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graphene heterostructure nanoribbons
Solid State Communications 211 (2015) 23–28
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
First-principles study on the electronic and magnetic properties of armchair graphane/graphene heterostructure nanoribbons W.X. Zhang a,n, C. He b,n, T. Li a, S.B. Gong a, L. Zhao a, J.Y. Tao a a b
School of Materials Science and Engineering, Chang’an University, Xi’an 710064, China State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China
art ic l e i nf o
a b s t r a c t
Article history: Received 11 February 2015 Received in revised form 16 March 2015 Accepted 17 March 2015 Communicated by Ralph Gebauer Available online 26 March 2015
In this paper, the electronic and magnetic properties of electronic and magnetic properties of armchair graphane/graphene heterostructure nanoribbons (AGA/GNRs) have been systematically investigated by first-principles calculations based on density functional theory. The calculated results indicate that 13armchair graphane nanoribbon (13-AGANR), 13-armchair graphene nanoribbons (13-AGNR) and hybrid armchair graphane/graphene nanoribbons (AGA13 x/GxNRs) are all direct semiconductors (13, 13 x and x are denoted as the nanoribbons’ widths). The band structures near the Fermi level of AGA13 x/GxNRs are mainly determined by the graphene section and the atomic charge transfers in the interface of AGA13 x/GxNRs are stronger. AGA7/G6NR with DB defects at AGANR edge obviously affect the magnetic properties. These diverse and tunable electronic and magnetic properties can be a theoretical guidance for the design of novel nanoelectronic devices. & 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Graphene nanoribbon D. Electronic properties E. First-principles
1. Introduction Graphene consists of a hexagonal monolayer network of sp2-hybridized carbon atoms. Since graphene was first experimentally fabricated in 2004 [1], graphene monolayers has motivated considerable interest in variety of one-atom-thick two-dimensional (2D) crystals [2–4], especially after large-scale synthesis methods like chemical vapor-deposition [6] and epitaxial growth [7] on metal and SiC substrates are developed. The quasi-one-dimensional (1D) graphene ribbons (GNRs) with armchair or zigzag edges have attracted much attention because of their electronic [8–11], magnetic [12,13], and quantum-transport properties [14,15]. A graphene nanoribbons (GNRs) can be realized by cutting mechanically exfoliated graphene or patterning epitaxially grown graphene structures [16,17]. Recently, the fascinating electronic properties associated with one-dimensional (1D) fully and partially hydrogenated graphene [18,19], graphane [20], BN [21], ZnO [22], SiC [23], GaN [24], and AlN [24,25] nanoribbons derived from either monolayer or multilayer sheets heavily depend on the ribbons’ width, thickness and edge modification. The fully and partially hydrogenated nanoribbons exhibit completely distinct properties from their pristine forms. The high quality graphane nanoribbons GANRs can be fabricated by selectively hydrogenating graphene or by carving GNRs on a graphane sheet [26,27]. Furthermore, hybrid graphane/graphene nanoribbons (GA/GNRs) could exhibit unique electronic properties that differ from the pristine armchair (AGNRs) and
zigzag GNRs (ZGNRs) [28,29]. These suggest such ribbon-hybridized graphene-like materials as promising candidates for applications in future electronic and optoelectronic nanodevices. Therefore, serious efforts are highly warranted to explore the physical properties of GNR for various technological applications. Yet a systematically theoretical understanding of electronic properties of these functionalized armchair graphane/graphene nanoribbons (AGA/GNRs) remains unclear. How and to what extent does the ratio of GA affect the electronic properties of different GA/GE NRs systems? Because the interaction of hydrogen with graphene is of great technological interest, compared with the unsaturated nanoribbon, how would its band gap change in a hydrogenated AGNRs? Therefore, the above questions are discussed in this paper. The structural, electronic properties of hybrid AGA/GNRs with the variation of the proportion are extensive carried out based on firstprinciples calculations with density functional theory (DFT). Meanwhile, Band structure distribution (BS), the Density of States (DOS), atom Mulliken charges and the population analysis are performed to determine changes of atomic and electronic structures of hybrid AGA/ GNRs. These studies provide us a deep understanding of the novel properties of AGA/GNRs, which is essential to employ them as building blocks for future nanodevices.
2. Computational methods n
Corresponding authors. E-mail addresses: [email protected] (W.X. Zhang), [email protected] (C. He). http://dx.doi.org/10.1016/j.ssc.2015.03.014 0038-1098/& 2015 Elsevier Ltd. All rights reserved.
