Electronic properties and carrier mobilities of 6,6,12 graphyne nanoribbons

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[.]

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,1Hongcun Bai,2and Yuanhe Huang1, a

1College of Chemistry, Beijing Normal University, Beijing, 100875, China

2Key Laboratory of Energy Sources and Chemical Engineering, Ningxia University,

Yinchuan, Ningxia 750021, China

(Received 2 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 semiconduc-tors 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 Gy-NRs can reach the order of 105cm2V–1s–1at 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 C60,1carbon nanotubes (CNTs)2and graphene3 repre-senting 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.48

Up to now, the approaches to construct new low-dimensional carbon nanostructures have not stopped.912 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 benzene14and cubane.15If the acetylenic (-C≡C-) or diacetylenic (-C≡C-C≡C-) linkages are introduced into graphene, new structures of carbon with combination

of sp and sp2carbon atoms could be produced, such as graphynes16and 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

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 calculations22–25have 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 , 29and 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 prop-erty with zero band gap, but the 1D graphene NRs with armchair edges exhibit semiconducting property.31Thus 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 – 34Li 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.35Though 2D 6,6,12-graphyne sheet has received much attention,26–30few 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 (Gy-NRs) 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 1 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 NRs28and graphdiyne NRs.20 , 21The 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 , 37for all the models stud-ied In the geometric optimization, symmetry constraint is always adopted (Pmm2) The exchange-correlation functional proposed by Perdew-Burke-Ernzerhof for solids (PBEsol)38 , 39and 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 10−7hartree/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 1 Models of GyNRs with (a) armchair edges (AGyNRs); (b) zigzag edges (ZGyNRs) and a 0 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 us-ing 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 a0range 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,40endohedral silicon nanowires41and graphdiyne NRs.20The Gibbs free energy per atom (δG) for GyNRs is obtained by

Where Ecohis the cohesive energy per atom of GyNRs, χHis the molar fraction of hydrogen atoms,

µH and µC are the chemical potential of the constituents at a given state We choose µH as the binding energy per atom of the H2molecule and µCas 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

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.

The obtained values of δG for the GyNRs with different width are listed in TableI 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.20Furthermore, 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 2 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.20But 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.42,43This result indicates that insertion of -C≡C-into graphene is able to alter the relative stabilities of the original structures

FIG 2 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.3for these GyNRs, in which the band struc-ture of 2-AGyNR is well in agreement with the previous study.32It 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 NRs21and graphdiyne NRs.20The calculated band gaps of these GyNRs are presented in TableI,

Eg1and Eg2corresponding to the band gaps at center and edge of Brillouin zone (Γ and X points), respectively Table Ishows 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> Eg2for AGyNRs, i.e., the position of the smallest band gap shifts from Γ to X point As for ZGyNRs, although Eg1is always smaller than Eg2, the difference between them (∆Eg= |Eg1 - Eg2|) becomes smaller and smaller When N>5 and N>7, ∆Egis 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 TableI, 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 , 30The 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 – 46The 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.44–46Since 6,6,12-graphyne,

FIG 3 Band structures of GyNRs with N =1-9 (a)AGyNRs; (b) ZGyNRs.

γ-graphyne and graphdiyne are absent of such honeycomb structures, their nanoribbons do not pres-ent three distinct behaviors This case indicates that insertion of different ratio sp1/sp2into 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,33but 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,20respectively, and are 0.872-1.097 for graphene NRs.40Obviously, 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 trans-port 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,8nanotubes,47 , 48graphene nanoribbons49and graphdiyne nanoribbons.20It can be expressed as

(2πkBT)1/2|m∗|3/2E2

1

(2) Where C = a0(∂2E/∂a2

)|a =a0is the stretching modulus of 1D crystal along the longitudinal ribbon,

aand a0are the deformed and equilibrium lattice constant m∗is the effective mass of charge carrier, which can be expressed as m∗= ~2

∂ 2 E

∂k 2

−1

E1is 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 TableII

It is found that the mobilities for the AGyNRs and ZGyNRs are in the range 10 – 105cm2V−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 <6, the mobilities of holes for the N -AGyNRs with the odd N are 1∼2 order of magnitude larger than those

of electrons, but just the opposite with the even N The case inverses when N ≥ 6 The relative change of mobility for the two kinds of charge carriers has a turning-point at N=6 with increase

of the NR sizes As for the ZGyNRs, the electron mobility increases monotonically with the NR width increasing; the hole mobility increases with the width increasing when N <7, but slightly oscillate when N >7 The mobilities of holes are always larger than those of electrons, indicating that ZGyNRs are more favorable to hole transport From TableII, we found the stretching modulus

