Abstract

Graphene, hydrogenated graphene, can be patterned into electronicdevices by selectively removing hydrogen atoms. The simplest of suchdevices is the so-called nanoroad, analogous to the graphene nanoribbonwhere confinement - and the opening of a gap - is obtained without theneed of breaking the carbon bonds. In this work we address the electronictransport properties of such systems considering different hydrogen im-purities within the conduction channel. We show, using a combinationof density functional theory and non-equilibrium Green’s functions thathydrogen leads to significant changes in the transport properties and insome cases to current polarization.

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Electronic transport in patterned graphene

nanoroads.

Antonio J. R. da Silva3,4

April 15, 2013

Figure 1: Image showing the various configurations of the patterned graphene(nanoroads) used in our calculations. In a), c) and h) the pristine nanoroad isshown. In a) the defect sites are indicated by the letters above the circles. Ind), e), f) and g) the defective nanoroads are shown. The dark colored atoms arehydrogen and the ligh colored ones are carbon. The cell sizes are 26.35A longand 15.11A wide. The central region is a 7.57A wide nanoroad.

1 Introduction

Since it’s synthesis in 2004 [1] graphene drew a lot of attention from the sci-entific community. [2, 3, 4] Mainly due to it’s unique geometry (a single layerof carbon atoms) [1] it has tantalizing mechanical, [5] thermal, [6] electronic [7]and transport [8] properties. The greatest issue hindering the use of grapheneas an electronic device, however, is the absence of a intrinsic band gap. Thusfar opening a gap on it’s band structure has been a difficult task. [9] A proposedalternative is to confine the system into a one dimensional structure, than aband gap opening due to quantum effects is expected. [10] In order to do thatseveral paths to synthesize graphene stripes, known as graphene nanoribbons(GNRs), have been tried; Chemical, [11] carbon nanotube unzipping [12, 13],lithographic [14] and ion implantation on SiC [15] are a few examples. Albeitlithographic patterning is promising for large scale production - since it is awell established technique - it faces problems with edge smoothness and widthcontrol, connected to limitations on the technique’s resolution.

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A different single layer material called graphane, [16] formed by fully hy-drogenated graphene, can also be patterned using a lithographic technique. [17]In this case hydrogen atoms are selectively removed from the structure forminga graphene-like region. The main advantage here is that the overall structurewould remain two-dimensional, and thus easier to integrate in a circuit. Thispatterned graphane, the so called nanoroads, was previously proposed and stud-ied by Singh et al. [18] They found that the graphene nanoroads mimic some ofthe isolated GNRs’ properties, such as band gap and magnetic ordering.

Albeit the synthesis of the nanoroads is possible, [17] perfect edge smoothnesscould still be a problem - in a manner similar to isolated GNRs - for synthesis.At the nanoscale, even a single impurity could alter the system’s electronicand transport properties. In particular, as a result of the fabrication process,hydrogen impurities and vacancies might be present in the system. Thus it isimportant for device fabrication to determine the effects of such defects.

In order to access the viability of nanoroads as electronic devices we per-formed ab initio electronic transport calculations, by means of density func-tional theory [19, 20] coupled to Green’s function methods (GF) [21, 22]. Wehave simulated systems containing several types of H impurities or vacancies.We have observed a high attenuation on the transmittance of almost all sys-tems in the presence of impurities, even a wider system as shown a perceptibleattenuation. Thus the presence of impurities significantly alter the transportproperties of the nanoroads, hindering it’s applications to electronic devices.

2 Methodology

The system used in our calculations is a patterned graphane in which the centralregion has no hydrogen atoms, forming a nanoroad with armchair edges. Thecalculations the simulation cell used was 26.35 A long (6 unit cells) and 15.11 Awide (8 unit cells), and the actual nanoroad - the hydrogen free region - was7.57 A wide, as shown in Fig 1.

For the transport calculations we divided our system in three regions, a cen-tral scattering region connected to two semi-infinite electrodes. [23] The elec-trodes were chosen to be nanoroads with the same width of the scattering region.To obtain the transmittance we used a Landauer-Buttiker like formula, basedon the GF method, [24, 25] within the two-spin fluid approximation (neglectingspin-orbit interactions).

For our DFT calculations we employed the SIESTA [26, 27] computationalcode. In this work we have used a double zeta basis set with polarizationorbitals, and the Generalized Gradient Approximation (GGA) - as parametrizedby Perdew-Burke-Ernzerhof [28] (PBE) - for the exchange-correlation functional.The atomic coordinates were relaxed until forces were lower than 0.03 eV/A.

