Electronic properties and carrier mobilities of 6,6,12 graphyne nanoribbons Electronic properties and carrier mobilities of 6,6,12 graphyne nanoribbons Heyu Ding, Hongcun Bai, and Yuanhe Huang, Citati[.]
Electronic properties and carrier mobilities of 6,6,12-graphyne nanoribbons Heyu Ding, Hongcun Bai, and Yuanhe Huang , Citation: AIP Advances 5, 077153 (2015); doi: 10.1063/1.4927497 View online: http://dx.doi.org/10.1063/1.4927497 View Table of Contents: http://aip.scitation.org/toc/adv/5/7 Published by the American Institute of Physics AIP ADVANCES 5, 077153 (2015) Electronic properties and carrier mobilities of 6,6,12-graphyne nanoribbons Heyu Ding,1 Hongcun Bai,2 and Yuanhe Huang1,a College of Chemistry, Beijing Normal University, Beijing, 100875, China Key Laboratory of Energy Sources and Chemical Engineering, Ningxia University, Yinchuan, Ningxia 750021, China (Received June 2015; accepted 13 July 2015; published online 23 July 2015) Structures, stabilities, electronic properties and carrier mobilities of 6,6,12-graphyne nanoribbons (GyNRs) with armchair and zigzag edges are investigated using the self-consistent field crystal orbital method based on density functional theory It is found that the 1D GyNRs are more stable than the 2D 6,6,12-graphyne sheet in the view of the Gibbs free energy The stabilities of these GyNRs decrease as their widths increase The calculated band structures show that all these GyNRs are semiconductors and that dependence of band gaps on the ribbon width is different from different types of the GyNRs The carrier mobility was calculated based on the deformation theory and effective mass approach It is found that the carrier mobilities of these GyNRs can reach the order of 105 cm2 V –1s–1 at room temperature and are comparable to those of graphene NRs Moreover, change of the mobilities with change of the ribbon width is quite different from different types of the GyNRs C 2015 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4927497] I INTRODUCTION Carbon has a broad range of unique physical and chemical properties due to the versatile flexibility of carbon in containing three distinct covalent bonds, namely, sp, sp2, sp3- hybridization states Thus, it can form various allotropes including naturally occurring diamond and graphite, as well as numerous synthetic carbon structures Among them, the most remarkable and well-known achievements are the discovery of fullerenes C60,1 carbon nanotubes (CNTs)2 and graphene3 representing new outstanding types of 0D-, 1D-, and 2D-like sp2-hybridized carbon materials, which in turn are capable to offer diverse and novel structural motifs for making high-performance carbon materials with new functionalities These low-dimensional carbon structures have been the focus of extensive research due to their unique structural, mechanical, electronic and superconducting properties.4–8 Up to now, the approaches to construct new low-dimensional carbon nanostructures have not stopped.9–12 It is known that carbon atoms have three hybridization states (sp, sp2, sp3), but all the carbon atoms in fullerenes, CNTs and graphene only present sp2 hybridization It has been pointed out that the -C≡C- unit can be inserted into each bond A-B of a molecule for the expansion of the system.13 Actually, several molecules with the -C≡C- unit insertion have been synthesized successfully, such as carbomers of benzene14 and cubane.15 If the acetylenic (-C≡C-) or diacetylenic (-C≡C-C≡C-) linkages are introduced into graphene, new structures of carbon with combination of sp and sp2 carbon atoms could be produced, such as graphynes16 and graphdiynes.17 Recently, Li and co-workers synthesized graphdiyne films on Cu surface by a cross-coupling reaction using hexaethynylbenzene,18 opening a new route to prepare 2D graphyne sheets Several theoretical a Author to whom correspondence should be addressed Electronic mail: yuanhe@bnu.edu.cn 2158-3226/2015/5(7)/077153/10 5, 077153-1 © Author(s) 2015 077153-2 Ding, Bai, and Huang AIP Advances 5, 077153 (2015) calculations have been performed on the electronic properties of graphdiyne and its family.19–21 Apart from that, four main types of graphynes have been proposed and identified, α-Graphynes, β-graphyne, γ-graphyne and 6,6,12-graphyne,16,22 each with different percentage of acetylenic linkages Previous first-principle calculations22–25 have shown that α-Graphynes, β-graphyne and 6,6,12-graphyne possess Dirac cone-like band strictures at the Fermi level.22,26,27 Regardless of the absence of the hexagonal (p6m) symmetry, 6,6,12-graphyne exhibits high carrier mobility like graphene More importantly, 6,6,12-graphyne exhibit exceptional