graphene nanoribbons

Accepted Manuscript Electronic transport through hybrid armchair graphane/graphene nanoribbons

W. Liu, F.H. Meng, J.H. Zhao, X.H. Jiang PII:

S0921-4526(18)30677-X

DOI:

10.1016/j.physb.2018.11.001

Reference:

PHYSB 311136

To appear in:

Physica B: Physics of Condensed Matter

Received Date:

12 July 2018

Accepted Date:

01 November 2018

Please cite this article as: W. Liu, F.H. Meng, J.H. Zhao, X.H. Jiang, Electronic transport through hybrid armchair graphane/graphene nanoribbons, Physica B: Physics of Condensed Matter (2018), doi: 10.1016/j.physb.2018.11.001

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ACCEPTED MANUSCRIPT

Electronic transport through hybrid armchair graphane/graphene nanoribbons W. Liu*, F.H. Meng, J.H. Zhao, X.H. Jiang Physics and Informational Engineering Department, Jining University, Qufu 273155, China Abstract Modulation of the electronic properties of graphene nanoribbons (GNRs) is an important issue for their application in nanoelectronics. Armchair GNRs (AGNRs) are semiconductors with energy gaps related to their width. Armchair graphane nanoribbons (AGaNRs) are insulators with wide gaps. Considering the gap size hierarchy of AGNRs, we construct a series of hybrid nanoribbon by substituting AGaNRs into AGNRs to tune the charge transport of the nanoribbons. Based on the non-equilibrium Green’s function method combined with the density functional theory, it is interesting to find that the energy gaps of these nanoribbons do not increase monotonically with the increasing proportion of AGaNRs as one expects intuitively. The charge transport of these systems can be enhanced or reduced due to the incorporation of AGaNRs. It suggests that such hybridization is an efficient way to modulate the electronic properties of the systems. Detailed analyses via transmission spectra, distribution of molecular projected self-consistent Hamiltonian states, frontier molecular orbital position and transmission pathways are given for a deeper insight. Keywords: Graphene; Graphane; Electronic transport; First-principles 1. Introduction Subsequent to the discovery of graphene, the synthesis of a 2D hydrocarbon in honeycomb structure, namely, graphane has been realized experimentally by exposing graphene in a hydrogen plasma environment [13]. Graphane is a graphene sheet fully saturated by hydrogen in such a way that hydrogen atoms adsorbed at different carbon sublattices are situated at opposite sides of the sheet plane. Graphane is a wide band gap nanostructure with all the carbon atoms in the sp3 hybridized state and thus has potential applications in graphehe-based electronics [4]. Singh et al. proposed a nanostructure, named “nanoroads" of pristine graphene, which can be manufactured by carving the fully hydrogenated

*Corresponding

author. E-mail address: [email protected].

ACCEPTED MANUSCRIPT graphane to remove hydrogen selectively and reported that this kind of “nanoroad” possesses similar band gap of equal wide pristine GNRs [5]. Following the idea of “nanoroad”, a lot of attention has turned to hybrid systems composed of graphene and graphane nanoribbons (GNRs and GaNRs for simplicity) due to their different electronic structures [6-13]. Such hybrid systems can be fabricated by patterning graphene at the nanometer scale via hydrogen desorption [14, 15]. Similar to GNR, GaNR can also be classified into zigzag GaNR (ZGaNR) and armchair GaNR (AGaNR) according to their edge shapes. On one hand, Zou et al. constructed a hybrid structure by substituting ZGaNRs into ZGNRs and studied their electronic properties at zero bias. Their ab initio calculation revealed that the transport properties of the hybrid systems can be enhanced compared with the pristine ZGNRs [10]. The electronic transport of ZGaNRs/ZGNRs under finite bias were further investigated. The first principles calculation suggested that the electronic transport of symmetric and asymmetric ZGNR-based hybrid nanoribbons behave distinctly different from each other even in the presence of the same substitution positions of ZGaNRs [11]. On the other hand, the interface between graphene and graphane or single-side fully hydrogenated graphehe (SSHG) were studied to account for the structural distortions induced by the interface. Armchair graphene/graphane interfaces are shown to be robust [12]. Moreover, armchair graphane/graphene nanoribbons with fixed width are found to be direct semiconductors and dangling band defects at AGaNR edges obviously affect the magnetic properties [13]. Yet a systematically theoretical understanding of charge transport of armchair graphane/graphene nanoribbons remains unclear. It is known that GaNRs are wide gap dielectrics; therefore will the gap size of the hybrid nanoribbons increase with the increasing proportion of GaNRs? How and to what extent does the incorporation

of

AGaNRs

affect

the

charge

transport

of

the

hybrid

nanoribbons? These questions are discussed in detail in this paper. 2. Model and Method Following previous convention [16, 17], the GNRs with armchair shaped edges on both sides are classified by the number of dimer lines (Na) across the ribbon width. We refer to an AGNR with Na dimer lines as Na-AGNR. It has been shown that the Na-AGNRs are semiconductors with energy gaps