The simulation is calculated by first-principles DFT, which is provided by DMOL3 [30–32]. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof scheme (PBE) [33] is
24
W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
employed to optimize geometrical structures and calculate properties. The all-electron relativistic Kohn–Sham wave functions are expanded in the local atomic orbital basis set for DMOL3 [30]. Pseudopotentials with C–2s22p2, and H–1s1 valence electron configurations are used for C and H atoms. Similar functional have been
successfully used to study the structural and electronic properties of water, Si and Cu nanowires [34,35]. The nearest distance between for edge–edge and layer–layer in neighboring cells is greater than 15 Å to ensure no interactions. For geometry optimization, both the cell and the atomic positions are allowed to fully relax. The Brillouin
Fig. 1. Schematic illustration of supercell 13-AGANR (a) and 13-AGNR (b) arrangements, where the gray and white spheres are C and H atoms, respectively.
Fig. 2. Band structure, Partial DOS and charge density isosurfaces of LUMO and HOMO at Gamma point of 13-AGANR (a) and 13-AGNR (b). The Ef is set to zero. Blue and yellow denote the positive and negative wave function contours, respectively, and the value of the isosurfaces is 0.025 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
zone is sampled by 1 8 1 k-points for all structures in the geometry optimization calculations, which brings out the convergence tolerance of energy of 1.0 10 5 Ha (1 Ha¼27.2114 eV), maximum force of 0.002 Ha/Å, and maximum displacement of 0.005 Å [34,35]. The electronic distributions of AGA/GENRs are carried out by Mulliken charge analysis, which is performed using a projection of a Linear Combination of Atomic Orbitals (LCAO) basis and to specify quantities such as atomic charge, bond population, charge transfer etc. LCAO supplies better information regarding the localization of the electrons in different atomic layers than a plane wave basis set does [36]. The obtained relative values of the charge e, but not the absolute magnitude, display a high degree of sensitivity to the atomic basis set and a relative distribution of charge [37,38]. To evaluate the structural stability of the hybrid AGA/GNRs, we calculated the formation energies for different systems. The formation energy (Ef) is expressed as Ef ¼Etot (χCμC þ χHμH), where Etot is the cohesive energy per atom of hybrid AGA/GNRs, μC is the cohesive energy per atom of the graphene single layer, μH is half of the binding energy of H2, and χC (χH) is molar fraction of the atom in the nanoribbons (H atom) [20,39].
25
3. Results and discussion In our simulation, the host AGANRs with W¼13 is represented by a supercell of C52H60, where the ribbon width (W) is defined by the number the total number of C–C chains across the ribbon width. In the armchair graphane nanoribbon (13-AGANR) configuration, every two adjacent C atoms are hydrogenated from the opposite sides of the graphene plane. The obtained C–C and C–H bond lengths of graphane are 1.529 and 1.109 Å, respectively, which are in good agreement with the previous reported data [4]. The supercells used for the 13-AGANR and 13-AGNR are shown in Fig. 1a and b, respectively. In addition, the edge C atoms of the considered structures are passivated with H atoms. After relaxation, 13-AGNR is completely flat. In this case, the geometry change is obvious: the atoms converge to just one planar layer, accompanied by a little C–C (1.450 Å) and C–H (1.087 Å) contraction. The electronic structures of 13-AGANR and 13-AGNR are also investigated here. Fig. 2 shows BS, Partial DOS and the corresponding charge density isosurfaces of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) at Gamma point of the two structures. Both of the 13-AGANR and 13AGNR are nonmagnetic semiconductors, and the direct band gaps are
Fig. 3. Schematic illustration of AGA13 x/GxNRs (x¼ 2, 4, 6, 8, 10 and 12) with H terminated at both edges. The x and 13 x are the number of armchair graphane and graphene chains, respectively.
