Electronic and Quantum Transport Properties of Atomically Identified

Letter pubs.acs.org/JPCL

Electronic and Quantum Transport Properties of Atomically Identified Si Point Defects in Graphene Alejandro Lopez-Bezanilla,*,† Wu Zhou,‡ and Juan-Carlos Idrobo§ †

Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, United States Materials Science and Technology Division, Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37831, United States § Center for Nanophase Materials Sciences Division, Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37831, United States ‡

ABSTRACT: We report high-resolution scanning transmission electron microscopy images displaying a range of inclusions of isolated silicon atoms at the edges and inner zones of graphene layers. Whereas the incorporation of Si atoms to a graphene armchair edge involves no reconstruction of the neighboring carbon atoms, the inclusion of a Si atom to a zigzag graphene edge entails the formation of five-membered carbon rings. In all the observed atomic edge terminations, a Si atom is found bridging two C atoms in a 2-fold coordinated configuration. The atomic-scale observations are underpinned by first-principles calculations of the electronic and quantum transport properties of the structural anomalies. Experimental estimations of Si-doped graphene band gaps realized by means of transport measurements may be affected by a low doping rate of 2-fold coordinated Si atoms at the graphene edges, and 4-fold coordinated at inner zones due to the apparition of mobility gaps. SECTION: Physical Processes in Nanomaterials and Nanostructures

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electronics. However, the absence of an electronic band gap represents an impediment for the integration of 2D graphene in digital logic gates requiring a switching between ON/OFF states. Based on both physical and chemical approaches, several methods have demonstrated effectiveness in opening a band gap in graphene, such as breaking the inversion and the orthogonal time-reversal symmetry by graphene−substrate interaction,1 controlled top-down lithography cutting 2D graphene into 1D nanoribbons,2 or patterned hydrogen adsorption.3,4 An interesting approach consists of enabling the apparition in a disordered medium of a range of allowed energy levels made of low or nonpropagating states as a result of the fluctuations in the local potential caused by the disordered distribution of impurities. Free carriers made with states in this region cannot propagate, and this region of energy states is identified as constituting a mobility gap.5 In this direction, successful band gap engineering in a graphene fieldeffect device was realized6 by means of field-induced chemical modification of the carbon network with functional groups, yielding enhanced graphene resistivity and the subsequent apparition of conductive (ON) and insulating (OFF) states. The effect of both p-type and n-type doping on quantum transport in low dimensional graphene has been suggested for band gap widening of graphene nanoribbons.7 Substitutional

he honeycomb lattice of graphene has been the object of intensive theoretical and experimental studies, revealing a large number of unique properties with potential applications in

Figure 1. (a) ADF STEM image of an open Si-terminated armchair edge of monolayer graphene. The unit cell of the pentagonal armchair edge point defects as in panel a is reproduced for a narrow graphene ribbon in b. Panels c, d, and e show the electronic band diagram of the nonpassivated, mono-, and dihydrogenated Si-edge ribbons, respectively. © 2014 American Chemical Society

Received: February 24, 2014 Accepted: May 1, 2014 Published: May 1, 2014 1711

dx.doi.org/10.1021/jz500403h | J. Phys. Chem. Lett. 2014, 5, 1711−1718

The Journal of Physical Chemistry Letters

Letter

Figure 2. (a) ADF-STEM images of a reconstructed Si-terminated zigzag edge of monolayer graphene. (b) Schematic of the structure model for this defect structure, overlaid with the ADF image. (c) Ribbon unit cell of the structural model. (d,e,f) Spin-resolved electronic band diagrams of the unit cell in panel c with zero, one, and two H atoms saturating the Si edge atom.