ACCEPTED MANUSCRIPT which decrease as a function of the increasing ribbon widths. The variations in energy gap however exhibit three distinct family behaviors. The gap size hierarchy

is

∆3𝑝 + 1 > ∆3𝑝 > ∆3𝑝 + 2

(where

p

is

a

positive

integer,

Na=3p,3p+1,3p+2)[18]. Therefore, we choose 6-AGNR, 7-AGNR and 8-AGNR (6A, 7A and 8A for simplicity) as representatives to build AGNR/AGaNR heterojunctions. The hybrid AGNR/AGaNR junctions are constructed by substituting

AGaNRs

into

pristine

AGNRs.

Side

views

of

the

hybrid

nanoribbons are shown in Figs. 1(a).Different substitution positions and proportions are considered. For 6A, for example, when chain 1 is substituted by AGaNR the hybrid nanoribbon is denoted as 6A-1. Same notation is adopted for 7A- and 8A-based hybrid nanoribbons, which is not shown here. As shown in Fig. 1(b), the system can be divided into three parts: left electrode (LE), scattering region (SR) and right electrode (RE). We have chosen a supercell with a large enough vacuum layer in the directions perpendicular to the transport direction so that the device has no interaction with its mirror images. Our first-principles transport calculations are performed by using the Atomistix Toolkit (ATK) package [19], which adopts the density functional theory (DFT) in conjunction with the nonequilibrium Green's function (NEGF) formalism. The generalized gradient approximation (GGA) with a PerdewBurke-Ernzerhof

(PBE)

functional

is

utilized

to

calculate

the

electron

exchange-correlation. Valence electrons are expanded in a double zeta plus polarization

(DZP)

basis,

and

the

norm-conserving

Troullier-Martins

pseudopotentials are used to model the core electrons. The electrode calculations are performed under periodical boundary conditions. The Brillouin zone samplings are done using 1 × 1 × 100 Monkhorst-Pack grids. The cutoff energy is set to 100 Ry. The atoms of SR are fully relaxed until the force acting on each atom is less than 0.05 eV/Å. With the NEGF formalism, the source-drain current I through the system at a finite source-drain bias 𝑉𝑏 can be calculated using the Landauer–Bütiker formula 𝜇𝐿 𝑒 𝑇(𝐸,𝑉𝑏)[𝑓𝐿(𝐸,𝑉𝑏) ‒ 𝑓𝑅(𝐸,𝑉𝑏)]𝑑𝐸 𝐼 = 2( ) ℎ 𝜇𝑅

∫

where 𝑓𝐿(𝑅) and 𝜇𝐿(𝑅) are the Fermi–Dirac distribution function and the electrochemical potential of LE (RE), respectively. 𝑇(𝐸,𝑉𝑏) is the transmission function for electrons incident at energy E through the device under the

ACCEPTED MANUSCRIPT applied bias 𝑉𝑏.

SR

RE

Fig. 1. (a) Side view of schematic confgurations of pristine 6A, 6A-1, 6A-1,2, 6A-1,2,3 and 6A-1,2,3,4. (b) Schematic configuration of 6A-1 device, which is divided into three regions: left electrode (LE), scattering region (SR), and right electrode (RE).

3. Results and Discussion To elucidate the influences of the substitution of graphane on the electronic properties of AGNRs, we first show in Fig. 2 the band structures of pristine nanoribbons 6A, 7A and 8A. It is clear that 6A and 7A are both semiconductors with direct gaps of about 1.07eV and 1.33eV, respectively, while 8A has a negligible one. The variation of the gap values is in agreement with the early reported gap size hierarchy ∆3𝑝 + 1 > ∆3𝑝 > ∆3𝑝 + 2 [18]. Therefore, there is no current through 6A and 7A devices in the bias range (0, 1.0)V we studied. For 8A, the situation is different. The current increases rapidly as the bias is beyond 0.2V, corresponding to its band structure feature.

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Fig. 2. Band structures of pristine (a) 6A, (b) 7A and (c) 8A nanoribbons. (d) I-V curves of 6A, 7A and 8A devices.