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W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
4.68, and 0.79 eV, respectively, which are corresponding to other theoretical values of 3.84 and 0.83 eV by DFT studies [20,29,40]. In comparison, some differences in HOMO and LUMO can be observed between 13-AGANR and 13-AGNR. In 13-AGANR (Fig. 2a), HOMO and LUMO orbitals distribute mainly along the C–C bonds. However, the densities are inhomogeneous over the whole region, much weak in the edge area. While in 13-AGNR (Fig. 2b), the charge densities are concentrated homogenously along the C–C bonds over the whole framework. Moreover, the charge densities of LUMO orbitals are mainly centered at single C atoms, which seems strong in the interior area. In addition, HOMO orbitals distribute mainly along the periodical direction. Similarly, the armchair graphane/graphene heterostructure nanoribbons (AGA13 x/GxNRs) are also constructed by removing H atoms from the 13-AGANR. The x and 13 x are the number of armchair graphane and graphene chains, respectively. Thus, the geometry structures of AGA13 x/GxNRs (x¼2, 4, 6, 8, 10 and 12) with H terminated at both edges are shown in Fig. 3a–e. After relaxation, the graphene regions for each systems are completely flat. However, since the hybridization of the C atoms at the interfaces changes from sp3 in graphane to sp2 in graphene, the interfaces are not flat. At the interface of graphane–graphene heterostructure, the adjacent C atoms bonded to the hydrogen move out of the plane in opposite directions,
which is similar to the case of triangular graphene nanoflakes embedded in graphane [4]. The average C–C bond length at the interface are 1.509 Å, between the C–C bond length of 13-AGANR (1.529 Å) and 13-AGNR (1.450 Å). It is also investigated in the present work by performing spinpolarized and non spin-polarized calculations for AGA13 x/GxNRs shown in Fig. 4a–f. The obtained results show that almost no energy difference can be found for them between these two methods, indicating that all AGA13 x/GxNRs exhibit the nonmagnetic characteristics. The band structures of AGA13 x/GxNRs indicate that they are all direct semiconductors since both LUMO orbitals and HOMO orbitals at Gamma point. Eg values vary with the composition and the corresponding Eg values of each AGAx/ G13 xNRs are 1.02, 2.41, 1.39, 0.51, 1.05 and 0.81 eV, respectively. Moreover, in order to deeply describe the electronic structure of AGA13 x/GxNRs, the corresponding electronic distributions at the Gamma point have been explored. For all the semiconducting systems AGA13 x/GxNRs, the electronic distributions of bands display similar behaviors. Thus, taken the system AGA7/G6NR as an example (in Fig. 4c), HOMO and LUMO orbitals are primarily localized on the right part of the structure, which mean that Eg values of AGA13 x/GxNRs is dominated by the graphene rather than graphane. Moreover, both of the electronic distribution for
Fig. 4. Band Structures of AGA13 x/GxNRs (x ¼2, 4, 6, 8, 10 and 12) with H terminated at both edges. HOMO and LUMO orbitals of AGA7/G6NR. Fermi level is set to zero.
W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
HOMO and LUMO orbitals also distribute along C–C bonds. However, the densities of HOMO orbitals are symmetric along the periodic direction, while LUMO are mainly centered at single C atoms in width direction of nanoribbon. In Fig. 4g, we show the width dependence of band gap of AGA7/ G6NR. It is clear that like as AGNRs [27,28], the variation is also separated into three different groups (3p, 3pþ1, 3pþ2), where p is a non-negative integer. The results are corresponding to the electronic distributions of HOMO and LUMO orbitals at the Gamma point and the band structures near the Fermi level of AGA13 x/GxNRs are thus mainly determined by the graphene section. The atomic charge transfers in 13-AGANR and 13-AGNR are analyzed by the Mulliken charge analysis [35] and the corresponding results are shown in Table 1. The location of the sites is shown in Fig. 1. The results indicate that the same atoms at the edge (inner) are equivalent and eC ¼ 0.138 ( 0.061) and eH ¼ 0.084 (0.063) for AGANR. Meanwhile, for AGNR, at the edge, eC ¼ 0.096 and eH ¼0.075. With the C atoms away from the edge, the changes of C atoms at sites I1, I2 and I3 (I is short for Inner) are 0.011, 0.08, and 0.03, respectively. Therefore, the C atom at the edge of AGANR ( 0.138) is more chemically active than the one AGANR (0.096) because it has more electrons. Similarly, the atomic charges of AGA13 x/GxNRs are also calculated by the Mulliken charge analysis [35]. Taken the system AGA7/G6NR as an example (in Fig. 3c), the atomic charges of atoms near the interface are shown in Table 1. The location of the sites is shown in Fig. 3. The interface atoms at site D (0.134) are more charged than other atoms. At the interface, C atoms are more negative and the corresponding H atoms are more positive. While the sites away from the interface, the