In this work we have initially explored three different positions for an extraH: On the edge (HE), right after the edge (HD) and at the center of the nanoroad(HF), as shown in Fig. 1a). We also considered a nanoroad with a single H atomremoved, a hydrogen vacancy (HV). Finally, we also explored the behaviorof either constricted or quantum-dot-like configurations in the system. Theconstricted (CX) arrengements were obtained by removing either a single line of4 atoms (C1) on one edge, or two lines (C2) on each side (fig. 1b). Analogouslythe widened regions (WX) are formed by removing 4 (W1) and 8 atoms (W2)

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respectively.In order to access the stability of these defective systems we have calculated

the binding (Eb) and formation energies (Ef) per H atom:

Eb =1

N(ETH − ETC ±N ∗ ETHA) (1)

Ef =1

N(ETH − ETC ±N ∗ µH2

) , (2)

where ETH is the total energy of the defective system, ETC is the total energyof the clean system (with a nanoroad), N is the number of inserted (removed)hydrogen atoms, ETHA is the total energy of a single isolated hydrogen atomand µH2 is the total energy per atom for a H2 molecule. The ∓ sign indicatesrespectively whether atoms have been added (constriction) or removed (widenednanoroad).

3 Results

Table 1: Binding (Eb) and formation energies (Ef) of the constrictions, widenednanoroads and single hydrogen defects, calculated with eq. 1 and eq. 2.

Structure Eb (eV) Ef (eV)HE -1.78 0.36HD -1.29 0.84HF -0.68 1.46HV 3.43 1.29C1 -2.53 -0.39C2 -2.54 -0.39W1 7.32 5.18W2 5.13 2.98

0

1

2 a )

c )

H V

H D

d )

H F

T(E)

H E

b )

- 2 - 1 0 1 20

1

2

S p i n U p S p i n D o w n P r i s t i n e

T(E)

E - E f ( e V )- 2 - 1 0 1 2

E - E f ( e V )

Figure 2: Spin polarized transmittances of the single hydrogen defects: a) HE,b) HD, c) HF and d) HV

From our calculations we infer that the three positions considered for theextra hydrogen are stable, as can be seen from the negative binding energies intable 1; with higher values near the edge. At the same time the formation ener-gies are positive, meaning that it’s unfavorable for a H2 molecule to dissociate

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Figure 3: a) The band structure, around the Fermi energy, for the HF defect.b), c) and d) The wavefunctions at the Γ point, for the corresponding levelspointed in a)

and then bind to the interface. These results are in line with calculations by Liet al. [29] The results for the addition (removal) of two hydrogen atoms indicatethat the introduction of pairs of hydrogen atoms is more likely and also showsa tendency towards a fully hydrogenated graphane structure as being the moststable one. These results indicate that the dehydrogenation process in grapheneare most likely to lead to defects.

The transmittances for single H systems are plotted in Fig. 2, and except forthe HF case they are highly attenuated. In the HF case the mirror symmetrypresent in the original system is restored. We can see from fig.3 a), that thelevel inserted by the hydrogen atom (pointed by letter d)), does not interactwith the delocalized levels of the pristine nanoroad. This is noted also in thewavefunctions at the Γ point, plotted in fig.3(b-d). The pristine bands, b) andc), are delocalized along the nanoroad, and the hydrogen level contributes tothe wavefunction only around the defect. Finally one also notes that the wave-function for the valence band has a node in the center of the nanoroad, thus theconduction channels are weakly affected by an impurity at that site. A similarfeature is observed for the conduction band. Consequently the transmittanceis not significantly altered in this case. In fig 2d) - the case of a vacancy - onenotes a strong spin polarization of the transmission reaching up to 100% at ap-proximately ±0.5eV around the Fermi level. In that region the device becomesperfectly spin polarized due to scattering at the perfectly spin-polarized defectstates.

For the case of the widened and constricted nanoroads, the effect of structurechange in the electronic transport is very pronounced. This can be seen inthe severely attenuated transmittances (compared to pristine nanoroads) shownin fig 4. In fact, in all cases shown here the first plateau for energies aboveand bellow EF is almost entirely quenched. In all cases considered here there

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S p i n U p S p i n D n P r i s t i n e

0

1

2

b )T(E

)

d )c )

- 2 - 1 0 1 20

1

2

E - E f ( e V )

W 2

T(E)

W 1

C 1 C 2

a )

- 2 - 1 0 1 2

E - E f ( e V )

Figure 4: Spin polarized transmittances of the constrictions and widenednanoroads. a) C1, b) C2, c) W1 and d) W2

was no polarization of the transmission coefficients. Thus, the modificationin the hybridization of few carbon atoms happens to play a big role for theelectronic transport. That is a problem for electronic devices, as a small amountof misplaced hydrogen atoms can greatly disturb the electronic transport.