Cincrease slightly with the NR width increasing, the electron effective mass me*and hole effective mass mh* are close to each other for the same GyNR Therefore, the relative change and difference among the stretching modulus and the effective mass of charge carriers for the same kind of the GyNRs cannot make so different dependence on the NR width for different charge carriers The key

077153-7 Ding, Bai, and Huang AIP Advances 5, 077153 (2015)

TABLE II The stretching moduli C, the electron and hole e ffective mass m e∗and m h∗, the electron and hole DP constants

E 1c and E 1v , the mobility of the electron and hole µ e and µ h at Γ-point (while that in brackets is the corresponding mobility

at X-point) and Young moduli Y for GyNRs(C in eV /Å; m e∗and m h∗in m e ; E 1c and E 1v in eV; µ e and µ h in cm 2 V −1 s −1 and Y in GPa).

3 (9.457 × 102)

8.159 × 104 (8.017 × 104) 769

5 (8.296 × 104)

1.806 × 103 (1.187 × 103) 645 3- AGyNR 428 0.108 0.097 4.577 0.522 4.600 × 10

3 (1.298 × 103)

4.166 × 105 (1.088 × 105) 615 4- AGyNR 523 0.382 0.479 0.609 4.547 4.773 × 10

4 (5.865 × 104)

6.098 × 102 (1.076 × 102) 584 5- AGyNR 622 0.069 0.105 4.067 0.603 1.651 × 10

4 (6.010 × 102)

4.018 × 105 (3.001 × 104) 567 6- AGyNR 742 0.150 0.154 4.617 0.651 4.788 × 10

3 (3.862 × 10)

2.315 × 105 (1.160 × 103) 572 7- AGyNR 861 0.071 0.077 0.653 4.319 8.530 × 10

5 (3.412 × 104)

1.726 × 104 (7.222 × 102) 574

4 (1.217 × 103)

6.685 × 105 (5.671 × 104) 559 9- AGyNR 1071 0.419 0.400 0.647 4.49 7.539 × 10

4 (6.366 × 104)

1.678 × 103 (4.956 × 102) 563

2 (1.981 × 10 2 )

3.912 × 102 (8.867 × 10 2 ) 568 2- ZGyNR 145 0.249 0.301 3.414 1.305 1.403 × 10

3 (2.374 × 10 2 )

7.229 × 103 (9.242 × 10 2 ) 636

3 (2.134 × 10 2 )

1.129 × 104 (1.415 × 10 3 ) 668

3 (3.983 × 10 2 )

1.398 × 104 (2.836 × 10 3 ) 698 5- ZGyNR 148 0.235 0.278 3.382 1.382 3.588 × 10

3 (4.401 × 10 2 )

1.671 × 104 (3.124 × 10 3 ) 697

3 (5.209 × 10 2 )

5.472 × 104 (3.701 × 10 3 ) 706 7- ZGyNR 150 0.161 0.272 3.219 1.501 9.645 × 10

3 (7.358 × 10 2 )

2.024 × 104 (1.910 × 10 3 ) 711 8- ZGyNR 151 0.164 0.171 3.108 1.585 1.144 × 10

4 (8.274 × 10 2 )

4.131 × 104 (2.785 × 10 3 ) 717 9- ZGyNR 152 0.158 0.201 2.975 1.678 1.483 × 10

4 (1.060 × 10 3 )

3.237 × 104 (1.763 × 10 3 ) 721

factor to determine the change of charge carrier mobility with the NR width is the DP constants

E1which reflect the scattering behavior of the charge carriers When N <6, the DP constants of the holes E1vwith odd and even N are of 0.52-0.60 and 4.55-4.71eV for the N -AGyNRs, respectively These DP constants of the holes are almost one order of magnitude smaller and larger than the corresponding DP constants of the electrons (4.07-4.74 eV and 0.53-0.61eV) Since carrier mobility

is inversely proportional to square of DP constant, consequently the difference of DP constants leads

to the difference of 1∼2 order of magnitude between the hole and electron mobilities The case inverse when N ≥6 It is the oscillating DP constants that results in the oscillating behavior of charge carriers for AGyNRs For ZGyNRs, it is found that the E1cis always almost twice larger than E1vfor each system, resulting in that the mobility of electrons is always smaller than that of holes

The above discussions show that the characteristic of the mobility for AGyNRs and ZGyNRs mainly arises from the DP constant E which characterize the coupling strength of the electron or