armchair edge terminated graphene layer with an in-plane Si atom bridging two edge C atoms. The edge C atoms of all graphene ribbons numerically simulated here were terminated with H atoms. The saturation of C edge σ dangling bonds remove electronic states at the vicinity of the Fermi level and allows us to focus on the influence of the edge Si atoms. To fully understand the effect of Si-terminated edges on the electronic properties of nanometer wide graphene ribbons, we systematically study various types of Si orbital hybridization as a result of different degrees of hydrogenation. Figure 1b shows a schematic model of the experimental image in the form of a 1D graphene ribbon, whose terminating Si atom is not passivated. This configuration is nonmagnetic, and the corresponding electronic band diagram in Figure 1c exhibits a semiconducting character. The attachment of a H atom to the Si atoms renders the system metallic (Figure 1d) and lowers the formation energy by 1.2 eV, with respect to the energies of the former configuration and half of an isolated H2 molecule. The sp2 hybridization of all Si and C atoms allows the ribbon to exhibit a planar geometry. Given the 1D nature of the atomic Si arrangement and that an electronic band is half-filled, the possibility of a Peierls instability and an additional lowering of energy was considered. However, no band gap opening was observed upon doubling the unit cell, concluding that the Peierls distortion and the concurrent Si atom chain dimerization does not occur. Si is prone to exhibit sp3 hybridization in a 2D extended layer (silicene),13,14 suggesting that a tetrahedral arrangement of the Si atomic orbital is preferred. Indeed, a further reduction of the formation energy of up to 2.7 eV is reached by bonding two H atoms to the Si edge atom in an out-of-plane configuration (see inset of Figure 1e). The electronic band diagram in Figure 1e recovers the semiconducting character. Interestingly, although both nonpassivated and dihydrogenated Si-terminated ribbons exhibit the same band gap distance of ∼0.42 eV (which is larger with respect to a pristine graphene ribbon), in the former it is smaller at the Brillouin zone edge, and in the latter at the Γpoint. Spin-polarized calculations showed that the three configurations are nonmagnetic. Notice that the incorporation of Si atoms to a graphene open armchair edge involves no reconstruction or displacement of

doping of graphene with B and N atoms leads inevitably to the disruption of the graphene hyperconjugated network, inducing significant local changes in its electronic properties.8 Technical issues to achieve a required low doping rate along with the production of rough graphene edges that could reduce the carrier mobility and deteriorate the device performance might make B and N doping to not completely satisfy the requirements on the precise control of the graphene electronic properties. Due to the same configuration of the outer electronic shells, Si and C are good candidates to exhibit interesting electronic properties when combined. The presence of Si in the quartz components of the equipment used to grow graphene with chemical vapor deposition (CVD) techniques9 makes Si atoms a frequently found substitutional impurity in graphene. Si is also expected to be present in epitaxial graphene obtained via thermal decomposition of SiC.10 As a matter of fact, Si defects have been detected in graphene films in singleand double-vacancy sites,11,12 both isolated and bonded to a lattice-impurity N atom. In this Letter we report the effect of Si point defects at both inner zones and open edges of highly crystalline graphene films grown by CVD methods. Si defected graphene was experimentally observed using aberration-corrected scanning transmission electron microscopy (STEM) annular dark field (ADF) imaging. We observed that the inclusion of a Si atom at both zigzag and armchair graphene edges entails the formation of five-membered rings. By means of first-principles calculations, we provide a description of the local electronic structure of reduced lateral size graphene with Si atoms terminating high symmetry edges. Quantum transport properties of edge- and bulk-modified 1D graphene lattices with various types of Si doping is modeled. The impact of individual Si defects on the conductance efficiency presents a strong dependency on both the Si chemical bonding and the position of the doping atoms with respect to the edges. The graphene structures with Si-terminated edge defects remain stable throughout the beam exposure and associated elevated dose, which is a requirement to obtain very high signal-to-noise ratios. Figure 1a shows a magnified view of an ADF (also known as Z-contrast because its intensity is proportional to the atomic number Z) STEM image of an 1712



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Figure 3. (a) ADF image showing the presence of a Si atom at a graphene lattice edge forming a pentagonal defect. (b) ADF image and overlaid structural model. (c) Transmission profile and band diagram for a nanoribbon with 14 carbon-dimers across the width and a nonsaturated Si atom. Panels d, f, and g show the ribbon transmission with one, two, and three contiguous edge pentagonal monohydrogenated Si-defects, respectively. The same is shown for dihydrogenated Si-defects in e, g and i. The average transmission as a function of energy for the semiconducting armchair graphene nanoribbons and three selected Si-doping rates is on diplay in panel j for the monohydrogenated and in panel k for the dihydrogenated Sidefect. The black lines indicate the transmission for the pristine ribbon. Averages are performed over 10 random configurations.

