Modeling Graphene with Nanoholes: Structure and Characterization

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Modeling Graphene with Nanoholes: Structure and Characterization by Raman Spectroscopy with Consideration for Electron Transport Jie Jiang, Ruth Pachter, Teresa Demeritte, Paresh Chandra Ray, Ahmad E. Islam, Benji Maruyama, and John J Boeckl J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10225 • Publication Date (Web): 21 Jan 2016 Downloaded from http://pubs.acs.org on January 29, 2016

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Modeling Graphene with Nanoholes: Structure and Characterization by Raman Spectroscopy with Consideration for Electron Transport Jie Jiang,1 Ruth Pachter,1* Teresa Demeritte,2 Paresh C. Ray,2 Ahmad E. Islam,1 Benji Maruyama1 and John J. Boeckl1 1

Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, OH 45433, USA 2

Jackson State University, Jackson, MS 39217, USA

*

Corresponding author: Ruth Pachter, [email protected] ACS Paragon Plus Environment

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ABSTRACT Recent advances in controlled synthesis and characterization of single-layer graphene nanostructures with defects provide the basis for gaining an understanding of the complex nanomaterial by theoretical investigation. In this work, we modeled defective single-layer graphene (DSLG), where nanostructures with divacancy, trivacancy, tetravacancy, pentavacancy, hexavacancy, and heptavacancy defects, having pore sizes from 0.1 to 0.5 nm, were considered. Nanostructures with molecular oxygen adsorption to mimic experimental conditions were also investigated. Based on calculated formation energies of the optimized nanostructures, a few DSLGs were selected for theoretical characterization of the defectinduced I ( D) / I ( D ') Raman intensity ratios. We found that the I ( D) / I ( D ') ratio decreases with increase in the nanohole size and in the number of adsorbed oxygens, which explains an experimental observation of a decrease in this characterization signature with increase in exposure time to oxygen plasma. The predicted ratio was also confirmed by Raman spectroscopy measurements for graphene oxide quantum dots. The results were rationalized based on an analytical analysis of the D’ band electron-defect matrix elements. Finally, consideration of patterned graphene nanostructures with vacancies for field effect transistor (FET) application, were shown to provide a route to bandgap generation, and potentially improvement of the I on / I off ratio in a FET by nanohole passivation, e.g. by hydrogenation. FETs based on patterned graphene with small pores could have similar high level of performance as graphene nanoribbons, however with the added benefit of no width confinement.


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1. INTRODUCTION Application of nanoporous graphene has been extensively reviewed1 (see references therein), for example for DNA sequencing2 or molecular sieving.3-5 Nanoporous graphene was also considered for gas separation,6,7 proton transfer,8 desalination9-11 or atomic species transport,12,13 because an ideal membrane is expected to have high permeability, selectivity, and mechanical strength, which is fulfilled by single-layer graphene (SLG).14 Generation of physical and topological defects and pores in graphene nanostructures can be induced by electron or ion irradiation,3,5,15-21 including sculpting and patterning,22,23 by oxygen plasma,24-28 oxygen gas,29 or through block copolymer lithography of graphene nanomeshes.27 For example, sub-nanometer pores with controlled diameters of about 0.4 nm were generated by ion bombardment and oxidative etching for ionic transport.12 Graphene oxide can be reduced to achieve graphene-like properties,30,31 resulting in defective graphene.32 Vacancies and nanoholes can also be generated by oxidation of reduced graphene,33 while interestingly, recently the structural restoration of graphene oxide/reduced graphene oxide to defect-free graphene has been described.34 However, because of specific nanohole requirements it is important to characterize the pores in such materials and understand effects of the environment, which can be assisted by theoretical calculation. Importantly, characterization of defects in graphene enables assessment in terms of utility of patterned graphene nanostructures in electronics,35 as graphene could be useful for FETs by bandgap formation.27,35-37 Raman spectroscopy is employed as a useful non-destructive tool to characterize defects in graphene. The Raman spectrum of SLG is composed of the G peak corresponding to the allowed E2g phonon of the Brillouin zone (BZ) at the  point at about 1580 cm-1 and the double-resonance 2D peak from the 𝐴1′ phonon in the BZ corner of K38 at about 2700 cm-1. Raman defect-induced D and D ' bands in defective SLG (DSLG) appear at ca. 1350 cm-1 and 1620 cm-1, respectively.39,40 The D band is due to the 𝐴1′ phonon and requires a defect for its activation, originating from an inter-valley double-resonance process, and D ' is due to an E2g phonon that results from an intra-valley double-resonance process connecting two points in the same Dirac cone around K (or K').40,41 It was shown that Raman ACS Paragon Plus Environment

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spectroscopy can be used to characterize defect types by the I ( D) / I ( D ') intensity ratio,42 and a theoretical analysis of the I ( D) / I ( D ') intensity ratio43 furthermore demonstrated an ability to discern among point defects. However, the interplay of effects of larger vacancies and of the number of oxygen atoms adsorbed was not considered. Indeed, I ( D) / I ( D ') ratios measured in a range of 2-6,24,29 which are smaller than those for point defects, of ca. 7 as previously identified,42 were not analyzed. In this work, we investigated theoretically the structure of larger vacancies in DSLG using density functional theory (DFT), and characterized the I ( D) / I ( D ') Raman intensity ratios. Specifically, divacancy (V2), trivacancy (V3), tetravacancy (V4), pentavacancy (V5), hexavacancy (V6), and heptavacancy (V7), having pore sizes from 0.1 to 0.5 nm, were considered. Interestingly, in addition to identification of the 555-777 and 5555-6-7777 reconstructed divacancy defects, shown to be thermodynamically stable,44 trivacancy and tetravacancy defects were identified experimentally,16,45,46 and were included in our analysis, noting that DSLG with vacancies and reconstructed vacancies are commonly induced by electron irradiation. We also examined effects of molecular oxygen adsorption to mimic experimental conditions, in comparison to experimental D and D ' Raman profiles of graphene oxide quantum dots. We found that the nanohole size and number of oxygen atoms adsorbed have pronounced effects on I ( D) / I ( D ') Raman intensity ratios. The ratios decreased with a larger number of adsorbed oxygens, and also the nanohole size, which is consistent with the work of Eckmann et al.,42 where the I ( D) / I ( D ') Raman intensity ratio was shown to decrease when changing from vacancies to edges. These results are useful for assessing utility of regularly patterned graphene nanostructures upon introduction of defects, specifically for FET application by analysis of a bandgap opening. We demonstrated that a graphene nanomesh with passivated nanoholes can potentially offer higher FET performance in comparison to graphene nanoribbons (GNRs). 2. METHODS 2.1 Structural optimization. DFT structural optimizations were performed using PWscf with ultrasoft pseudopotentials.47 A 10 Å vacuum region was used. The Perdew-Burke-Ernzerhof (PBE)48 ACS Paragon Plus Environment