charge distributions are weaker. Thus, an interface influences mainly the atoms at the conjunction of AGANR and AGNR. It is known that the atomic charge is mostly affected by the atoms belonging to the same carbon ring, especially the nearest atoms. For the carbon and hydrogen atoms at site E, they have similar nearest atoms as sites in graphane region far apart from the interface, where the three nearest C atoms are bonded by sp3 orbitals. For the C and H atoms at site D, only two nearest C atoms are bonded by sp3 orbitals; the other one on its right hand side at site C is bonded by sp2 orbitals. Therefore, the effect of the interface on site D is stronger than that on site E. Therefore, the C atom at site D ( 0.134) is more chemically active than the one at site E ( 0.080). It is well-known that DB (dangling band) defects around the vacancy sites or at the tips significantly influences their electronic properties [41]. Therefore, in present work, we investigate the spin-polarized band structures of AGA7/G6NR with DB defects at AGANR and AGNR edges. Both of them are still semiconductors with direct band gaps, the direct band gaps of AGA7/G6NR with DB defects at AGANR and AGNR edges are 1.306 eV and 0.93 eV,
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respectively. When AGA7/G6NR with DB defects at AGNR edge, the up-spin and down-spin are fully superimposed. While in AGA7/G6NR with DB defects at AGANR edge, the asymmetry of BS between the up and down spins is slightly enlarged at the Fermi level, which is shown in Fig. 5a. To deeply study the electronic and magnetic properties of AGA7/ G6NR with DB defects at AGANR edge, the spin density distribution (Δρ ¼ ρup ρdown) of AGA7/G6NR with DB defects at AGANR edge are shown in Fig. 5b. A significant fact can be seen that the net spin-up
Fig. 5. (a) Band structure, (b) DOS and (c) isosurfaces of the spin density distribution (Δρ ¼ρup ρdown) of AGA7/G6NR with DB defects at AGANR edge. The black lines and the red lines represent the spin up and down bands, respectively. Fermi level is set to zero. Dark blue and light orange surfaces correspond to the isosurfaces of up (positive) and down (negative) spin density. The isosurfaces are set to be 7 0.001 electrons/au3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Atom Mulliken charges of 13-AGANR, 13-AGNR, and AGA7/G6NR. The location of the sites is shown in Figs. 1 and 3. The unit of charge is e. Structure
Atom site
C atom
H atom
AGANR
Edge Inner Edge I1 I2 I3 A B C D E F G
0.138 0.061 0.096 0.011 0.008 0.003 0.007 0.007 0.029 0.134 0.080 0.062 0.062
0.084 0.063 0.075
AGNR
AGA7/G6NR
0.102 0.074 0.067 0.065
Fig. 6. The formation energies of 13-AGANR, AGA13 x/GxNRs, and 13-AGNR. (a–f) Denote the structures of AGA13 x/GxNRs (x¼ 2, 4, 6, 8, 10 and 12), respectively. The solid line serves as a guide to the eye.
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W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
charge mainly accumulates at the dangling C atoms, resulting in a magnetic moment of 2.0 μB per supercell. This is in good agreement of the previous calculated results of DOS in Fig. 5a. It is important to discuss the experimental preparation of hybrid AGA/GNRs. To evaluate the structural stability of the hybrid AGA/GNRs, we calculated the formation energies for 13-AGANR, AGA13 x/GxNRs and 13-AGNR, which are shown in Fig. 6. According to this definition, a system with smaller Ef value is more favorable. The formation energy increases monotonically with decreasing the molar fraction of the H atoms. The negative formation energies indicate that AGA13 x/GxNRs are more stable than the experimentally available 13-AGNR. which suggests that AGA13 x/GxNRs are more likely to be accessible.
4. Conclusions In summary, we have systematically investigated atomic Mulliken charges, electronic and magnetic properties of armchair graphane/graphene heterostructure nanoribbons by using firstprinciples calculations based on DFT. The calculated results reveal that 13-AGANR, 13-AGNR and hybrid AGA13 x/GxNRs are all direct semiconductors since both LUMO orbitals and HOMO orbitals at Gamma point. The band structures near the Fermi level of AGA13 x/GxNRs are mainly determined by the graphene section and the atomic charge transfers in the interface of AGA13 x/GxNRs are stronger. Meanwhile, AGA7/G6NR with DB defects at AGANR edge obviously affect the magnetic properties results in a magnetic moment of 2.0 μB per supercell, which is more favorable for the design of novel nanoelectronic devices.
Acknowledgements The authors acknowledge supports by National Natural Science Foundation of China (NSFC, nos. 51177006, 51301020 and 51471124), Natural Science Foundation of Shaanxi province, China (2014JQ6196), Ph.D. Programs Foundation of Ministry of Education of China (Grant no. 20110201120002), the special fund for basic scientific research of central colleges of Chang’an University (no. 2013G1311053) and State Key Laboratory for Mechanical Behavior of Materials.