directional anisotropy in its mechanical properties28,29 and electronic properties.26,30 As 6,6,12-graphyne itself is a zero-gap semiconductor,26 the opening of the energy gap is needed to extend its practical application It is known that 2D graphene present metallic property with zero band gap, but the 1D graphene NRs with armchair edges exhibit semiconducting property.31 Thus the property of the materials may be greatly influenced when the dimensionality is reduced It is expected to open up the energy gap in 6,6,12-graphyne by cutting the 2D sheet into 1D nanoribbons Recently the transport properties of 2D 6,6,12-graphyne sheet and, several 1D 6,6,12-graphyne nanoribbons (GyNRs) were studied using density functional theory coupling with the non-equilibrium Green’s function method, exhibiting highly anisotropic electrical transport properties.32–34 Li decorated 6,6,12-graphyne have shown that hydrogen storage capacity is high up to 19.3 wt%, so it would be a potential material for hydrogen storage.35 Though 2D 6,6,12-graphyne sheet has received much attention,26–30 few works involved in the effect of geometric size and edge chirality on the electronic property for the 1D GyNRs Moreover, the relationship between carrier mobility and the 1D GyNR width has not been studied until now Hence, a detailed and systematic study on 1D 6,6,12-graphyne nanoribbons with different edges and widths would be helpful for better understanding the electronic properties and providing the fundamental guidelines for the application of 6,6,12-graphyne In this paper, we perform a theoretical investigation on 1D 6,6,12-graphyne nanoribbons (GyNRs) using the self-consistent field crystal orbital (SCF-CO) method under the periodic boundary condition The structures, stabilities, electronic properties and carrier mobilities of these GyNRs are calculated and compared with those of graphene NRs and graphdiyne NRs We hope these efforts can accelerate the development of modern carbon-based materials II MODEL AND COMPUTATIONAL METHOD The 1D 6,6,12-graphyne NRs are constructed by cutting the 2D sheet, as shown in Fig Edges of all these nanoribbons are saturated by hydrogen atoms to remove the effect of dangling bonds, which is similar to the treatments for the graphene NRs28 and graphdiyne NRs.20,21 The size of the unit cells of 1D 6,6,12-graphyne NRs is indexed by the number N For simplicity, we use N-AGyNRs and N-ZGyNRs to represent armchair and zigzag 6,6,12-graphyne nanoribbons with different widths, respectively Here we set N=1-9 to study the effect of the quantum confinement for the 1D GyNRs The unit cell contains (18N+8) carbon atoms and four hydrogen atoms for AGyNRs and (18N+6) carbon atoms and six hydrogen atoms for ZGyNRs For comparison, the structure of the 2D 6,6,12-graphyne sheet is also calculated In contrast to graphene and graphdiyne, the geometric structures of the 6,6,12-graphyne sheet exhibits rectangular (pmm) symmetry rather than hexagonal symmetry (p6m) Geometry, band structures and electronic properties are calculated by means of SCF-CO method based on DFT with full structural optimization and CRYSTAL09 program36,37 for all the models studied In the geometric optimization, symmetry constraint is always adopted (Pmm2) The exchangecorrelation functional proposed by Perdew-Burke-Ernzerhof for solids (PBEsol)38,39 and a double-ξ plus polarization basis set 6-21G* are adopted in our DFT SCF-CO calculation In the first Brillouin zone 40 and 20×20 k-point samplings are adopted for 1D and 2D structures, respectively The default values of convergence criteria in CRYSTAL09 are used (total energy change less than 10−7 hartree/cell and geometry optimization with maximum force less than 0.00045 hartree / bohr) 077153-3 Ding, Bai, and Huang AIP Advances 5, 077153 (2015) FIG Models of GyNRs with (a) armchair edges (AGyNRs); (b) zigzag edges (ZGyNRs) and a is the lattice constant of GyNRs III RESULTS AND DISCUSSION A Structures and relative stabilities The optimized lattice constants for 2D 6,6,12-graphyne are 6.905 Å and 9.456 Å along the armchair and zigzag direction, respectively, which is in agreement with the reported values using the projector augmented wave method.26,27 For AGyNRs, the widths are in the range of 1.380-8.944 nm for N=1-9 The optimized lattice parameters a0 is 6.901 Å in 1-AGyNRs and it gradually increase to 6.905 Å in 9-AGyNRs, close to the lattice length 6.906 Å in the 2D 6,6,12-graphyne sheet along the armchair direction For ZGyNRs, the widths are in the range of 1.192-6.717 nm for N=1-9 The optimized lattice parameters a0 range from 9.467 Å to 9.456 Å, and it decreases as N increase The lattice length of 9-ZGyNR