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exchange-correlation functional was used, with a planewave energy cutoff of 30 Ry. Atomic positions were fully relaxed until forces were less than 10-3 Ry/a.u. Structures with nanoholes were generated by omitting carbon atoms, as shown schematically in Figure 1(a) for V2 - V7. Supercell sizes 6×6, 7×7, 8×8, 10×10, and 12×12, were tested for the formation energy convergence for V7. The 10×10 supercell was found to be large enough, and therefore selected for all vacancies. A 1×3×3 k-point sampling and a Gaussian smearing width of 0.1 eV for k-space integrals were used. The nudged elastic band (NEB) method was used for finding minimum energy paths.49 2.2 Defect-induced Raman intensities. D and D ' processes involve photon absorption, phonon emission, electron-defect collision, and photon emission. We considered all possible processes in the scattering amplitude, including electron-electron, hole-hole, and electron-hole processes, given by50

(1) where i is the initial and f final states with a scattered photon at frequency intermediate state where an e-h is created;

| s1 

and

| s2 

L   ph ; | s0  is an

are intermediate states where an e-h pair and

a phonon are present; El  0,1,2 are energies;  is a decay factor (set to 0.043 eV). The Raman intensity depends on the electron-defect matrix element ( M

def

) , optical matrix element ( M op ) , and the electron-

ph

phonon (el-ph) matrix element (M ) . The electron-defect matrix elements from an initial | k  state to a final | k '  state are given by M def  k ' | V | k  , where V is the defect potential

V  VDSLG  VSLG

VDSLG

(2).

describes the DFT self-consistent potential of DSLG and

VSLG

is the corresponding value for

pristine SLG. The electron-defect atomic matrix element is defined by

ml ,l '   ( Rl ' ) | V |  ( Rl ) 

(3),


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where  ( Rl ) is a C 2pz orbital centered at the atom Rl . M def is then given by

M kdefk ' 

1 Cl*' (k ')Cl (k )  ei ( k Rl k Rl ' )   ( Rl ' ) | V |  ( Rl )   N l ,l ' Rl , Rl '

(4),

 1  1  where Ckl  f *  ; -1/+1 denotes conduction and valence bands, respectively. f is expressed as  2   | f |

f (k )  e



ik y a 3

ik y a

k a  2ie 2 3 cos  x  and a is the graphene lattice constant. The optical matrix elements were  2 

calculated using the dipole approximation51 and the el-ph matrix elements approximated as the hopping integral variation by bond length change due to phonon vibration,52 as we have previously described.43 The intensity is given by

I ( ) 

1 Nq

 I   ( q

L

    q )[n( q )  1]

(5),

q

where N q is the number of phonon wave vectors, n( ) the Bose-Einstein distribution, and 2

I q

1 ph , where N k is the number of intermediate states. To calculate the Raman intensity we  K Nk

integrated 𝑘 and 𝑞 over graphene’s BZ, using uniform 𝑘 and 𝑞 2D meshes. A 𝑘 mesh of 840 × 840 and q mesh of 120 × 120 were used to get convergence. For analysis of the results, we considered the electron-defect matrix elements of the D ' band, an intravalley backscattering process. As we previously explained,43 upon neglecting off-site atomic matrix elements and structure optimization, M def for the intra-valley scattering is given by

M kdefk ' 

 i (  ) u  i ( k  k ') RA  e k k'  ei ( k k ')RB   e N  RA RB 

where k and k' are initial and final electron wave-vectors measured from K 

(6),

2  1 1  , , a  2 3 

u  20eV is the on-site atomic matrix element due to a missing carbon atom, and N the number of ACS Paragon Plus Environment

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unit cells in the supercell. The wave-vector k is much smaller than 2

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a

. We can replace the phase

factors in Equation (6) by 1. We further neglect the constant u , and Equation (6) can be simplified to N

i ( k  k ' ) M kdef  k '  n A  nB e

(7),

where n A and nB are the number of missing A and B sub-lattice atoms, respectively. 2.3 Nanopatterned DSLG. Following the work of Dvorak, et al.,35 the supercell lattice vectors of a regularly patterned graphene nanostructure with vacancies can be written as R1  n1a1  m1a2 and

R2  n2a1  m2a2 , with the primitive lattice vectors a1 and a2 denoted by (n1 , m1 , n2 , m2 ) . For a rectangular lattice with R1 along a zigzag direction and R2 along an armchair direction, m1   n1 and

m2  n2 , and the condition for a gap opening is mod( n1 ,3)=0.35 The V2(a) vacancy was first chosen as an example application with n2  4 , corresponding to R2 = 1.7 nm, and n1 assumed 15 and 16, corresponding to R 1 = 3.7 and 4.0 nm, respectively (see schematic of supercells and lattice vectors in supplementary information Figures S1(a) and S1(b)). Motivated by the possible increase in performance, we further studied transport properties of patterned graphene nanostructures passivated by hydrogen. As an example, the V6(b) defect with H passivation was considered. We considered n2  14 , corresponding to R2  6.0 nm, and n1 =3 and 4, which are metallic and semiconducting, with R 1  0.7 and 1.0 nm, respectively (schematic in Figures S1(c) and S1(d)), as bandgap opening depends on n1 but not on n2 . Note that for the hydrogen passivated structure R2 was set as z (transport direction) and R1 is in the y direction, unlike for V2(a). Taking R2 as the transport direction could potentially be an easier way to fabricate the electronic device with the target properties. 2.4 Electron transport calculations. The modeled patterned graphene nanostructure device consists of left and right graphene electrodes, a central scattering region and a gate. It is assumed that the ACS Paragon Plus Environment