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Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
First-principles study on the electronic and magnetic properties of armchair graphane/graphene heterostructure nanoribbons W.X. Zhang a,n, C. He b,n, T. Li a, S.B. Gong a, L. Zhao a, J.Y. Tao a a b
School of Materials Science and Engineering, Chang’an University, Xi’an 710064, China State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China
art ic l e i nf o
a b s t r a c t
Article history: Received 11 February 2015 Received in revised form 16 March 2015 Accepted 17 March 2015 Communicated by Ralph Gebauer Available online 26 March 2015
In this paper, the electronic and magnetic properties of electronic and magnetic properties of armchair graphane/graphene heterostructure nanoribbons (AGA/GNRs) have been systematically investigated by first-principles calculations based on density functional theory. The calculated results indicate that 13armchair graphane nanoribbon (13-AGANR), 13-armchair graphene nanoribbons (13-AGNR) and hybrid armchair graphane/graphene nanoribbons (AGA13 x/GxNRs) are all direct semiconductors (13, 13 x and x are denoted as the nanoribbons’ widths). The band structures near the Fermi level of AGA13 x/GxNRs are mainly determined by the graphene section and the atomic charge transfers in the interface of AGA13 x/GxNRs are stronger. AGA7/G6NR with DB defects at AGANR edge obviously affect the magnetic properties. These diverse and tunable electronic and magnetic properties can be a theoretical guidance for the design of novel nanoelectronic devices. & 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Graphene nanoribbon D. Electronic properties E. First-principles
1. Introduction Graphene consists of a hexagonal monolayer network of sp2-hybridized carbon atoms. Since graphene was first experimentally fabricated in 2004 [1], graphene monolayers has motivated considerable interest in variety of one-atom-thick two-dimensional (2D) crystals [2–4], especially after large-scale synthesis methods like chemical vapor-deposition [6] and epitaxial growth [7] on metal and SiC substrates are developed. The quasi-one-dimensional (1D) graphene ribbons (GNRs) with armchair or zigzag edges have attracted much attention because of their electronic [8–11], magnetic [12,13], and quantum-transport properties [14,15]. A graphene nanoribbons (GNRs) can be realized by cutting mechanically exfoliated graphene or patterning epitaxially grown graphene structures [16,17]. Recently, the fascinating electronic properties associated with one-dimensional (1D) fully and partially hydrogenated graphene [18,19], graphane [20], BN [21], ZnO [22], SiC [23], GaN [24], and AlN [24,25] nanoribbons derived from either monolayer or multilayer sheets heavily depend on the ribbons’ width, thickness and edge modification. The fully and partially hydrogenated nanoribbons exhibit completely distinct properties from their pristine forms. The high quality graphane nanoribbons GANRs can be fabricated by selectively hydrogenating graphene or by carving GNRs on a graphane sheet [26,27]. Furthermore, hybrid graphane/graphene nanoribbons (GA/GNRs) could exhibit unique electronic properties that differ from the pristine armchair (AGNRs) and
zigzag GNRs (ZGNRs) [28,29]. These suggest such ribbon-hybridized graphene-like materials as promising candidates for applications in future electronic and optoelectronic nanodevices. Therefore, serious efforts are highly warranted to explore the physical properties of GNR for various technological applications. Yet a systematically theoretical understanding of electronic properties of these functionalized armchair graphane/graphene nanoribbons (AGA/GNRs) remains unclear. How and to what extent does the ratio of GA affect the electronic properties of different GA/GE NRs systems? Because the interaction of hydrogen with graphene is of great technological interest, compared with the unsaturated nanoribbon, how would its band gap change in a hydrogenated AGNRs? Therefore, the above questions are discussed in this paper. The structural, electronic properties of hybrid AGA/GNRs with the variation of the proportion are extensive carried out based on firstprinciples calculations with density functional theory (DFT). Meanwhile, Band structure distribution (BS), the Density of States (DOS), atom Mulliken charges and the population analysis are performed to determine changes of atomic and electronic structures of hybrid AGA/ GNRs. These studies provide us a deep understanding of the novel properties of AGA/GNRs, which is essential to employ them as building blocks for future nanodevices.
2. Computational methods n
Corresponding authors. E-mail addresses: [email protected] (W.X. Zhang), [email protected] (C. He). http://dx.doi.org/10.1016/j.ssc.2015.03.014 0038-1098/& 2015 Elsevier Ltd. All rights reserved.