- 2 - 1 0 1 20

2

4

6

8

T(E)

E - E f ( e V )

S p i n ↑ S p i n ↓ P r i s t i n e

- 1 0 10

1

2

Figure 5: Spin polarized transmittances of a 15 atom wide nanoroad (ACR15)with a HE defect.

Finally one could point that for wider nanoroads the attenuation effectscan be lowered. In order to access that we have simulated a 15 atom widenanoroad (17.45A wide), with a HE defect (ACR15HE). In figure 5 we showthe transmittance plotted for the ACR15HE. It can be seen that attenuationstill occurs, but specially near the Fermi energy the up and down spin channelsare not evenly affected. In particular a current polarization close to 100% isreached. Than even for wider systems the effect of a single hydrogen atomcan be harmful to applications in electronic devices. Thus on the one hand forsystems with many defects, this attenuation could be even more severe, as theconductance decays very rapidly with the lenght [30]. This behavior is similarto edge disorder in graphene nanoribons, as observed by Mucciolo et al. [31].On the other hand, if a asymmetry between up and down spin channels ofthe transmittance is present, polarization effects can arise, and be enhanced forlonger systems [32]. This kind of behaviour is desired for spin filters, a importantdevice for spintronics [33]. This effect is related to the fact that conductanceand valence bands are largely dominated by the edge states.

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4 Conclusion

In summary we have demonstrated that it’s energetically favorable for hydrogenatoms to bond to nanoroads. That leads to a high suppression of the electronictransmittance, creating problems to applications in electronic devices. Even asingle hydrogen can disturb the electronic transport, making a difficult task tosynthesize a clean system with single atom precision, to be useful for electronicdevices. Despite the problems for electronic devices the graphane/grapheneinterface can be interesting to spintronics, as they show an asymmetry on thetransmittance of spin up and spin down channels. This effect can be enhancedfor longer systems, making the nanoroads good candidates to spin filter devices.

5 Acknowledgements

The authors acknowledge to FAPESP and CNPq for financial support. Andalso CCE-USP, HPC-UFABC and CENAPAD/SP for the computational time.

References

[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V.Dubonos, I. V. Grigorieva, and A. A. Firsov. Electric field effect in atomi-cally thin carbon films. Science, 306(5696):666–669, 2004.

[2] A. K. Geim and K. S. Novoselov. The rise of graphene. Nature Materials,6(3):183–191, MAR 2007.

[3] KS Novoselov, AK Geim, SV Morozov, D Jiang, MI Katsnelson, IV Grig-orieva, SV Dubonos, and AA Firsov. Two-dimensional gas of massless diracfermions in graphene. Nature, 438(7065):197–200, NOV 10 2005.

[4] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K.Geim. The electronic properties of graphene. Reviews Of Modern Physics,81(1):109–162, JAN-MAR 2009.

[5] Changgu Lee, Xiaoding Wei, Jeffrey W. Kysar, and James Hone. Measure-ment of the elastic properties and intrinsic strength of monolayer graphene.Science, 321(5887):385–388, 2008.

[6] Alexander A. Balandin, Suchismita Ghosh, Wenzhong Bao, Irene Calizo,Desalegne Teweldebrhan, Feng Miao, and Chun Ning Lau. Superior thermalconductivity of single-layer graphene. Nano Letters, 8(3):902–907, Mar2008.

[7] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K.Geim. The electronic properties of graphene. Rev. Mod. Phys., 81(1):109–162, Jan 2009.

[8] Jean-Christophe Charlier, Xavier Blase, and Stephan Roche. Electronicand transport properties of nanotubes. Rev. Mod. Phys., 79(2):677–732,May 2007.

7

[9] Kostya Novoselov. Graphene: Mind the gap. Nature Materials, 6(10):720,2007.

[10] L. Brey and H. A. Fertig. Electronic states of graphene nanoribbons studiedwith the dirac equation. Phys. Rev. B, 73:235411, Jun 2006.

[11] Jessica Campos-Delgado, Jose Manuel Romo-Herrera, Xiaoting Jia,David A. Cullen, Hiroyuki Muramatsu, Yoong Ahm Kim, Takuya Hayashi,Zhifeng Ren, David J. Smith, Yu Okuno, Tomonori Ohba, Hirofumi Kanoh,Katsumi Kaneko, Morinobu Endo, Humberto Terrones, Mildred S. Dres-selhaus, and Mauricio Terrones. Bulk production of a new form of sp2carbon: Crystalline graphene nanoribbons. Nano Letters, 8(9):2773–2778,2008. PMID: 18700805.

[12] Liying Jiao, Li Zhang, Xinran Wang, Georgi Diankov, and HongjieDai. Narrow graphene nanoribbons from carbon nanotubes. Nature,458(7240):877, 2009.