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dielectric layer has a thickness of 3 Å. The permittivity of SiO2 was used in all cases. A thin metal layer is included to provide a fixed potential. The gate, including the dielectric and metal layers, is treated as a continuous region and is described self-consistently. The Perdew-Zunger exchange-correlation functional and Troullier-Martins norm-conserving pseudopotentials were used. A double-zeta plus polarization basis set was used for all atoms. The mesh cutoff was set as 200 Ry for the grid integration. In the absence of a gate voltage, periodic boundary conditions were used in the three directions in the Poisson solver. When a gate voltage was applied, Neumann, periodic, and Dirichlet boundary conditions were used in the x, y, and z directions, respectively. The Monkhorst-Pack k sampling was 1´ 20 ´100 for the (3,-3,14,14) and (4,-4,14,14) nanostructures in electron transport calculations. Electron transport calculations were carried out with the non-equilibrium Green’s function formalism combined with DFT, based on the Landauer-Bϋttiker approach,53,54 implemented in ATK v14.2.55,56 In the simulated devices the system is divided into a left (L) electrode, central region, and right (R) electrode. Under an applied bias (Vb), the chemical potentials in each electrode will shift as 𝜇𝐿 (𝑉𝑏 ) = 𝜇𝐿 (0) + 𝑒𝑉𝑏 /2 and 𝜇𝑅 (𝑉𝑏 ) = 𝜇𝑅 (0) − 𝑒𝑉𝑏 /2, where 𝜇𝐿 (0) and 𝜇𝑅 (0) are the chemical potentials at zero bias for the L and R electrodes, respectively. The transmission is given as a function of the energy E and Vb, i.e. 𝑇(𝐸, 𝑉𝑏 ) = 𝑇𝑟[Γ𝐿 (𝐸, 𝑉𝑏 )𝐺 𝑅 (𝐸)Γ𝑅 (𝐸, 𝑉𝑏 )𝐺 𝐴 (𝐸)], where 𝐺 𝑅 and 𝐺 𝐴 are the retarded and advanced Green’s functions, respectively; Γ is the contact broadening for L and R electrodes. The current is calculated from the transmission as a function of bias by 2𝑒

μ (V )

𝐼(𝑉𝑏 )= h ∫μ R(V b) 𝑇(𝐸, 𝑉𝑏 ) [𝑓(𝐸, μL ) − 𝑓(𝐸, μR )]𝑑𝐸 L

b

(8).

2.5 Synthesis of graphene oxide quantum dots. In the first step, graphene oxide was prepared from graphite by the modified Hummers method, as previously reported.57-60 In the next step, graphene oxide quantum dots were prepared from graphene oxide, using a hydrothermal cutting process. For this purpose, 0.2 g of freshly synthesized graphene oxide was treated with 50 ml of DMF at 250°C for five hours. After finishing the reaction, the solid product of graphene oxide quantum dots was vacuum


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filtered using a 0.2 micrometer nylon membrane. Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy and a JEOL 2010-F TEM were used for characterization. 3. RESULTS AND DISCUSSION 3.1 Vacancy structures. Although a large number of isomers are possible for the vacancies considered, we selected for optimization nanoholes that were observed experimentally or that were previously calculated.61 Optimized DSLG structures are shown in Figure 1(b). We note that there is no indication of out-of-plane distortion in the structures. Indeed, geometry optimization of periodic DSLG systems with a monovacancy with dangling bonds, resulted in planar structures.62,63 Moreover, any outof-plane displacement of about 0.2 – 0.5 Å would not affect significantly the I ( D) / I ( D ') Raman intensity ratio because the carbon 2pz orbital at the original site overlaps with both the positive and negative defect potentials at the new site, partially cancelling the contribution, and the resulting electron-defect matrix element is small. Formation energies 𝐸𝑓 , defined by 𝐸𝑓 = 𝐸𝑑 − 𝑁𝜇(𝐶), where 𝐸𝑑 is the total energy of the system with a defect, 𝑁 the number of atoms in the DSLG, and 𝜇(𝐶) the chemical potential of carbon, calculated as the total energy per carbon atom in pristine SLG,64 were calculated for DSLG structures. DSLGs having the lowest formation energies were selected for calculation of the Raman intensities. For the divacancy and its reconstructed 555-777 and 5555-6-7777 defects43 (V2(a) - V2(c)), formation energies of 7.07, 6.55, and 6.62 eV were calculated, respectively, and these defects were considered for calculation of I ( D) / I ( D ') Raman intensity ratios.

Stability and reconstruction of the odd and even V3 and V4 vacancies were examined experimentally and theoretically by Robertson, et al.16,46 For V3, we considered three atoms taken out in a zigzag chain (V3(a)), which was generated with energetic gold particles in PLD,45 as well as the bridged reconstructed vacancy generated by electron irradiation and characterized by aberration corrected TEM46 (V3(b)). Formation energies of 11.10 eV and 12.78 eV for V3(a) and V3(b) were calculated, respectively, and both were considered further. Five vacancies were considered for V4 (V4(a) - V4(e)),


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generated as shown in Figure 1(a), including the two most frequently observed with aberration corrected TEM (V4(d) and V4(e)).16 Note that vacancies V3(b), V4(d) and V4(e) comprise so-called extended vacancies, where the removed carbon atoms are not consecutively connected. Calculated formation energies were 10.71, 14.46, 13.18, 11.90, and 10.43 eV for V4(a) - V4(e), respectively. V4(a), V4(d) and V4(e) were selected for calculation of the Raman intensity ratios. Four topologically different structures were considered for V5 (V5(a) - V5(d)), with formation energies of 15.04, 16.27, 17.49, 16.82 eV, respectively, and Raman calculations were performed for V5(a). V6 and V7 have a large number of possible structures, with formation energies of 15.69 and 18.42 eV for V6(a) and V6(b), respectively, and of 18.20 and 19.63 eV for V7(a) and V7(b), respectively. V6(a) and V7(a) were found to be more favorable also in previous work.61 The considered vacancies for Raman intensity calculations were V2(a), V2(b), V2(c), V3(a), V3(b), V4(a), V4 (d), V4(e), V5(a), V6(a) and V7(a). Even vacancies with dangling bonds are reconstructed by pentagons at the edges of the vacancy, and are therefore more stable than odd vacancies that have an unsaturated carbon with a dangling bond. We note that on the nanohole, pentagonal C-C bonds are lengthened compared to hexagonal bonds. Average hexagonal bond lengths were 1.45, 1.45, 1.50, 1.45, 1.47, 1.46 Å, and pentagonal bond lengths were 1.77, 1.79, 1.70, 1.92, 2.07, 2.10 Å for V2(a), V3(a), V4(a), V5(a), V6(a) and V7(a), respectively. 3.2 O2 adsorption onto DSLG. Optimized geometries with O2 adsorption are shown in Figure 2(a). In an odd vacancy, O2 dissociates and chemisorbs onto the vacancy, where one of the oxygen atoms attaches to the unsaturated C atom, pulling it out-of-plane, while the other interacts with a pentagonal CC bond on the ring, and transforms the pentagon to a hexagon in the graphene plane. Dissociation of oxygen on a graphene surface with vacancies has been shown to be preferable as compared to inert SLG.65,66 For an even vacancy, O2 adsorption may occur by physisorption or chemisorption, where for physisorption O2 stays intact at 3.0, 2.0, and 2.4 Å above the nanohole for V2(a), V4(a), and V6(a), respectively. For chemisorption, O2 dissociates on the surface, where the two oxygen atoms transform two pentagons to hexagons in the graphene plane, except for the divacancy. In this case, interaction ACS Paragon Plus Environment

