLG-1, BLG-2 and BLG-3 structures [60, 61]. A smallbandgap of BLG-1 induces small S , ZT and L , while thelargest bandgap of BLG-2 gives the maximum values of S , ZT and L . Therefore, one can expect a higher thermo-electric performance for the BLG-2. We explore the optical properties of pure BLG andBN-codoped BLG which may be interesting for optoelec-tronic use of graphene-based materials. The rise in in-terest of BLG in optoelectronics is presented by its ap-plications ranging from solar cells and light-emitting de-vices to touch screens, photo-detectors and ultrafast lasers.These all come from the unique optical and electronicproperties of BLG and their relevance for nano-photonics[62, 27, 63, 64].
Figure 6: Imaginary part of dielectric function, ε , versus energy forpure BLG (golden), BLG-1 (green), BLG-2 (blue), BLG-3 (red), andBLG-4 (purple), in the E in (a), and E out (b). In our pure BLG, two main peaks in the imaginary partof the dielectric function are formed at 4 .
01 and 14 .
03 eVrepresenting π to π ∗ transitions when the applied electricfield is parallel to the BLG structure, and two peaks at 11 . .
42 eV corresponding to the σ and σ ∗ transition are6 igure 7: Absorption coefficient versus energy for pure BLG(golden), BLG-1 (green), BLG-2 (blue), BLG-3 (red), and BLG-4(purple), in the E in (a), and E out (b). seen for perpendicular applied electric field (not shown).We observe a red shift in all four peaks in the presenceof BN-codoped BLG with more or less the same intensityof the peaks (not shown). The red shift of the peaks iscaused by the decreased energy spacing between the π andthe π ∗ , and the σ and the σ ∗ along the Γ-M and the M-Kdirections (see Fig. 2). The detailes of these transitionsare shown in our recent publication [49]. In addition tothese peaks, extra peaks in the low energy range from 0 to3 . in , (a) and a per-pendicular or out of plane, E out , (b) electric field appliedto the BLG structure [65, 66, 67]. The peaks in the imag-inary part of the dielectric function in the presence of E in are due to optical transitions in the bandgap or very closeto the bandgap. We therefore see peaks formed at differ-ent values of energy indicating the bandgap energy. Weshould remember that values of the bandgaps are under-estimate as the DFT with a local density approximationhas been used here. Therefore, the peak position is notexactly equal to the bandgap energy. Furthermore, thepeaks in the presence of E out represent the σ and σ ∗ tran-sitions around the Γ-points. It can clearly be seen that thepeak intensity of ε in the presence of E out for BLG-2 andBLG-3 are maximum while a minimum peak intensity isfound for BLG-4.In addition, the energy loss-function, EELS characteriz-ing inelastic scattering processes of the BN-codoped BLGstructures is calculated for light polarization E in and E out ,and compared to BLG. The EELS is displayed in Fig. 8for E in (a), and E out (b) in a low energy range.We observe from the plots of EELS that with increas- Figure 8: Energy loss-function, EELS, versus light energy for pureBLG (golden), BLG-1 (green), BLG-2 (blue), BLG-3 (red), andBLG-4 (purple), in the E in (a), and E out (b). ing the bandgap of the BN-codoped structures the peak isshifted to higher energy indicating that an inelastic scat-tering process occurs at a high energy of the light for thestructure with a larger bandgap.
4. Conclusion
This study uses DFT techniques based on the local den-sity (LDA) approach to investigate electronic, mechanical,thermal and optical properties of BLG systems with Boronand Nitrogen dopant atoms. The DFT is implementedin Quantum espresso code and the Boltztrap package isused for further properties of the system. We show thatthe bandgap of AA-stacked BN-codoped BLG decreaseswith increasing interlayer spacing, while the bandgap ofAB-stacked BN-codoped BLG increases. In addition, theattractive interaction between the B and the N atoms de-teriorates the mechanical, thermal and optical propertiesof the system. In contrast, a repulsive interaction improvethe high mechanical, thermal and optical characteristicsof the system. Our results are relevant for optoelectronicapplications of graphene-based devices.
5. Acknowledgment
This work was financially supported by the Universityof Sulaimani and the Research center of Komar Univer-sity of Science and Technology. The computations wereperformed on resources provided by the Division of Com-putational Nanoscience at the University of Sulaimani.
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