The simulation is calculated by first-principles DFT, which is provided by DMOL3 [30–32]. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof scheme (PBE) [33] is
24
W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
employed to optimize geometrical structures and calculate properties. The all-electron relativistic Kohn–Sham wave functions are expanded in the local atomic orbital basis set for DMOL3 [30]. Pseudopotentials with C–2s22p2, and H–1s1 valence electron configurations are used for C and H atoms. Similar functional have been
successfully used to study the structural and electronic properties of water, Si and Cu nanowires [34,35]. The nearest distance between for edge–edge and layer–layer in neighboring cells is greater than 15 Å to ensure no interactions. For geometry optimization, both the cell and the atomic positions are allowed to fully relax. The Brillouin
Fig. 1. Schematic illustration of supercell 13-AGANR (a) and 13-AGNR (b) arrangements, where the gray and white spheres are C and H atoms, respectively.
Fig. 2. Band structure, Partial DOS and charge density isosurfaces of LUMO and HOMO at Gamma point of 13-AGANR (a) and 13-AGNR (b). The Ef is set to zero. Blue and yellow denote the positive and negative wave function contours, respectively, and the value of the isosurfaces is 0.025 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
zone is sampled by 1 8 1 k-points for all structures in the geometry optimization calculations, which brings out the convergence tolerance of energy of 1.0 10 5 Ha (1 Ha¼27.2114 eV), maximum force of 0.002 Ha/Å, and maximum displacement of 0.005 Å [34,35]. The electronic distributions of AGA/GENRs are carried out by Mulliken charge analysis, which is performed using a projection of a Linear Combination of Atomic Orbitals (LCAO) basis and to specify quantities such as atomic charge, bond population, charge transfer etc. LCAO supplies better information regarding the localization of the electrons in different atomic layers than a plane wave basis set does [36]. The obtained relative values of the charge e, but not the absolute magnitude, display a high degree of sensitivity to the atomic basis set and a relative distribution of charge [37,38]. To evaluate the structural stability of the hybrid AGA/GNRs, we calculated the formation energies for different systems. The formation energy (Ef) is expressed as Ef ¼Etot (χCμC þ χHμH), where Etot is the cohesive energy per atom of hybrid AGA/GNRs, μC is the cohesive energy per atom of the graphene single layer, μH is half of the binding energy of H2, and χC (χH) is molar fraction of the atom in the nanoribbons (H atom) [20,39].
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3. Results and discussion In our simulation, the host AGANRs with W¼13 is represented by a supercell of C52H60, where the ribbon width (W) is defined by the number the total number of C–C chains across the ribbon width. In the armchair graphane nanoribbon (13-AGANR) configuration, every two adjacent C atoms are hydrogenated from the opposite sides of the graphene plane. The obtained C–C and C–H bond lengths of graphane are 1.529 and 1.109 Å, respectively, which are in good agreement with the previous reported data [4]. The supercells used for the 13-AGANR and 13-AGNR are shown in Fig. 1a and b, respectively. In addition, the edge C atoms of the considered structures are passivated with H atoms. After relaxation, 13-AGNR is completely flat. In this case, the geometry change is obvious: the atoms converge to just one planar layer, accompanied by a little C–C (1.450 Å) and C–H (1.087 Å) contraction. The electronic structures of 13-AGANR and 13-AGNR are also investigated here. Fig. 2 shows BS, Partial DOS and the corresponding charge density isosurfaces of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) at Gamma point of the two structures. Both of the 13-AGANR and 13AGNR are nonmagnetic semiconductors, and the direct band gaps are
Fig. 3. Schematic illustration of AGA13 x/GxNRs (x¼ 2, 4, 6, 8, 10 and 12) with H terminated at both edges. The x and 13 x are the number of armchair graphane and graphene chains, respectively.