the edge C atoms, whose positions are mostly preserved as in a defectless edge. Quite the opposite, the inclusion of a Si atom to a zigzag graphene edge entails the formation of fivemembered C rings in order to accommodate the larger size atom. Figure 2a shows the atomic structure for a 2-fold coordinated Si impurity at a reconstructed graphene zigzag edge. The inclusion of a Si atom in a hexagonal ring replacing the outermost C atom on the edge entails the lateral displacement of the two C to which the Si is covalently bonded. This is possible at the expense of a C atom removal from the pristine network and the formation of a pentagonal ring in between two adjacent Si edge atoms. A schematic of the structure model for this defect structure, overlaid with the corresponding ADF image, is shown in Figure 2b, and in Figure 2c the nanoribbon model is shown. The electronic band

diagram of this configuration with a nonpassivated Si-edge is plotted in Figure 2d, and exhibits a metallic character with a total spin of ∼0.53 μB. By bonding a H atom to the Si atom, two metallic σ-states are removed (see Figure 2e), and the Si point defect increases its magnetic moment to ∼0.60 μB, while it lowers the formation energy by 1.83 eV. An additional H atom bonded to the Si atom rehybridizes its atomic orbitals to sp3 and reduces the formation energy of the defect by 2.37 eV, with respect to the energy of the nonsaturated defect and an isolated H2 molecule. The ribbon remains metallic (see Figure 2f) with a magnetic moment of ∼0.55 μB. Interestingly, the accommodation of Si atoms in all the observed atomic edge reconstructions involves the formation of pentangonal rings. It is worth remembering that the high reactivity of the edge atom dangling bonds are responsible for 1713



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The lower coordination and enhanced chemical reactivity make graphene edge atoms the preferable sites in the hexagonal lattice for introducing substitutional doping atoms and attaching functional groups.21,22 A large variability on the transport properties of the final structure can be obtained as a result of the different types of atomic orbital hybridization of the foreign atom. We analyze the impact on the quantum transport properties of a graphene nanoribbon modified by an edge isolated single Si point defect with different degrees of orbital hybridization. Figure 3a,b shows an experimental ADF image of an isolated Si atom with nonsaturated orbitals and the overlaid atomic model, respectively. Notice that, unlike the edge termination observed in Figure 1a, this defect consists of a five-membered ring formed by the exchange of two C atoms at the graphene edge for one silicon atom. The minimal atomic model of the Si modified system was constructed by repeating an armchair unit cell 8 times, with 14 C dimers across the width, along the z-axis such that the geometric and energetic perturbations caused by the doping element vanish at the edges of the supercell. Figure 3c shows the calculated transmission for energy values close to the Fermi level and electronic state diagram of a system with a nonpassivated Si edge atom. A dramatic drop of conductance with respect to the pristine ribbon is observed, which has its origin on the numerous band gaps and low-dispersive states introduced by the impurity atom, as observed in the electronic band diagram. An average over 10 disordered configurations shows a mobility gap as a consequence of the accumulated effect of multiple backscattering phenomena, leading the system to an effective insulating state. Although the most stable configuration corresponds to the doubly hydrogenated edge Si atoms, it is worth exploring the sensitivity of transport properties of weakly Si doped ribbons with only one σ bond saturated. Figure 3d shows the asymmetric transmission profile of a ribbon with a monohydrogenated Si atom, similar to the one reported for N-doped graphene nanoribbons.8 Transport through the short-range potential induced by the impurity results in a decrease of the hole conductance, exhibiting a pronounced dip in the first transmission plateau, whereas the electron band is less affected by the Si doping. A careful analysis of the electronic states of the supercell reveals that states above the Fermi level remain practically unaltered while at lower energies a disruption of the π-conjugated network is manifested with the apparition of small gaps and bands with narrow energy spread (quasibound states). Notice that the metallic character of the periodic arrangement vanishes when the electronic states are coupled to the continuum and the infinite nanoribbon imposes the small electronic band gap. On the contrary, the modification of the hyperconjugated network imposed by a single dihydrogenated Si edge atom leads to an evident decrease of both the hole and electron bands conductance. The barely asymmetric transmission profile plotted in Figure 3e is similar to that observed in sp3-defected graphene ribbons.23 For two and three contiguous five-membered Si defects at the edge of the ribbon, the perturbation of the hyperconjugated network is amplified, as illustrated in Figure 3f−i, for both mono- and dihydrogenated Si atoms. Resonant and antiresonant scattering effects introduce fluctuations on the transmission profiles, which are accompanied by different arrangements of the electronic states. Although these conductance estimations are appropriate to describe backscattering phenomena of single Si defects, the average transmission profile of an