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between the oxygen atoms results in two hexagons above and below the graphene plane. Chemisorbed configurations are about 8-10 eV lower in energy than those upon physisorption, specifically, of -8.39, 8.83, and -10.87 eV for V2(a), V2(a) and V2(a), respectively. The O2 adsorption energy is defined as 𝐸𝑎𝑑 = 𝐸𝑑+𝑂2 − 𝐸𝑑 − 𝐸𝑂2 , with 𝐸𝑑+𝑂2 , 𝐸𝑑 , and 𝐸𝑂2 the energies for DSLG with O2, DSLG, and O2, respectively. The calculated adsorption energies for chemisorption are -8.55, -8.85, -9.32, -9.90, -11.01, -9.97 eV for V2(a), V3(a), V4(a), V5(a), V6(a) and V7(a), respectively. In case of physisorption, adsorption energies are -0.17, -0.50, and -0.14 eV for V2(a), V4(a), and V6(a). Activation barriers for oxygen dissociation are shown in Figure 2(b). For V2(a) and V4(a), transition states are shown for the third step, with activation energy barriers of 0.53 and 0.62 eV, respectively. For V6(a), the transition state is at the second step, with a small activation energy barrier (0.034 eV). Although O2 dissociation may be prevented by higher barriers for V2(a) and V4(a), it can easily dissociate in DSLG with the larger V6(a) defect, a typical result for large even vacancies. Elongated pentagonal C-C bonds make the large even vacancies more active chemically, leading to smaller barriers. A recent study pointed out that physisorption is more preferred in DSLG.61 Our calculations indicate that physisorption is favored for small vacancies, e.g. V2(a) and V4(a), while chemisorption is more favorable for V2n(a) with 𝑛 ≥ 3. 3.3 Raman band profiles. Based on the optimized vacancy structures, we calculated defect-induced Raman band intensity profiles. Defect potential isosurfaces (Equation (2)) for the vacancies considered are given in Figure 3, showing δ-potentials centered at the missing atoms, with structural rearrangements that induce additional potentials near the edge of vacancies. Using the calculated defect potentials, atomic matrix elements were calculated by Equation (3) and Raman intensities by Equations (4-5), as summarized in Table 1. We note that V2(a) has a larger formation energy and is unlikely to be observed experimentally, and therefore the intensity ratio may not be observed, while the other two reconstructed divacancies result in an average I ( D) / I ( D ') value of about 3.7. For V3(a) and V3(b), observed experimentally,45,46 an average ratio of about 3 resulted, while for the observed V4(d) and


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V4(e)16 the average value is larger, of about 5.7. The average ratio is 4.1 for V2, V3 and V4 that were observed experimentally, which is smaller than the ratio of 7 measured experimentally for graphene with point defects.42 Notably, for vacancies larger than V4, the I ( D) / I ( D ') ratio is less than 2, thus enabling differentiation between smaller and larger nanoholes. To gain an understanding of the response, we considered the electron-defect matrix elements of the

D ' band, which is an intra-valley scattering process. M def for this band measures the deviation from the so-called backscattering node effect at  k   k    , where  k and  k  are the initial and final angles of the wave-vectors,43 and the smaller the value due to backscattering, the larger the intensity ratio. Figure 4 shows the intra-valley electron-defect matrix elements in the backscattering region. The extended vacancies V3(b), V4(d), and V4(e) have a divacancy or reconstructed 5555-6-7777 divacancy character and the node effect is preserved, with a relatively large I ( D) / I ( D ') ratio. The node effect is lifted for V3(a), V4(a), V5(a), and V7(a) by a change to a parabolic dispersion with a minimum at

 k   k    . M def values of 0.06, 0.14, 0.38, 0.23, 0.39, and 0.20, for V2(a), V3(a), V4(a), V5(a), V6(a), and V7(a), respectively, indicate that the variation in the D ' intensity is smallest for V2(a) and largest for V4(a) and V6(a). V6(a) preserves a node, but is shifted from  to 1.1 . The position of the shift is related to the pore symmetry, and for V6(b), generated by removing a graphene hexagon, the node is very close to  , and the corresponding I ( D) / I ( D ') ratio is 6 instead of 1. The M def value at

 k   k    in this case is 0.39. Further understanding of the results is provided by analysis of Equation (7), which indicates that a missing atom A contributes a factor of 1, and a missing atom B contributes a factor of ei ( k  k ' ) , so that if nA  nB , there is a node at  i   f   . Otherwise, the node effect is lifted, and M def is proportional to nA  nB . It can be shown from Equation (7) that M def for V2(a) - V7(a) are 1  ei (k k ' ) , 1  2ei (k k ' ) , 1  3ei ( k k ' ) , 2  3ei (k k ' ) , 3  3ei ( k  k ' ) , and

4  3ei (k k ' ) , respectively. The corresponding values at backscattering are 0, 1, 2, 1, 0, and 1 for V2(a), V3(a), V7(a), V5(a), V4(a), and V6(a), respectively. Overall, the increasing order of M def at ACS Paragon Plus Environment