are close to 2D lattice constant 9.456 Å along the zigzag direction To study the influence of the edge and width on the thermodynamic stability of these systems, we calculated the Gibbs free energy δG Since the edges are saturated by hydrogen atoms, these GyNRs have different chemical compositions Consequently, the approach customary used in binary phased thermodynamics are adopted This method has been used successfully to analyze the relative stability of graphene NRs,40 endohedral silicon nanowires41 and graphdiyne NRs.20 The Gibbs free energy per atom (δG) for GyNRs is obtained by δG = −Ecoh + χHµH + (1 − χH)µC (1) Where Ecoh is the cohesive energy per atom of GyNRs, χ H is the molar fraction of hydrogen atoms, µ H and µC are the chemical potential of the constituents at a given state We choose µ H as the binding energy per atom of the H2 molecule and µC as the cohesive energy per atom of the single graphene sheet This definition allows for a direct energy comparison of GyNRs with different edges and widths 077153-4 Ding, Bai, and Huang AIP Advances 5, 077153 (2015) TABLE I Widths (W ), Gibbs free energies (δG) and band gaps (E g1 at Γ-point and E g2 at X-point) for the GyNRs NR W /nm δG/eV E g1/eV E g2/eV 1-AGyNR 2-AGyNR 3-AGyNR 4-AGyNR 5-AGyNR 6-AGyNR 7-AGyNR 8-AGyNR 9-AGyNR 1.380 2.325 3.271 4.217 5.162 6.108 7.054 7.999 8.944 0.574 0.657 0.694 0.716 0.730 0.740 0.747 0.753 0.757 0.278 0.242 0.249 0.059 0.213 0.032 0.124 0.072 0.055 0.819 0.384 0.199 0.098 0.041 0.019 0.033 0.048 0.060 1-ZGyNR 2-ZGyNR 3-ZGyNR 4-ZGyNR 5-ZGyNR 6-ZGyNR 7-ZGyNR 8-ZGyNR 9-ZGyNR 1.192 1.882 2.573 3.264 3.955 4.645 5.336 6.027 6.717 0.485 0.602 0.655 0.686 0.705 0.719 0.729 0.736 0.743 0.738 0.401 0.241 0.155 0.103 0.071 0.047 0.033 0.022 1.331 0.669 0.386 0.237 0.150 0.095 0.063 0.041 0.024 The obtained values of δG for the GyNRs with different width are listed in Table I It is found that the values of δG for GyNRs are in the range of 0.485 - 0.757 eV, which are smaller than that of 2D 6,6,12-graphyne (δG=0.795 eV) calculated at the same computational level The system with smaller δG is more stable Thus these GyNRs are more stable than the 2D 6,6,12-graphyne sheet, exhibiting a feature similar to graphdiyne NRs.20 Furthermore, the stabilities of these GyNRs with the same edges decrease as their widths increase When N=9, δG of AGyNRs and ZGyNRs are 0.757 eV and 0.743 eV respectively, which are close to 0.795 eV for the 2D 6,6,12-graphyne sheet Additionally, from Fig it can be seen that the ZGyNRs are a little more stable than the AGyNRs with the same width, similar to the case of graphdiyne NRs.20 But this fact is different from the case in graphene NRs, since the armchair graphene NRs are more stable than the zigzag structures according to the previous calculations.42,43 This result indicates that insertion of -C≡Cinto graphene is able to alter the relative stabilities of the original structures FIG δG -W relationship of GyNRs with N =1-9 077153-5 Ding, Bai, and Huang AIP Advances 5, 077153 (2015) B Band structures and electronic properties The calculated band structures are shown in Fig for these GyNRs, in which the band structure of 2-AGyNR is well in agreement with the previous study.32 It can be seen that all the GyNRs have a band gap (Eg) between top of the highest occupied band (HOB) and bottom of the lowest unoccupied band (LUB) Therefore these 1D GyNRs are predicated to be semiconductors The semiconducting property of these GyNRs is edge-independent, similar to the case of γ-graphyne NRs21 and graphdiyne NRs.20 The calculated band gaps of these GyNRs are presented in Table I, Eg1 and Eg2 corresponding to the band gaps at center and edge of Brillouin zone (Γ and X points), respectively Table I shows Eg1 < Eg2 for narrower GyNRs From Fig 3, it can be seen that the bottoms of original LUB+1 and tops of HOB-1 descend and ascend rapidly as the NR widths increase, which results in the quick decrease of energy difference between the highest occupied and lowest crystal orbitals (HOCO and LUCO) at X-point When N ≥6, Eg1 > Eg2 for AGyNRs, i.e., the position of the smallest band gap shifts from Γ to X point As for ZGyNRs, although Eg1 is always smaller than Eg2, the difference between them (∆Eg = |Eg1 - Eg2|) becomes smaller and smaller When N>5 and N>7, ∆Eg is less than 0.025eV which is the average energy of thermal motion at room temperature, respectively for ZGyNRs and AGyNRs The status of electron excitation should be comparable at both Γ and X points for wider GyNRs due to small ∆Eg From Table I, it can also be seen that the band gaps of AGyNRs fall with fluctuation but those of ZGyNRs monotonically decrease as NR widths