Figure 4. Formation energies with respect to the number of C atoms to the ribbon edge, of the 3-fold (red) and 4-fold (blue) coordinated substitutional Si atom-doped configurations shown in Figures 5 and 6. The closer the Si point defect to the edge, the lower the formation energy is. Formation energies are relative to the most stable configurations of Figures 5 and 6.

zigzag edge reconstructions reported in pristine graphene,15 where two hexagons transform into a pentagon and a heptagon, as a line of Stone−Wales defects.16 The formation of a nearly linear armchair edge based on triple-bonds and wide bond angles reduces the hybridization energy and increases the stability of the nonpassivated graphene open fringes.17 On the contrary, our experimentally identified defects suggest that Si atoms reduce the formation energy of unpassivated edges by forming a mixed zigzag-armchair geometry, with Si atoms bridging two C atoms in the outermost position, allowing the graphene edge to partially recover the hexagonal geometry. To account for the description of the electronic quantum transport properties of Si-doped graphene, we present a 1D model of graphene in which interstitial Si atoms are present at several positions across the nanoribbon width, and with the geometries observed in the experimental images of this and our former papers.11,18,19 The limited lateral size of the graphitic structure presents a 2-fold competitive advantage with respect to 2D graphene. On one side, it allows for the exploration of the influence of edges on the electronic properties when the substitutional Si atoms are located both at the edges and in the inner zone of the lattice. On the other side, the 1D geometry allows us to resort to the Landauer−Büttiker (LB) approach for the study of electronic quantum transport properties of long and disordered systems. The electronic transport properties were studied by estimating the probability of an electron to be transmitted as crossing the modified graphene ribbon. In our model, the system is phase-coherent, and all the scattering events occur in the defective channel, which is connected to two semi-infinite leads with reflectionless contacts. Within the LB scheme, the transmission coefficients Tn(E) for a given channel n are computed to obtain the probability of an electron to be transmitted at a certain energy E when it quantum mechanically interferes with the scattering centers. For a pristine graphene ribbon, Tn(E) assumes integer values corresponding to the total number of open propagating modes at the energy E. The conductance is thus expressed as G(E) = G0 ∑nTn(E), where G0 is the quantum of conductance. A quantitative estimation of resulting ON/OFF ratios is subjected to the self-consistent computation of the charge flow to account for the accumulation of charges at the ribbon, which in turn screens the impurity potential.20 Further analysis based on this effect might provide additional information on the reported mobility gaps. 1714



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Figure 5. (a) experimental ADF image of a 3-fold Si point defect. (b) Schematic representation of the defect superimposed to the image in panel a. Upper panels in c show the transmission versus charge carrier energy for graphene ribbons with 3-fold coordinated substitutional Si atoms at different positions across the ribbon width. Central and lower panels show three-dimensional fully relaxed structures of the corresponding atomic models. Si atoms are in green, C in gray, and H in red.

backscattering efficiency of this type of point defect is remarkable, which is able to superimpose a mobility gap at all energies in the vicinity of the Fermi level. As pointed out above, this phenomenon is related to the enhanced contribution of quantum interferences that yield localization of states and insulating regime. In addition to the Si-rich defects at the graphene edge described above, Si atoms have also been detected at inner lattice sites. Two types of Si−C bonds were directly observed, namely, a Si atom bonded to three other C atoms in a singlevacancy site (Figure 5a,b), or with four C atoms in a doublevacancy site (Figure 6a,b). In the former, the Si atomic orbitals exhibit a sp3 hybridization and the corresponding tetrahedral geometry, whereas in the latter the atomic orbitals are arranged in a sp2d-like hybridization11 allowing the Si atom to stay in the graphene plane. It is therefore timely to inspect the impact on the electronic conductance of Si-doped graphene with such

increasing number of these type of pentagonal Si defects distributed in a random fashion along a micrometer long graphene edge is expected to yield a more accurate description of the conductance of a realistic device. Indeed, Figure 3j shows the development of an ∼1 eV mobility gap as a result of the multiple reflections experienced by the carriers as they travel through the randomly fluctuating potential caused by the spatially distributed monohydrogenated impurities. The successive accumulation of backscattering events for some energies in the hole band leads the system to the localized transport regime, with a full suppression of the conductance ability of the graphene strip even for a little amount of edge defects. On the contrary, the conductance in the electron band is less affected by the doping atoms. As opposed to the allatoms sp2 hybridization, for an sp3-based Si defect, Figure 3k shows how the averaged conductances of disordered ribbons drop and widen the initial electronic band gap. The strong 1715