Next we turn to the AGNR/AGaNR systems and first focus on the 6A-based heterojunctions. The transmission spectra of these systems under zero bias voltage are shown in Fig. 3. Pristine 6A is also included for comparison. One main

feature

of

the

transmission

spectrum

of

6A

is

the

quantized

transmission plateaus. It is known that the electron transport in graphene nanoscale structures is ballistic transport without scattering, therefore, an 2

energy band corresponds to a conductance quantum of 𝐺0 = 2𝑒 /ℎ. Quantized conductance corresponds to quantized transmission. In addition, a wide transmission gap appears around the Fermi level 𝐸𝑓. When the edge chain is substituted by a graphane carbon chain, i.e., 6A-1, the gap around 𝐸𝑓 is reduced to a narrower one and the quantized transmission plateau far away from 𝐸𝑓 is broken. However, when the next chain is also substituted by a graphane carbon chain, that is 6A-1,2, the gap is widened. Meanwhile, the feature of quantization is completely broken. The situation is similar for 6A1,2,3. When the graphane proportion is further increased as shown in Fig. 2(e), the transmission in the energy region (-1.3, 1.3)eV is greatly enhanced except the very narrow valley around 𝐸𝑓. Therefore, it can be concluded that the substitution of graphane has a significant impact on the electron transmission of the nanoribbons. The band gap of these hybrid nanoribbons can be tuned from a relatively large one (1.33eV) to a much smaller one (0.2eV) or a negligible one, owing to the incorporation of graphane. When all the graphene carbon chains are substituted by graphane, the system turns into 6AGaNR which is a dielectric with a very large gap. It is interesting to note that the band gaps of these hybrid nanoribbons do not increase monotonically with the increasing proportion of AGaNR. These results can be reasonably understood in that for AGNRs themselves there is a gap size hierarchy ∆3𝑝 + 1 > ∆3𝑝 > ∆3𝑝 + 2, that is, the band gap and electronic transport in the system change non monotonically with the increasing width of the AGNRs. Take 6A-1,2 for example, as two sp3 hybrid graphane carbon chains are substituted into AGNR, the number of sp2 hybrid graphene carbon chains becomes four. Therefore, the electronic transport of 6A-1, 2 behaves like that

ACCEPTED MANUSCRIPT of 4A to a certain extent since sp3 hybridization will not contribute to the transport.

Fig. 3. (a)–(e) Calculated zero-bias transmission spectra of 6A, 6A-1, 6A-1, 2, 6A-1, 2, 3 and 6A-1, 2, 3, 4 in the energy region (-2.0, 2.0)eV. (f)-(j) Band structures of 6A, 6A-1, 6A-1, 2, 6A-1, 2, 3 and 6A-1, 2, 3, 4 nanoribbons.

I-V curves can provide a more intuitive picture of the variation in the electronic transport properties after hybridization, which is shown in Fig.4. Great changes take place in the I-V characteristics owing to the inclusion of AGaNR, which can be classified into three categories: 1. No current is observed in system 6A, 6A-1,2 and 6A-1,2,3 in the bias range (0, 1.0)V we studied, due to the wide gap in their transmission spectra. 2. In contrast to that, the current of A6-1,2,3,4 begins to increase steadily as soon as the bias is applied. 3. Obvious current is observed after a threshold bias voltage of 0.2V because of the existence of the narrow transmission gap~0.2eV (fig.

ACCEPTED MANUSCRIPT 3(b) for 6A-1).

Fig. 4. (a)–(c) I-V curves of 6A-, 7A- and 8A-based hybrid nanoribbons in the bias region (0, 1.0)V.

To give a deeper insight of the electronic transport behavior of these systems, we calculated the bias evolution of several frontier molecular orbitals as shown in fig. 5. Take 6A-1and 6A-1,2 for examples. It is found that for 6A-1 the location of these frontier orbitals nearly keeps unchanged as the bias increases. LUMO enters bias window at 𝑉𝑏 = 0.2𝑉 and then stays inside all through the bias range (0.2, 1.0)V, which leads to the obvious increase in the current after 𝑉𝑏 = 0.2𝑉. Different from 6A-1, most of these frontier orbitals shift downwards suddenly at 𝑉𝑏 = 0.4𝑉, indicating that the coupling between central region and two electrodes becomes weak at this point. Although LUMO or HOMO stays within the bias window, no current passes through the nanoribbon. To understand this, we plot in Fig. 5 the molecular projected self-consistent Hamiltonian (MPSH) of some relevant orbitals for these two systems at several bias voltages. It is clear that LUMO of 6A-1 is delocalized all over the scattering region and thus contributes to the charge transport. LUMO and HOMO of 6A-1,2, however, are much localized over the middle part and can not become effective transport channels.

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Fig. 5. Bias-dependent evolution of frontier molecular orbitals within the bias window (denoted by dot lines) for systems (a)6A-1 and (b)6A-1,2. MPSH of several frontier orbitals are indicated by arrows.