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 k   k    for V2(a), V3(a), V7(a), V5(a), V4(a), and V6(a), correlates with the decreasing order of the I ( D) / I ( D ') ratios (see Table 1). 3.4 Defect-induced Raman intensity ratio for oxygen adsorbed DSLG. Next, we examined the I ( D) / I ( D ') ratios for DSLG with O2 adsorption (see Table 1). Note that upon O2 physisorption, the

calculated Raman intensity ratios do not change. Thus, the values for V2(a) - V7(a) are 7.6, 2.8, 4.5, 6.5, 2.3, 5.7, 6.1, 5.2, 1.4, 1.1 and 0.9, respectively. We note that for the smaller vacancies that were observed experimentally, namely V2(b), V2(c), V3(a), V3(b), V4(d), and V4(e), the average I ( D) / I ( D ') ratio is 4.6. On the other hand, for the larger nanoholes (V5 – V7) the average ratio is 1.1, thus indicating that with increase in the nanohole size, a decrease in the I ( D) / I ( D ') ratio will occur. However, an increase of the number of oxygen atoms is not clearly taken into account. High-resolution TEM images of graphene oxidized for 5 h at 533K found 5-7 oxygen atoms adsorbed at a divacancy (DV).29 Thus, to evaluate effects of increasing the number of oxygen atoms adsorbed, we calculated the Raman profiles for an oxygen lactone at a monovacancy (MV1) (a), an epoxy (MV2) (b),67 as well as of 5 (c) and 7 (d) oxygen atoms adsorbed at a divacancy (DV1 and DV2), as was considered by Yamada, et al.29 Raman profiles and the corresponding structures are shown in Figure 5. I ( D) / I ( D ') ratios of 3.7, 3.9, 1.2 and 1.0 were calculated for the structures 5(a) - 5(d), respectively. The trend demonstrated a decrease in the I ( D) / I ( D ') ratio with the number of oxygen atoms adsorbed onto a vacancy. Overall, the value of 4.6 for V2(b), V2(c), V3(a), V3(b), V4(d), and V4(e) changes to 3.7 when including DV1 and DV2 defect-induced Raman ratio results with more oxygens adsorbed. This value is consistent with our recent in situ Raman measurements for oxidized graphene. Raman intensity variations because of O2 adsorption can be understood in terms of changes in the defect potentials due to structural rearrangements. For adsorption onto odd vacancies, O attaches to a pentagon edge and transforms the pentagon to a hexagon, removing a δ-potential (Figure 3). The other oxygen atom attaches to the unsaturated carbon atom and pulls the atom out-of-plane, which creates a δpotential in the plane, as shown in Figure 3. These two effects are partially cancelled in the electronACS Paragon Plus Environment

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defect matrix elements. O2 chemisorption on even vacancies transforms two pentagons to hexagons, removing two δ-potentials. The potential of V2n(a) with O2 varies similarly to that of V2n-2(a) without O2, and the Raman profiles are expected to be similar. The Raman profile of V2(a) with O2 adsorption is expected to convert to that of pristine graphene. However, due to a structural rearrangement, the defect potential is similar to that of V2 (a) without O2 with a smaller potential amplitude. The Raman intensity ratio is thus still large, of 7.6, while the intensity amplitudes are much quenched. The intensity ratio of V4(a) with O2 is increased to 5.7 since the ratio of DSLG V2(a) without O2 is large. The intensity ratio of V6(a) with O2 is about 1, similar to that of V4(a) without O2. Recent measurements found that when graphene was exposed to oxygen plasma for varying exposure times, the I ( D) / I ( D ') ratio changed, presumably reflecting a variation from sp3-type to vacancy defects,24 and decreased with plasma exposure time. As the time of the experiment increases, the nanohole size and number of oxygens adsorbed increase and the ratio decreases according to our calculations, consistent with the observation that the ratio decreased from about 6 at 20-25 s to 1 at 50 s duration. In addition, X-ray photoemission spectra for a graphite surface upon prolonged exposure to atomic O found that in addition to epoxy groups, oxygens appear also in ether, semiquinone, and lactone functionalities.68,69 Generation of more realistic oxygen adsorbed graphene oxide nanostructures will be undertaken in future work. To further compare the calculated I ( D) / I ( D ') ratio, the Raman spectrum was measured for wellcharacterized graphene oxide quantum dots (see Methods section). Raman spectroscopy of the D, G, D’, 2D, D+D’ bands at 1350, 1585, 1620, 2680, and 2945 cm-1, respectively, are shown in Figure 6(a), as well as a TEM image of the sample. The D and D’ band intensity ratio measured was ca. 2.5. As mentioned, we calculated a value of 3.7 for the smaller vacancies that were observed experimentally, but upon inclusion of larger vacancies with values of about 1, the ratio will decrease. The observed ratio of 2.5 is indicative of larger vacancies and/or more oxygen adsorption, with a possible relatively larger contribution from edges with adsorbed oxygens in the graphene oxide quantum dots. The FTIR


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spectrum is shown in Figure 6(b), where the observed C=O and (CO)-H stretches clearly indicate oxygen adsorption at vacancies. 3.5 Electron transport. Electronic band structures along with the patterned graphene nanostructures are shown in Figures 7(a)-7(d). According to the bandgap opening condition, (15, 15, 4, 4) is expected to be a semiconductor. Indeed, we show a small bandgap opening at of ~ 0.1 eV for the bulk states A defect band appears in the bandgap, caused by defect states localized near V2(a), due to an incomplete saturation of carbon atoms at the two pentagons, as compared to bulk states defined as extended states. The pentagonal C-C bond at the V2(a) ring is elongated to 1.69 Å. The (16, 16, 4, 4) graphene nanostructure is expected to be a semimetal. However, the defect band near the Fermi level opens a bandgap of about 0.26 eV for the bulk states To examine the performance of FET devices patterned from DSLG nanostructures, the transmission, I-V, and I-Vg at low bias ( Vb  20 mV) curves were calculated for DSLG patterned with a V2(a) vacancy (Figures S2((a)-(c)) for (15, 15, 4, 4) and S2((d)-(f)) for (16, 16, 4, 4) ). Transmission gaps near the Fermi level of about 0.1 and 0.26 eV for (15, 15, 4, 4) and (16, 16, 4, 4) , respectively, correspond to the bulk bandgaps. Since the defect states are localized near the defect, their contribution to the transmission is small, and the I-V curves for both nanostructures show semiconductor characteristics, with no current from 0 to 0.05 and 0.13 V, respectively. The I on current is ca. 1  for (15, 15, 4, 4) , and the off-state minimum leakage current about 6.7 103 , resulting in a I on / I off ratio of ca. 136 at the channel length of 3.7 nm. For (16,-16,4,4) , the ratio is ca. 124 for a 4.0 nm channel. The large leakage current from the left to right electrodes is due to defect states at the Fermi level. To examine effects of nanohole size, the transmission, I-V and I-Vg curves for (15, 15, 4, 4) and (16, 16, 4, 4) patterned graphene nanostructures with a V6(a) defect were also calculated (Figure S3). It is demonstrated that the nanohole size does not change significantly the transport behavior, and the