increase The different electrical behavior for the GyNRs with different edge structures may be related to the direction-dependent electronic property of the 2D 6,6,12-graphyne sheet, which is the result of the rectangular symmetry.26,30 The electronic properties of GyNRs is obviously different from those of graphene NRs, α-graphyne NRs and α-graphdiyne NRs, in which all armchair-edged structures are semiconductors and the gap variation can be classified into three families with N=3l+1, 3l, 3l+2 (l is a positive integer) but all zigzag-edged structures exhibit metallic property.44–46 The gap dependence of these GyNRs on the NR width is also different from that of γ-graphyne NRs and graphdiyne NRs in which the energy gaps decrease monotonically with width increasing for both armchair-edged and zigzag-edged structures.20,21 Of particular interest, we find that α-graphyne and α-graphdiyne all contain honeycomb structures and can be viewed as ideal analogs of graphene This may account for the features: for α-graphyne, α-graphdiyne and graphene NRs, the energy gaps of armchair-edged structures exhibit three distinct behaviors with the size change and zigzag-edged structures show metallic properties.44–46 Since 6,6,12-graphyne, FIG Band structures of GyNRs with N =1-9 (a)AGyNRs; (b) ZGyNRs 077153-6 Ding, Bai, and Huang AIP Advances 5, 077153 (2015) γ-graphyne and graphdiyne are absent of such honeycomb structures, their nanoribbons not present three distinct behaviors This case indicates that insertion of different ratio sp1/sp2 into graphene results in the variation of electronic property due to change of the structures Besides, we would like to point that the same type of GyNRs with different edge structure may also have different electronic property A 6,6,12-Z′GyNR showed metallic property with zero band gap, in which half of the six-membered rings at the protruding edge are eliminated,33 but the six-membered rings of ZGyNRs here are all completed In order to get a quantitative relationship of Eg with respect to the widths of ZGyNRs, we fit the corresponding data to the equation Eg = aW −b (eV), similar to the treatment for graphdiyne NRs where the W is the width (in nm) of the ZGyNRs The values of a and b obtained are 1.337 and 0.633, respectively (R2=0.996) The exponent b reflects the sensitive degree of the width changes for the GyNRs The DFT calculations show that the values of the exponent b are 0.302 and 0.593 for armchair graphdiyne and zigzag graphdiyne NRs,20 respectively, and are 0.872-1.097 for graphene NRs.40 Obviously, the b exponents of the GyNRs are smaller than those of graphene NRs, but larger than those of graphdiyne NRs, suggesting that the band gaps of GyNRs change more smoothly with the changes of the NR widths than those of graphene NRs but more sharply than graphdiyne NRs C Carrier mobilities Carrier mobility which describes the ability of charge carriers to move in materials is the central issue for nanoelectronic semiconducting materials In order to better understand the transport behavior of the 1D GyNRs, we calculate the carrier mobilities of the GyNRs using a simple model based on the deformation potential (DP) theory and effective mass approximation This model has been successfully employed to study the carrier mobility in some one-dimensional cases, such as fullerenes,8 nanotubes,47,48 graphene nanoribbons49 and graphdiyne nanoribbons.20 It can be expressed as µ= e~2C (2πk BT)1/2|m∗|3/2 E12 (2) Where C = a0(∂ E/∂a2)|a=a0 is the stretching modulus of 1D crystal along the longitudinal ribbon, a and a0 are the deformed and equilibrium lattice constant m∗ is the effective mass of charge carrier, −1 which can be expressed as m∗ = ~2 ∂∂kE2 E1 is the deformation potential (DP) constant, defined as δE = E1(δa/a0) where δE is the energy shift of the band edge position with respect to the lattice deformation The calculated data are shown in Table II It is found that the mobilities for the AGyNRs and ZGyNRs are in the range 10 – 105 cm2V−1s−1 and 102 – 104 cm2V−1s−1, respectively As the difference of the band gaps at Γ- and X- point are small for wider NRs, even less than 0.025 eV when N>7, thus the mobilities at both Γ- and X- point are considered At Γ- and X- point, the mobilities show same trends with the variation of the NR widths for the same type of GyNRs Besides, the mobilities of charge carriers at Γ- point are always larger than those at X- point for the same GyNR except for 1-ZGyNR But the carrier mobility presents different characters for different types of the GyNRs For the AGyNRs, the mobilities of electrons and holes exhibit an oscillating behavior with increase of the NR widths When N