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Figure 6. (a) Experimental ADF image of a 4-fold Si point defect. (b) Schematic representation of the defect superimposed to the image in panel a. Upper panels in c show three-dimensional fully relaxed structures of graphene ribbons with 4-fold coordinated substitutional Si atoms at different positions across the ribbon width. Lower panels in c show the transmission versus charge carrier energy profiles and the electronic band diagrams of the doped structures. Dashed red ovals indicate the position in energy of the antiresonant states responsible of the transmission dips. Si atoms are in green, C in gray, and H in red.

In sharp constrast with the Si 3-fold coordination doping, the impact on the geometrical, electronic and quantum transport properties of a Si atom bonded simultaneouly to the four nearest C atoms is more greatly marked. A 4-fold Si point defect consists of two adjoining 5-fold rings formed by the substitution of two C atoms for one Si atom. Figure 6a,b shows an ADF image displaying the presence of a Si atom at a graphene inner lattice site and a schematic of the structure model. Along with a decrease in energy as the reconstructed Si point defect approaches the edge (Figure 4), electronic band diagrams in Figure 6c show that a low-dispersive state shifts up to higher energy levels. One notices the coincidence in energy of the quasibound states (pointed out by red ovals) with the broad conductance dips that reduce the conductance in one transmission channel and cause the marked asymmetric electron−hole transmission pattern. This rather large variation of the resonant energies with the doping atom position indicates that random distribution of 4-fold impurities over the ribbon will inevitably yield a rather uniform backscattering efficiency for a wide range of energies and, in consequence, to a conductance reduction over the occupied and inoccupied states of the first plateau. Fully relaxed geometries of the ribbons remain flat upon Si 4-fold coordination defect reconstruction. To sum up, grounded in experimentally observed Si-defects and underpinned on first-principles calculations, we have analyzed the electronic and quantum transport properties of Si-doped graphene. Using atomically resolved quantitative STEM-ADF imaging, the presence of isolated silicon atoms

type of defects, and the dependency of the defect formation energy with respect to its proximity to the edge. In Figure 4 the evolution of the formation energy of each doped configuration (relative to the most stable configuration of each series) with respect to the number of C atoms between the Si atom and the edge is shown. A clear reduction of the binding energy of the impurity atom is associated with its distance to the edge which, in the case of the 3-fold coordination, is accompanied by a gradually lower outward displacement of the Si from the graphene plane (see fully relaxed structures in Figure 5). Both types of interstitial Si doping do not exhibit localized magnetic moments. According to the transmission profiles plotted in Figure 5, all 3-fold coordination configurations exhibit low efficiency in inducing electronic backscattering, and only for certain dopant positions is a narrow-in-energy transmission dip observed. For the energy values within the first plateau, backscattering events barely occur despite the presence of impurity atoms. Consequently, graphene is expected to be transparent to Si 3fold doping. The small variation of the transport coefficients with the dopant position indicates that random distributions of impurities will not lead to a reduction of the conductance for energies near the Fermi level. Therefore, the transmission pattern of a defect such as the pentagonal edge termination will prevail over the rest. This analysis suggests that the selective incorporation of Si atoms at the graphene edges in the form of pentagonal defects could lead to a doping strategy to engineer the transport ability of the graphitic layer. 1716



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which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22725. This work was supported in part by NSF grant No. DMR-0938330 (W.Z.), by a Wigner Fellowship through the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UTBattelle, LLC, for the U.S. DOE (W.Z.), and the Center for Nanophase Materials Sciences (CNMS), which is sponsored at ORNL by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. DOE (J.-C.I.).

have been unambiguously detected at the edges of graphene layers. Si atoms have been identified terminating armchair graphene edges in pentagonal rings as well as part of reconstructed pentagonal-hexagonal rings in zigzag edges. Charge transport features created upon the incorporation of Si atoms at random positions along a graphene sheet exhibit a wide variability depending on both the position and hybridization of the impurity atom. The mobility gaps created at low doping rates could lead to greater efficiency in the design of new graphene-based devices, providing the ability for timelier control of graphene strips band gap and enhancing the graphene competitive advantage over other carbon-based materials.