The transmission pathway analysis can split the transmission coefficient into local bond contributions. The pathway figures out where (and how) the electron propagates on certain energy. The radius of each arrow indicates the magnitude of local transmission between each pair of atoms. The angle 0 (colored in blue) represents that electrons transmit from atom to atom linearly parallel with z axis and angel π indicates that electrons are reflected back. We show in Fig.6 the pathways of the frontier orbitals within the bias window at several bias voltages for 6A-1 and 6A-1,2. It is evident that the electron transmission only occurs between several carbon atoms near the left electrode (Fig. 6(c) and (d)). Therefore, there is no available pathway for electrons to transmit from electrode to electrode for 6A-1,2. For 6A-1, it has been known that LUMO stay inside the bias window contributing to the transmission. We plot in Fig. 6(a) and (b) the pathways of LUMO at Vb=0.5V, 0.9V, corresponding to those indicated by arrows in Fig. 5(a). Indeed, two dominant pathways can be observed in LUMO where electrons can flow through the nanoribbon arriving at the right electrode smoothly.

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Fig. 6. The pathways of the electron transmission for 6A-1 (a) LUMO at Vb=0.5V and (b) LUMO at Vb=0.9V. The pathways of the electron transmission for 6A-1,2 (c) HOMO at Vb=0.4V and (d) LUMO at Vb=0.9V. The color represents the angle of electron transmission direction, and the width of lines represents the magnitude of the transmission coefficients.

Finally, we briefly take a look at 7A- and 8A-based nanoribbons. I-V curves of these system are shown in Fig.4(b) and (c), respectively. Pristine 7A nanoribbon is semiconductor with a gap of about 1.33eV. Similar to 6A-based hybrid nanoribbons, the substitution of AGaNR enables the systems to vary from wide-gap semiconductors to a metallic material (7A-1,2,3,4,5). As for 8A nanoribbon, a semiconductor with a very narrow gap as shown in Fig. 2(c), the inclusion of AGaNR makes the nanoribbons to turn into wide gap semiconductors (8A-1,2 and 8A-1,2,3,4,5) or metallic conductor (8A1,2,3,4,5,6).

Detailed discussion can refer to that performed on 6A-based

nanoribbons. 4. Summary We construct AGaNR/AGNR junctions by substituting AGaNRs into pristine AGNRs owing to their different electronic structures. The electronic properties are investigated by using the density functional theory and nonequilibrium Green’s function formalism. It is interesting to find that the energy gaps of these nanoribbons do not increase monotonically with the increasing proportion of AGaNRs, although GaNRs have large gaps. Moreover, the substitution of AGaNR enables the hybrid nanoribbons to range from wide band gap semiconductors to metallic conductors. Therefore, our findings could be useful for designing graphene-based electronic devices. Acknowledgements

ACCEPTED MANUSCRIPT The authors acknowledge supports by National Science Foundation of China (Grant no. 11574118 ). References [1] J.O. Sofo, A.S. Chaudhari, G.D. Barber, Phys. Rev. B 75 (2007) 153401. [2] D.W. Boukhvalov, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 77 (2008) 035427. [3] A.D. Hern andez-Nieves, B. Partoens, F.M. Peeters, Phys. Rev. B 82 (2010) 165412. [4] H. Sahin, C. Ataca, S. Ciraci, Phys. Rev. B 81 (2010) 205417. [5] A.K. Singh, B.I.Yakobson, Nano. Lett. 9 (2009) 1540. [6] L.F. Huang, X.H. Zheng, G.R. Zhang, L.L. Li, Z.Zeng, J. Phys. Chem. C 115 (2011) 21088 [7] F.W. Averill, J.R. Morris, Phys. Rev. B 84 (2011) 035411. [8] A.R. Wei, Y.F. Li, Y. Li, H. Ye, Comput. Mater. Sci. 138 (2017) 192. [9] Y.E. Yang, Y. Xiao, X.H. Yan, Solid State Commun. 229 (2016) 43. [10] W Zou, Z Yu, C.X. Zhang, J.X. Zhong, L.Z. Sun, Appl. Phys. Lett. 100 (2012) 103109. [11] W. Liu, F.H. Meng, J. H. Zhao, X.H. Jiang, J. Theor. Comput. Chem. 16 (2017) 1750032. [12] A. I. Podlivaev, L. A. Openov. Physica E. 44 (2012) 1894. [13] W.X. Zhang, C. He, T. Li, S.B. Gong, L. Zhao, J.Y. Tao, Solid State Commun. 211(2015)23. [14] P. Sessi, J.R. Guest, M. Bode, N. P. Guisinger, Nano. Lett. 9 (2009) 4343. [15] J.D. Jones, K.K. Mahajan, W.H. Williams, P.A. Ecton, J.M. Perez, Carbon 48 (2010) 2335. [16] M. Ezawa, Phys. Rev. B 73 (2006) 045432. [17] L. Brey, H.A. Fertig, Phys. Rev. B (2006)73 235411. [18] Y.W. Son, M.L. Cohen, S. G. Louie, Phys. Rev. Lett. 97 (2006) 216803. [19] X.Q. Deng, Z.H. Zhang, C.H. Yang, H.L. Zhu, B. Ling, Org. Elec. 14 (2013) 3240.