FIG 4 Frontier crystal orbitals at Γ-point for (a) 3-AGyNR; (b) 4-AGyNR; (c) 6-AGyNR; (d) 7-AGyNR; (e) 5-ZGyNR.

hole to the acoustic phonon Thus the different electron and hole mobilities are due mainly to the

different scattering behaviors in the GyNRs This fact may be understood by examining the frontier crystal orbitals which construct the pathway of charge carriers When the lattice slightly expand-ing or shrinkexpand-ing, the site energy changes Consequently, the energy bands shift If the orbital has more nodes in the stretching direction, its site energy will be more prone to change, namely, more stronger scattering by acoustic phonon.50 To explain clearly, the highest occupied crystal orbital (HOCO) and lowest unoccupied crystal orbital (LUCO) of 3-, 4-, 6-, 7-AGyNR, and 5-ZGyNR at Γ-point are showed in Fig.4 The HOCO of 3-AGyNR exhibit bonding character, therefore it has less nodes in the lattice dilating x-direction Whereas the LUCO exhibits anti-bonding character so

it has more nodes, which makes the electrons more strongly scattered by the acoustic phonon than holes Therefore, the electrons have larger deformation potential than the holes However, the case is just the reverse for 4-AGyNR When N ≥6, the bonding characteristic of the frontier crystal orbitals with odd or even N is just contrary to the situation for N<6 As shown in Fig.4(c)and4(d), the HOCO of 6-AGyNR exhibits bonding character but the LUCO shows anti-bonding character As

a representative, the FCOs of 5-ZGyNRs are given in Fig 4(e) It can be seen that the bonding

or anti-bonding character in the two frontier crystal orbitals is not obvious, leading to smaller

difference of magnitude between µhand µe

Obviously, the variation of the mobility with change of the NRs for GyNRs is significantly

different from that for graphene NRs, which shows the distinct alternating change49 with the NR width increasing and can be grouped into three families with N=3l, 3l + 1, 3l + 2 This indicates insertion of -C≡C- into graphene can significantly change the transportation property of original graphene In addition, the variation in the mobility for GyNRs is also different from that for graphdiyne NRs which show monotonically increasing as the NR width increase.20This manifests that the different ratio of sp1/sp2 lead to different transportation property (the ratio of sp1/sp2 is 41.67 % in 6,6,12-graphyne and 50% in graphdiyne) for these graphene-derived nanoribbons These are due mainly to that the different ratio of sp1/sp2leads to different structures

Finally, we calculate Young’s modulus Y which is used to describe the stiffness of 1D GyNRs The values of Young’s modulus are also listed in TableII It can be seen that the Young’s modulus are of 559–769 GPa for AGyNRs and 568–721 GPa for ZGyNRs There is no obvious difference

in the values of Young’s modulus, indicating the elastic property of GyNRs is nearly independent

on edges and widths According to the previous work,20we know that the Young’s modulus of the graphene NRs can reach as high as about 1000 GPa at the same computational level, significantly larger than those of GyNRs This is because the graphene NRs have more compact net structure than the GyNRs

IV CONCLUSIONS

We present a detailed analysis of the stability, electronic property and carrier mobility of the GyNRs using the SCF-CO method based on DFT calculations Our results show that all these 1D GyNRs are more stable than the 2D 6,6,12-graphyne in the view of the Gibbs free energy Different

077153-9 Ding, Bai, and Huang AIP Advances 5, 077153 (2015)

from the graphene NRs, the ZGyNRs are more stable than the AGyNRs with the same width The calculated band structures show that these GyNRs are all semiconductors The gap dependence of these GyNRs on the NR width is different from that of α-graphyne NRs and γ-graphyne NRs The band gaps of AGyNRs are not changed monotonically with the NR width, but those of ZGyNRs monotonically decrease with width increasing Moreover, both AGyNRs and ZGyNRs tend to have similar band gaps at center and edge of Brillouin zone The carrier mobility is calculated to reach the order of 105cm2V−1s−1based on DP theory and effective mass approximation, which is compa-rable to that of graphene NRs Also, it is found that the mobilities of electron and hole for AGyNRs exhibit oscillation while the mobilities of hole are always larger than those of electron for ZGyNRs These differences come from the deformation potential constants which characterize the coupling strength of the charge carrier with the acoustic phonons Finally, we calculate the Young moduli of these GyNRs and find the elastic properties of these GyNRs with different edges and widths don’t present much difference and these GyNRs are softer than graphene NRs as a result of the inserting acetylenic linkage

ACKNOWLEDGEMENTS

This work is supported by the National Natural Science Foundation of China (Grant No

20873009 and 21363017)

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