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(1) Guinea, F.; Katsnelson, M. I.; Geim, A. K. Energy Gaps and a Zero-Field Quantum Hall Effect in Graphene by Strain Engineering. Nat. Physics 2010, 6, 30−33. (2) Han, M. Y.; Oezyilmaz, B.; Zhang, Y.; Kim, P. Energy Band-Gap Engineering of Graphene Nanoribbons. Phys. Rev. Lett. 2007, 98, 206805−206809. (3) Meyer, J. C.; Girit, C. O.; Crommie, M. F.; Zettl, A. Hydrocarbon Lithography on Graphene Membranes. Appl. Phys. Lett. 2008, 92, 123110−123113. (4) Kaul, I.; Joshi, N.; Ballav, N.; Ghosh, P. Hydrogenation of Ferrimagnetic Graphene on a Co Surface: Significant Enhancement of Spin Moments by C−H Functionality. J. Phys. Chem. Lett. 2012, 3, 2582−2587. (5) Mattis, D. C.; Yonezawa, F. Mobility Gap and Anomalous Dispersion. Phys. Rev. Lett. 1973, 31, 828−831. (6) Echtermeyer, T.; Lemme, M. C.; Baus, M.; Szafranek, B.; Geim, A.; Kurz, H. Nonvolatile Switching in Graphene Field-Effect Devices. Electron Device Letters, IEEE 2008, 29, 952−954. (7) Roche, S.; Biel, B.; Cresti, A.; Triozon, F. Chemically Enriched Graphene-Based Switching Devices: A Novel Principle Driven by Impurity-Induced Quasibound States and Quantum Coherence. Phys. E: (Amsterdam, Neth.) 2012, 44, 960−962. (8) Biel, B.; Blase, X.; Triozon, F.; Roche, S. Anomalous Doping Effects on Charge Transport in Graphene Nanoribbons. Phys. Rev. Lett. 2009, 102, 096803−096807. (9) Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J.-H.; Kim, P.; Choi, J.-Y.; Hong, B. H. Large-Scale Pattern Growth of Graphene Films for Stretchable Transparent Electrodes. Nature 2009, 457, 706−710. (10) Berger, C.; Song, Z.; Li, T.; Li, X.; Ogbazghi, A. Y.; Feng, R.; Dai, Z.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; et al. Ultrathin Epitaxial Graphite: 2D Electron Gas Properties and a Route toward Graphene-Based Nanoelectronics. J. Phys. Chem. B 2004, 108, 19912− 19916. (11) Zhou, W.; Kapetanakis, M. D.; Prange, M. P.; Pantelides, S. T.; Pennycook, S. J.; Idrobo, J.-C. Direct Determination of the Chemical Bonding of Individual Impurities in Graphene. Phys. Rev. Lett. 2012, 109, 206803−206807. (12) Zhou, W.; Lee, J.; Nanda, J.; Pantelides, S. T.; Pennycook, S. J.; Idrobo, J.-C. Atomically Localized Plasmon Enhancement in Monolayer Graphene. Nat. Nanotechnol. 2012, 7, 161−165. (13) Guzmán-Verri, G. G.; Lew Yan Voon, L. C. Electronic Structure of Silicon-Based Nanostructures. Phys. Rev. B 2007, 76, 075131− 075141. (14) Guzmán-Verri, G. G.; Lew Yan Voon, L. C. Band Structure of Hydrogenated Si Nanosheets and Nanotubes. J. Phys.: Condens. Matter 2011, 23, 145502−145508. (15) Koskinen, P.; Malola, S.; Häkkinen, H. Evidence for Graphene Edges beyond Zigzag and Armchair. Phys. Rev. B 2009, 80, 073401− 073404. (16) Jacobson, P.; Stöger, B.; Garhofer, A.; Parkinson, G. S.; Schmid, M.; Caudillo, R.; Mittendorfer, F.; Redinger, J.; Diebold, U. Disorder and Defect Healing in Graphene on Ni(111). J. Phys. Chem. Lett. 2012, 3, 136−139.