I on / I off ratios were 148 and 131 for (15, 15, 4, 4) and (16, 16, 4, 4) , respectively. ACS Paragon Plus Environment

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A hexagonal nanohole with H passivation was considered for the (3, 3,14,14) and (4, 4,14,14) nanostructures patterned with a V6(b) vacancy (band structures in Figures 7(c)-7(d)). As expected, the defect band disappears in both nanostructures due to H passivation of the nanohole. The transmission, IV, and I-Vg results are summarized in Figures and S2((g)-(i)) and S2((j)-(k)) respectively. The bandgap for (3, 3,14,14) is about 0.32 eV and the transmission and I-V curves are typical of a semiconductor, however the values are smaller because of a narrower channel width. To study the quality of a FET in this case, the I on / I off ratio and subthreshold swing S  Vg / d log I values were evaluated. The response of (3, 3,14,14) is characteristic of an ambipolar transistor, with an I on of about 0.1 . At the off-state of zero gate voltage, the minimum leakage current is about 4.7  10 6  translating to the very large

I on / I off ratio of 2 104 . Indeed, in comparing the near-symmetrical I-Vg curves for FETs fabricated from (15,-15,4,4) and (3, 3,14,14) for Vb  20 mV, as shown in Figures 8(a) and 8(b), respectively, a very large difference is noted. Since (3, 3,14,14) has a channel length of 6 nm, the I on / I off ratio is 10 times the ratio predicted for a (4,0) GNR-FET with the same channel length.70 The S ~ 63 meV/decade value is similar to that in GNR-FETs70 and for single-wall carbon nanotube FETs.71 The value is also close to the theoretical limit of conventional Si-based FETs, of 60 meV/decade.72 We also examined the

I on / I off ratio by changing the channel length and found that a value of 5  103 at 3 nm length can be achieved, which is much larger than the ratio from a (16, 16, 4, 4) nanostructure FET with a channel length of 3.7 nm. I on / I off and subthreshold swing values in this case indicate excellent FET performance for the patterned graphene nanostructure upon hydrogenation. 4. CONCLUSION To enable understanding of the characterization of defective single-layer graphene by Raman spectroscopy we carried out a comprehensive study on the effects of nanoholes with varying size and oxygen adsorption on the I ( D) / I ( D ') intensity ratio. Formation energy calculations of optimized DSLG structures with vacancies that range from two to seven missing carbon atoms (V2 - V7) were ACS Paragon Plus Environment

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performed by DFT calculations, and were shown to be consistent with those that were characterized experimentally, e.g. for V3 and V4. Upon O2 adsorption, we found that chemisorption occurs for odd vacancies, while for even vacancies, although physisorption is preferred on small vacancies, chemisorption occurs for larger vacancies. DSLG structures with the lowest formation energies were selected for analysis of the Raman spectroscopy I ( D) / I ( D ') ratio. The ratios were demonstrated to decrease with increase in the nanohole size and the number of adsorbed oxygen atoms. The results explain the observed decrease in I ( D) / I ( D ') with exposure time to oxygen plasma, and are consistent with our measurements for oxidized graphene and graphene oxide quantum dots. Results were rationalized qualitatively based on an analytical analysis of the intra-valley D’ band electron-defect matrix elements. Electronic structure calculations of patterned graphene nanostructures with specific meshes demonstrated opening of a bandgap and moreover potential improvement of the I on / I off ratio by passivation of a nanohole, e.g. by hydrogenation, as compared to GNRs where the width of the nanostructure limits the current. ACKNOWLEDGEMENTS We gratefully acknowledge support by the Air Force Office of Scientific Research and computational resources and helpful assistance provided by the AFRL DSRC. Supplementary Information Supercell and lattice vectors of patterned graphene nanostructures, and transmission, I-V and I-Vg plots for these models. This information is available free of charge at http://pubs.acs.org. References (1) Yuan, W.; Chen, J.; Shi, G. Nanoporous Graphene Materials. Mater. Today (Oxford, U. K.) 2014, 17, 77-85. (2) Postma, H. W. C. Rapid Sequencing of Individual DNA Molecules in Graphene Nanogaps. Nano Lett. 2010, 10, 420-425. (3) Garaj, S.; Liu, S.; Golovchenko, J. A.; Branton, D. Molecule-Hugging Graphene Nanopores. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 12192-12196,S12192/12191-S12192/12193. (4) Koenig, S. P.; Wang, L.; Pellegrino, J.; Bunch, J. S. Selective Molecular Sieving through Porous Graphene. Nat. Nanotechnol. 2012, 7, 728-732.