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4.68, and 0.79 eV, respectively, which are corresponding to other theoretical values of 3.84 and 0.83 eV by DFT studies [20,29,40]. In comparison, some differences in HOMO and LUMO can be observed between 13-AGANR and 13-AGNR. In 13-AGANR (Fig. 2a), HOMO and LUMO orbitals distribute mainly along the C–C bonds. However, the densities are inhomogeneous over the whole region, much weak in the edge area. While in 13-AGNR (Fig. 2b), the charge densities are concentrated homogenously along the C–C bonds over the whole framework. Moreover, the charge densities of LUMO orbitals are mainly centered at single C atoms, which seems strong in the interior area. In addition, HOMO orbitals distribute mainly along the periodical direction. Similarly, the armchair graphane/graphene heterostructure nanoribbons (AGA13 x/GxNRs) are also constructed by removing H atoms from the 13-AGANR. The x and 13 x are the number of armchair graphane and graphene chains, respectively. Thus, the geometry structures of AGA13 x/GxNRs (x¼2, 4, 6, 8, 10 and 12) with H terminated at both edges are shown in Fig. 3a–e. After relaxation, the graphene regions for each systems are completely flat. However, since the hybridization of the C atoms at the interfaces changes from sp3 in graphane to sp2 in graphene, the interfaces are not flat. At the interface of graphane–graphene heterostructure, the adjacent C atoms bonded to the hydrogen move out of the plane in opposite directions,
which is similar to the case of triangular graphene nanoflakes embedded in graphane [4]. The average C–C bond length at the interface are 1.509 Å, between the C–C bond length of 13-AGANR (1.529 Å) and 13-AGNR (1.450 Å). It is also investigated in the present work by performing spinpolarized and non spin-polarized calculations for AGA13 x/GxNRs shown in Fig. 4a–f. The obtained results show that almost no energy difference can be found for them between these two methods, indicating that all AGA13 x/GxNRs exhibit the nonmagnetic characteristics. The band structures of AGA13 x/GxNRs indicate that they are all direct semiconductors since both LUMO orbitals and HOMO orbitals at Gamma point. Eg values vary with the composition and the corresponding Eg values of each AGAx/ G13 xNRs are 1.02, 2.41, 1.39, 0.51, 1.05 and 0.81 eV, respectively. Moreover, in order to deeply describe the electronic structure of AGA13 x/GxNRs, the corresponding electronic distributions at the Gamma point have been explored. For all the semiconducting systems AGA13 x/GxNRs, the electronic distributions of bands display similar behaviors. Thus, taken the system AGA7/G6NR as an example (in Fig. 4c), HOMO and LUMO orbitals are primarily localized on the right part of the structure, which mean that Eg values of AGA13 x/GxNRs is dominated by the graphene rather than graphane. Moreover, both of the electronic distribution for
Fig. 4. Band Structures of AGA13 x/GxNRs (x ¼2, 4, 6, 8, 10 and 12) with H terminated at both edges. HOMO and LUMO orbitals of AGA7/G6NR. Fermi level is set to zero.
W.X. Zhang et al. / Solid State Communications 211 (2015) 23–28
HOMO and LUMO orbitals also distribute along C–C bonds. However, the densities of HOMO orbitals are symmetric along the periodic direction, while LUMO are mainly centered at single C atoms in width direction of nanoribbon. In Fig. 4g, we show the width dependence of band gap of AGA7/ G6NR. It is clear that like as AGNRs [27,28], the variation is also separated into three different groups (3p, 3pþ1, 3pþ2), where p is a non-negative integer. The results are corresponding to the electronic distributions of HOMO and LUMO orbitals at the Gamma point and the band structures near the Fermi level of AGA13 x/GxNRs are thus mainly determined by the graphene section. The atomic charge transfers in 13-AGANR and 13-AGNR are analyzed by the Mulliken charge analysis [35] and the corresponding results are shown in Table 1. The location of the sites is shown in Fig. 1. The results indicate that the same atoms at the edge (inner) are equivalent and eC ¼ 0.138 ( 0.061) and eH ¼ 0.084 (0.063) for AGANR. Meanwhile, for AGNR, at the edge, eC ¼ 0.096 and eH ¼0.075. With the C atoms away from the edge, the changes of C atoms at sites I1, I2 and I3 (I is short for Inner) are 0.011, 0.08, and 0.03, respectively. Therefore, the C atom at the edge of AGANR ( 0.138) is more chemically active than the one AGANR (0.096) because it has more electrons. Similarly, the atomic charges of AGA13 x/GxNRs are also calculated by the Mulliken charge analysis [35]. Taken the system AGA7/G6NR as an example (in Fig. 3c), the atomic charges of atoms near the interface are shown in Table 1. The location of the sites is shown in Fig. 3. The interface atoms at site D (0.134) are more charged than other atoms. At the interface, C atoms are more negative and the corresponding H atoms are more positive. While the sites away from the interface, the charge distributions are