METHODOLOGIES The graphene sample for STEM analysis was obtained from Graphene-Supermarket. The graphene material was grown on a nickel film on a silicon wafer using a CVD method, and transferred onto a 2000-mesh copper grid for STEM analysis. The atomic configuration of Si impurities in graphene was studied using ADF imaging on an aberration-corrected Nion UltraSTEM-100 operating at an acceleration voltage of 60 kV,24 which is below the knock-on damage threshold of graphene. The convergence semiangle was set to 30 mrad, and the ADF images were collected for a half-angle range of ∼54 to ∼200 mrad. The enhanced signal-to-noise ratio in the ADF images allows quantitative atom-by-atom analysis at the Si point-defect sites. Self-consistent calculations of the electronic structure of modified graphene were performed with the SIESTA density functional theory-based code.25,26 A double-ζ basis set within the local density approximation (LDA) approach for the exchange-correlation functional was used. Atomic positions were relaxed with a force tolerance of 0.01 eV/Å. The integration over the Brillouin zone was performed using a Monkhorst sampling of 1 × 1 × 4 k-points. The radial extension of the orbitals had a finite range with a kinetic energy cutoff of 50 meV. The numerical integrals were computed on a real space grid with an equivalent cutoff of 300 Ry. To avoid any artificial backscattering effect in the region where the segments match, the supercell in the ab initio calculation is chosen long enough to avoid any overlap between the perturbed potentials caused by the doping atoms. A special feature of the electronic transport model is an approach that combines the accuracy of the self-consistent and parameter-free system description obtained from the firstprinciples calculations, with with real-space renormalization techniques27 for the determination of the electronic structure of long and disordered systems.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the computing resources provided on the Blues compute cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. This research also used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, 1717



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(17) Kim, K.; Coh, S.; Kisielowski, C.; Crommie, M. F.; Louie, S. G.; Cohen, M. L.; Zettl, A. Atomically Perfect Torn Graphene Edges and Their Reversible Reconstruction. Nat. Commun. 2013, 4, 1−6. (18) Zhou, W.; Oxley, M. P.; Lupini, A. R.; Krivanek, O. L.; Pennycook, S. J.; Idrobo, J.-C. Single Atom Microscopy. Microsc. Microanal. 2012, 18, 1342−1354. (19) Zhou, W.; Pennycook, S. J.; Idrobo, J.-C. Localization of Inelastic Electron Scattering in the Low-Loss Energy Regime. Ultramicroscopy 2012, 119, 51−56. (20) Marconcini, P.; Cresti, A.; Triozon, F.; Fiori, G.; Biel, B.; Niquet, Y.-M.; Macucci, M.; Roche, S. Atomistic Boron-Doped Graphene Field-Effect Transistors: A Route toward Unipolar Characteristics. ACS Nano 2012, 6, 7942−7947. (21) Lopez-Bezanilla, A.; Roche, S. Embedded Boron Nitride Domains In Graphene Nanoribbons For Transport Gap Engineering. Phys. Rev. B 2012, 86, 165420. (22) Jiang, D.-e.; Sumpter, B. G.; Dai, S. How Do Aryl Groups Attach to a Graphene Sheet? J. Phys. Chem. B 2006, 110, 23628−23632. (23) Lóp ez-Bezanilla, A.; Triozon, F.; Roche, S. Chemical Functionalization Effects on Armchair Graphene Nanoribbon Transport. Nano Lett. 2009, 9, 2537−2541. (24) Krivanek, O. L.; Corbin, G.J.; Dellby, N.; Elston, B. F.; Keyse, R. J.; Murfitt, M. F.; Own, C. S.; Szilagyi, Z. S.; Woodruff, J. W. An Electron Microscope For The Aberration-Corrected Era. Ultramicroscopy 2008, 108, 179−195. (25) Ordejón, P.; Artacho, E.; Soler, J. M. Self-Consistent Order-N Density-Functional Calculations for Very Large Systems. Phys. Rev. B 1996, 53, R10441−R10444. (26) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The Siesta Method For Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745. (27) López-Bezanilla, A.; Triozon, F.; Latil, S.; Blase, X.; Roche, S. Effect of the Chemical Functionalization on Charge Transport in Carbon Nanotubes at the Mesoscopic Scale. Nano Lett. 2009, 9, 940− 944.

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Electronic and Quantum Transport Properties of Atomically Identified

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