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(25) Rozada, R.; Solis-Fernandez, P.; Paredes, J. I.; Martinez-Alonso, A.; Ago, H.; Tascon, J. M. D. Controlled Generation of Atomic Vacancies in Chemical Vapor Deposited Graphene by Microwave Oxygen Plasma. Carbon 2014, 79, 664-669. (26) Childres, I.; Jauregui, L. A.; Tian, J.; Chen, Y. P. Effect of Oxygen Plasma Etching on Graphene Studied Using Raman Spectroscopy and Electronic Transport Measurements. New J. Phys. 2011, 13, 025008/025001-025008/025012. (27) Bai, J.; Zhong, X.; Jiang, S.; Huang, Y.; Duan, X. Graphene Nanomesh. Nat. Nanotechnol. 2010, 5, 190-194. (28) Liu, L.; Ryu, S.; Tomasik, M. R.; Stolyarova, E.; Jung, N.; Hybertsen, M. S.; Steigerwald, M. L.; Brus, L. E.; Flynn, G. W. Graphene Oxidation: Thickness-Dependent Etching and Strong Chemical Doping. Nano Lett. 2008, 8, 1965-1970. (29) Yamada, Y.; Murota, K.; Fujita, R.; Kim, J.; Watanabe, A.; Nakamura, M.; Sato, S.; Hata, K.; Ercius, P.; Ciston, J.; et al. Subnanometer Vacancy Defects Introduced on Graphene by Oxygen Gas. J. Am. Chem. Soc. 2014, 136, 2232-2235. (30) Dreyer, D. R.; Park, S.; Bielawski, C. W.; Ruoff, R. S. The Chemistry of Graphene Oxide. Chem. Soc. Rev. 2010, 39, 228-240. (31) Larciprete, R.; Fabris, S.; Sun, T.; Lacovig, P.; Baraldi, A.; Lizzit, S. Dual Path Mechanism in the Thermal Reduction of Graphene Oxide. J. Am. Chem. Soc. 2011, 133, 17315-17321. (32) Gomez-Navarro, C.; Meyer, J. C.; Sundaram, R. S.; Chuvilin, A.; Kurasch, S.; Burghard, M.; Kern, K.; Kaiser, U. Atomic Structure of Reduced Graphene Oxide. Nano Lett. 2010, 10, 11441148. (33) Solis-Fernandez, P.; Paredes, J. I.; Villar-Rodil, S.; Guardia, L.; Fernandez-Merino, M. J.; Dobrik, G.; Biro, L. P.; Martinez-Alonso, A.; Tascon, J. M. D. Global and Local Oxidation Behavior of Reduced Graphene Oxide. J. Phys. Chem. C 2011, 115, 7956-7966. (34) Rozada, R.; Paredes, J. I.; Lopez, M. J.; Villar-Rodil, S.; Cabria, I.; Alonso, J. A.; Martinez-Alonso, A.; Tascon, J. M. D. From Graphene Oxide to Pristine Graphene: Revealing the Inner Workings of the Full Structural Restoration. Nanoscale 2015, 7, 2374-2390. (35) Dvorak, M.; Oswald, W.; Wu, Z. Bandgap Opening by Patterning Graphene. Sci. Rep 2013, 3, 2289. (36) Baskin, A.; Kral, P. Electronic Structures of Porous Nanocarbons. Sci. Rep. 2011, 1, 36; pp. 1-37. (37) Kim, M.; Safron, N. S.; Han, E.; Arnold, M. S.; Gopalan, P. Fabrication and Characterization of Large-Area, Semiconducting Nanoperforated Graphene Materials. Nano Lett. 2010, 10, 1125-1131. (38) Dresselhaus, M.; Jorio, A.; Cançado, L.; Dresselhaus, G.; Saito, R.: Raman Spectroscopy: Characterization of Edges, Defects, and the Fermi Energy of Graphene and sp 2 Carbons. In Graphene Nanoelectronics; Springer, 2012; pp 15-55. (39) Cancado, L. G.; Pimenta, M. A.; Neves, B. R. A.; Dantas, M. S. S.; Jorio, A. Influence of the Atomic Structure on the Raman Spectra of Graphite Edges. Phys. Rev. Lett. 2004, 93, 247401/247401-247401/247404. (40) Ferrari, A. C.; Basko, D. M. Raman Spectroscopy as a Versatile Tool for Studying the Properties of Graphene. Nat. Nanotechnol. 2013, 8, 235-246. (41) Thomsen, C.; Reich, S. Double Resonant Raman Scattering in Graphite. Phys. Rev. Lett. 2000, 85, 5214-5217. (42) Eckmann, A.; Felten, A.; Mishchenko, A.; Britnell, L.; Krupke, R.; Novoselov, K. S.; Casiraghi, C. Probing the Nature of Defects in Graphene by Raman Spectroscopy. Nano Lett. 2012, 12, 3925-3930. (43) Jiang, J.; Pachter, R.; Mehmood, F.; Islam, A. E.; Maruyama, B.; Boeckl, J. J. A Raman Spectroscopy Signature for Characterizing Defective Single-Layer Graphene: Defect-Induced I(D)/I(D') Intensity Ratio by Theoretical Analysis. Carbon 2015, 90, 53-62. ACS Paragon Plus Environment

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(44) Robertson, A. W.; Allen, C. S.; Wu, Y. A.; He, K.; Olivier, J.; Neethling, J.; Kirkland, A. I.; Warner, J. H. Spatial Control of Defect Creation in Graphene at the Nanoscale. Nat. Commun. 2012, 3, 2141/2141-2141/2147. (45) Wang, H.; Wang, Q.; Cheng, Y.; Li, K.; Yao, Y.; Zhang, Q.; Dong, C.; Wang, P.; Schwingenschloegl, U.; Yang, W.; et al. Doping Monolayer Graphene with Single Atom Substitutions. Nano Lett. 2012, 12, 141-144. (46) Robertson, A. W.; Lee, G.-D.; He, K.; Yoon, E.; Kirkland, A. I.; Warner, J. H. The Role of the Bridging Atom in Stabilizing Odd Numbered Graphene Vacancies. Nano Lett. 2014, 14, 39723980. (47) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys. Conden. Matter 2009, 21, 395502; pp 1-19. (48) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (49) Henkelman, G.; Jonsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 9978-9985. (50) Venezuela, P.; Lazzeri, M.; Mauri, F. Theory of Double-Resonant Raman Spectra in Graphene: Intensity and Line Shape of Defect-Induced and Two-Phonon Bands. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 035433/035431-035433/035425. (51) Gruneis, A.; Saito, R.; Samsonidze, G. G.; Kimura, T.; Pimenta, M. A.; Jorio, A.; Souza Filho, A. G.; Dresselhaus, G.; Dresselhaus, M. S. Inhomogeneous Optical Absorption around the K Point in Graphite and Carbon Nanotubes. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 165402/165401-165402/165407. (52) Ando, T. Anomaly of Optical Phonon in Monolayer Graphene. J. Phys. Soc. Jpn. 2006, 75, 124701/124701-124701/124705. (53) Landauer, R. Spatial Variation of Currents and Fields due to Localized Scatterers in Metallic Conduction. IBM Journal of Research and Development 1957, 1, 223-231. (54) Büttiker, M.; Imry, Y.; Landauer, R.; Pinhas, S. Generalized Many-Channel Conductance Formula with Application to Small Rings. Phys. Rev. B 1985, 31, 6207-6215. (55) Atomistix; Toolkits; Version; 11.8.2. QuantumWise A/S (www.quantumwise.com). (56) Brandbyge, M.; Mozos, J.-L.; Ordejon, P.; Taylor, J.; Stokbro, K. Density-Functional Method for Nonequilibrium Electron Transport. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 165401/165401-165401/165417. (57) Viraka Nellore, B. P.; Kanchanapally, R.; Pramanik, A.; Sinha, S. S.; Chavva, S. R.; Hamme, A.; Ray, P. C. Aptamer-Conjugated Graphene Oxide Membranes for Highly Efficient Capture and Accurate Identification of Multiple Types of Circulating Tumor Cells. Bioconjugate Chem. 2015, 26, 235-242. (58) Pramanik, A.; Chavva, S. R.; Fan, Z.; Sinha, S. S.; Nellore, B. P. V.; Ray, P. C. Extremely High Two-Photon Absorbing Graphene Oxide for Imaging of Tumor Cells in the Second Biological Window. J. Phys. Chem. Lett. 2014, 5, 2150-2154. (59) Pramanik, A.; Fan, Z.; Chavva, S. R.; Sinha, S. S.; Ray, P. C. Highly Efficient and Excitation Tunable Two-Photon Luminescence Platform For Targeted Multi-Color MDRB Imaging Using Graphene Oxide. Sci. Rep. 2014, 4, 6090; pp 1-6. (60) Fan, Z.; Kanchanapally, R.; Ray, P. C. Hybrid Graphene Oxide Based Ultrasensitive SERS Probe for Label-Free Biosensing. J. Phys. Chem. Lett. 2013, 4, 3813-3818. (61) Oubal, M.; Picaud, S.; Rayez, M.-T.; Rayez, J.-C. Structure and Reactivity of Carbon Multivacancies in Graphene. Comput. Theor. Chem. 2012, 990, 159-166. (62) Dharma-wardana, M. W. C.; Zgierski, M. Z. Magnetism and Structure at Vacant Lattice Sites in Graphene. Phys. E (Amsterdam, Neth.) 2008, 41, 80-83. ACS Paragon Plus Environment