weaker. Thus, an interface influences mainly the atoms at the conjunction of AGANR and AGNR. It is known that the atomic charge is mostly affected by the atoms belonging to the same carbon ring, especially the nearest atoms. For the carbon and hydrogen atoms at site E, they have similar nearest atoms as sites in graphane region far apart from the interface, where the three nearest C atoms are bonded by sp3 orbitals. For the C and H atoms at site D, only two nearest C atoms are bonded by sp3 orbitals; the other one on its right hand side at site C is bonded by sp2 orbitals. Therefore, the effect of the interface on site D is stronger than that on site E. Therefore, the C atom at site D ( 0.134) is more chemically active than the one at site E ( 0.080). It is well-known that DB (dangling band) defects around the vacancy sites or at the tips significantly influences their electronic properties [41]. Therefore, in present work, we investigate the spin-polarized band structures of AGA7/G6NR with DB defects at AGANR and AGNR edges. Both of them are still semiconductors with direct band gaps, the direct band gaps of AGA7/G6NR with DB defects at AGANR and AGNR edges are 1.306 eV and 0.93 eV,
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respectively. When AGA7/G6NR with DB defects at AGNR edge, the up-spin and down-spin are fully superimposed. While in AGA7/G6NR with DB defects at AGANR edge, the asymmetry of BS between the up and down spins is slightly enlarged at the Fermi level, which is shown in Fig. 5a. To deeply study the electronic and magnetic properties of AGA7/ G6NR with DB defects at AGANR edge, the spin density distribution (Δρ ¼ ρup ρdown) of AGA7/G6NR with DB defects at AGANR edge are shown in Fig. 5b. A significant fact can be seen that the net spin-up
Fig. 5. (a) Band structure, (b) DOS and (c) isosurfaces of the spin density distribution (Δρ ¼ρup ρdown) of AGA7/G6NR with DB defects at AGANR edge. The black lines and the red lines represent the spin up and down bands, respectively. Fermi level is set to zero. Dark blue and light orange surfaces correspond to the isosurfaces of up (positive) and down (negative) spin density. The isosurfaces are set to be 7 0.001 electrons/au3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Atom Mulliken charges of 13-AGANR, 13-AGNR, and AGA7/G6NR. The location of the sites is shown in Figs. 1 and 3. The unit of charge is e. Structure
Atom site
C atom
H atom
AGANR
Edge Inner Edge I1 I2 I3 A B C D E F G
0.138 0.061 0.096 0.011 0.008 0.003 0.007 0.007 0.029 0.134 0.080 0.062 0.062
0.084 0.063 0.075
AGNR
AGA7/G6NR
0.102 0.074 0.067 0.065
Fig. 6. The formation energies of 13-AGANR, AGA13 x/GxNRs, and 13-AGNR. (a–f) Denote the structures of AGA13 x/GxNRs (x¼ 2, 4, 6, 8, 10 and 12), respectively. The solid line serves as a guide to the eye.
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charge mainly accumulates at the dangling C atoms, resulting in a magnetic moment of 2.0 μB per supercell. This is in good agreement of the previous calculated results of DOS in Fig. 5a. It is important to discuss the experimental preparation of hybrid AGA/GNRs. To evaluate the structural stability of the hybrid AGA/GNRs, we calculated the formation energies for 13-AGANR, AGA13 x/GxNRs and 13-AGNR, which are shown in Fig. 6. According to this definition, a system with smaller Ef value is more favorable. The formation energy increases monotonically with decreasing the molar fraction of the H atoms. The negative formation energies indicate that AGA13 x/GxNRs are more stable than the experimentally available 13-AGNR. which suggests that AGA13 x/GxNRs are more likely to be accessible.
4. Conclusions In summary, we have systematically investigated atomic Mulliken charges, electronic and magnetic properties of armchair graphane/graphene heterostructure nanoribbons by using firstprinciples calculations based on DFT. The calculated results reveal that 13-AGANR, 13-AGNR and hybrid AGA13 x/GxNRs are all direct semiconductors since both LUMO orbitals and HOMO orbitals at Gamma point. The band structures near the Fermi level of AGA13 x/GxNRs are mainly determined by the graphene section and the atomic charge transfers in the interface of AGA13 x/GxNRs are stronger. Meanwhile, AGA7/G6NR with DB defects at AGANR edge obviously affect the magnetic properties results in a magnetic moment of 2.0 μB per supercell, which is more favorable for the design of novel nanoelectronic devices.
Acknowledgements The authors acknowledge supports by National Natural Science Foundation of China (NSFC, nos. 51177006, 51301020 and 51471124), Natural Science Foundation of Shaanxi province, China (2014JQ6196), Ph.D. Programs Foundation of Ministry of Education of China (Grant no. 20110201120002), the special fund for basic scientific research of central colleges of Chang’an University (no. 2013G1311053) and State Key Laboratory for Mechanical Behavior of Materials.
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