[13] Chenggang Tao, Liying Jiao, Oleg V. Yazyev, Yen-Chia Chen, JuanjuanFeng, Xiaowei Zhang, Rodrigo B. Capaz, James M. Tour, Alex Zettl,Steven G. Louie, Hongjie Dai, and Michael F. Crommie. Spatially re-solving edge states of chiral graphene nanoribbons. Nature Physics, 7(8),2011.

[14] Melinda Y. Han, Barbaros Ozyilmaz, Yuanbo Zhang, and Philip Kim.Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett.,98:206805, May 2007.

[15] S. Tongay, M. Lemaitre, J. Fridmann, A. F. Hebard, B. P. Gila, and B. R.Appleton. Drawing graphene nanoribbons on SiC by ion implantation.Applied Physics Letters, 100(7), 2012.

[16] Jorge O. Sofo, Ajay S. Chaudhari, and Greg D. Barber. Graphane: Atwo-dimensional hydrocarbon. Physical Review B, 75(15), APR 2007.

[17] Yu Wang, Xiangfan Xu, Jiong Lu, Ming Lin, Qiaoliang Bao, BarbarosOezyilmaz, and Kian Ping Loh. Toward high throughput interconvertiblegraphane-to-graphene growth and patterning. ACS Nano, 4(10):6146–6152,OCT 2010.

[18] Abhshek K. Singh and Boris I. Yakobson. Electronics and magnetism ofpatterned graphene nanoroads. Nano Letters, 9(4):1540–1543, APR 2009.

[19] P Hohenberg and W Kohn. Inhomogeneous electron gas. Physical ReviewB, 136(3B):B864, 1964.

[20] W Kohn and Lj Sham. Self-consistent equations including exchange andcorrelation effects. Physical Review, 140(4A):1133, 1965.

[21] Alexandre R. Rocha, Victor M. Garcia-suarez, Steve W. Bailey, Colin J.Lambert, Jaime Ferrer, and Stefano Sanvito. Towards molecular spintron-ics. Nature Materials, 4(4):335, 2005.

8

[22] Frederico D. Novaes, AntA´nio J. R. da Silva, and A. Fazzio. Density func-tional theory method for non-equilibrium charge transport calculations:Transampa. Brazilian Journal of Physics, 36:799 – 807, 09 2006.

[23] C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James. A direct calcu-lation of the tunneling current. J. Phys. C, 4:916, 1971.

[24] M Buttiker. 4-terminal phase-coherent conductance. Physical Review Let-ters, 57(14):1761–1764, Oct 6 1986.

[25] R Landauer. Electrical resistance of disordered one-dimensional lattices.Philosophical Magazine, 21(172):863–&, 1970.

[26] JM Soler, E Artacho, JD Gale, A Garcia, J Junquera, P Ordejon, andD Sanchez-Portal. The siesta method for ab initio order-n materials sim-ulation. Journal Of Physics-Condensed Matter, 14(11):2745–2779, Mar 252002.

[27] Emilio Artacho, E. Anglada, O. Dieguez, J. D. Gale, A. Garcia, J. Jun-quera, R. M. Martin, P. Ordejon, J. M. Pruneda, D. Sanchez-Portal, andJ. M. Soler. The siesta method; developments and applicability. JournalOf Physics-Condensed Matter, 20(6), Feb 13 2008.

[28] JP Perdew, K Burke, and M Ernzerhof. Generalized gradient approxi-mation made simple. Physical Review Letters, 77(18):3865–3868, Oct 281996.

[29] Yafei Li, Zhen Zhou, Panwen Shen, and Zhongfang Chen. Structural andelectronic properties of graphane nanoribbons. The Journal of PhysicalChemistry C, 113(33):15043–15045, 2009.

[30] J. M. de Almeida, A. R. Rocha, Antonio J. R. da Silva, and A. Fazzio. Spinfiltering and disorder-induced magnetoresistance in carbon nanotubes: Abinitio calculations. Phys. Rev. B, 84:085412, 2011.

[31] E. R. Mucciolo, A. H. Castro Neto, and C. H. Lewenkopf. Conductancequantization and transport gaps in disordered graphene nanoribbons. Phys.Rev. B, 79:075407, Feb 2009.

[32] A R Rocha, Thiago B Martins, A Fazzio, and Antnio J R da Silva. Disorder-based graphene spintronics. Nanotechnology, 21(34):345202, 2010.

[33] Igor Zutic, Jaroslav Fabian, and S. Das Sarma. Spintronics: Fundamentalsand applications. Rev. Mod. Phys., 76:323–410, 2004.

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