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Table 1. Calculated Raman D and D’ peak intensities (normalized to the D intensity for V2(a)) and their ratio. DSLG with O2 adsorptiona

DSLG I(D)

I(D’)

I(D)/I(D’)

I(D)

I(D’)

I(D)/I(D’)

V2(a)

1.00

0.27

11.6

0.16

0.02

7.6

V2(b)

0.40

0.14

2.8

V2(c)

1.07

0.23

4.5

V3(a)

1.18

0.30

3.9

0.91

0.14

6.5

V3(b)

0.65

0.28

2.3

V4(a)

0.42

0.42

1.0

1.43

0.25

5.7

V4(d)

3.04

0.50

6.1

V4(e)

2.28

0.44

5.2

V5(a)

1.79

1.15

1.6

1.54

1.07

1.4

V6(a)

1.48

1.29

1.1

1.69

1.54

1.1

V7(a)

1.27

0.75

1.7

1.42

1.60

0.9

a

The values listed are for oxygen chemisorbed DSLG structures, while upon physisorption the I(D)/I(D’) values do not change and are the same as for the non-adsorbed DSLG.


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(a) V2(a)

V2(c)

V2(b)

V4(d)

V3(a)

V3(b)

V5(a)

V4(b)

V4(a)

V4(e)

V5(c)

V5(b)

V4(c)

V5(d)

V6(a)

V6(b)

V7(a)

V7(b)


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(b)

V2(a)

V4(a)

V2(b)

V4(b)

V5(a)

V5(b)

V6(a)

V6(b)

V3(b)

V3(a)

V2(c)

V4(c)

V4(d)

V5(c)

V4(e)

V5(d)

V7(a)

V7(b)

Figure 1. (a) Schematic illustration of V2 - V7 vacancy generation in SLG by carbon atom omission (denoted in color). The dashed lines indicate a 90° bond rotation. (b) Optimized structures of DSLG with V2 - V7 vacancies.


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Page 26 of 33

(a)

V2(a)

V3(a)

V4(a)

V5(a)

V6(a)

V7(a)

(b) V2(a) 0.53

V4(a) dissociation

0.62

V6(a) dissociation dissociation 0.034


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Figure 2. (a) Optimized structures with O2 adsorption (physisorption and chemisorption for even vacancies, and chemisorption for odd vacancies). (b) Reaction pathways for O2 adsorption on V2(a), V4(a) and V6(a), and activation energy barriers (in eV).


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V2(a)

V3(a)

V3(b)

V4(d)

V2(a)-O2

V3(a)-O2

V4(a)

Page 28 of 33

V5(a)

V6(a)

V5(a)-O2

V6(a)-O2

V7(a)

V4(e)

V4(a)-O2

V7(a)-O2

Figure 3. Defect potential isosurfaces for DSLG nanostructures with V2 - V7 vacancies (red-positive and blue negative).


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Figure 4. Intra-valley electron-defect matrix elements for DSLG with vacancies V2 - V7.


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Page 30 of 33

Figure 5. Raman D and D’ bands profiles for a lactone at MV1, (a), epoxy at MV2 (b), five O atoms around DV1 (c), and seven O atoms around DV2 (d).


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(a)

(b)

Figure 6. (a) Raman spectrum of graphene oxide quantum dots, showing the D, G, D’, 2D, D+D’ bands at 1350, 1585, 1620, 2680, and 2945 cm-1, respectively. The inset shows a TEM image of freshly prepared graphene oxide quantum dots, with an average size 10 nm, and its inset is a high-resolution TEM image, indicating high crystallinity with a lattice spacing around 0.32 nm. (b) The FTIR spectrum of the graphene oxide quantum dots, exhibiting very strong and broad band at 3600 cm−1 due to -OH vibrations. The carbonyl (–C=O) stretch observed at 1720 cm-1 and (CO)-H stretch at 2730 cm-1 correspond to the carboxylic acid groups.


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(a)

(c)

Page 32 of 33

(b)

(d)

Figure 7. Band structures along with the corresponding graphene nanostructures for (a) (15, 15, 4, 4) , (b) (16, 16, 4, 4) , (c) (3,-3,14,14) , and (d) (4,-4,14,14) .


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(a)

Left electrode

Left electrode

(b)

Channel Gate

Channel Gate

Right electrode

Right electrode

Figure 8. (a) Device schematics of (15,-15,4,4) (upper panel) and (3,-3,14,14) (lower panel) patterned nanostructure FETs. Dielectric is in pink and metal gate in gray. (b) I-Vg curves for model (15,-15,4,4) (black) and (3,-3,14,14) (red).


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Modeling Graphene with Nanoholes: Structure and Characterization

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