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Cite this: Phys. Chem. Chem. Phys., 2015, 17, 16545

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Adatom bond-induced geometric and electronic properties of passivated armchair graphene nanoribbons Yu-Tsung Lin,a Hsien-Ching Chung,a Po-Hua Yang,b Shih-Yang Lin*a and Ming-Fa Lin*a The geometric and electronic properties of passivated armchair graphene nanoribbons, enriched by strong chemical bonding between edge-carbons and various adatoms, are investigated by first-principle calculations. Adatom arrangements, bond lengths, charge distributions, and energy dispersions are dramatically changed by edge passivation. Elements with an atomic number of less than 20 are classified into three types depending on the optimal geometric structures: planar and non-planar structures, the latter of which are associated with specific arrangements and stacked configurations of adatoms. Especially, the nitrogen passivated nanoribbon is the most stable one with a heptagon–pentagon structure

Received 16th April 2015, Accepted 28th May 2015

at the edges. The low-lying band structures are drastically varied, exhibiting non-monotonous energy

DOI: 10.1039/c5cp02226f

longer exists, and some adatoms further induce a semiconductor–metal transition. All the main character-

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istics are directly reflected in the density of states, revealing dip structures, plateaus, symmetric peaks, and square-root divergent asymmetric peaks.

dispersions and adatom-dominated bands. A relationship between energy gaps and ribbon widths no

Introduction Quasi-one-dimensional graphene nanoribbons (GNRs) have attracted a lot of research, mainly owing to the honeycomb lattice and the finite-size quantum confinement. GNRs could be successfully fabricated by several techniques. The most common ones are to cut graphene, achieved by a metal-catalyzed cutting process,1 lithographic patterning,2 and plasma etching.3,4 Another approach is to unzip carbon nanotubes (CNTs) by using metal nano-clusters as scalpels5 and a wet chemical method based on acid reactions.6 For mass production, required in the semiconductor industry, the chemical vapor deposition method for GNRs has been developed.7 An especially important process has recently been reported in which very narrow edge-precise GNRs have been synthesized from molecular precursors.8–10 From a geometric point of view, each GNR could be regarded as a finite-width graphene strip or an unzipped CNT. The electronic properties, being dominated by the ribbon width and edge structure, are very sensitive to changes in dopants,11–13 layer numbers,14,15 stacking configurations,16,17 external electric18–20 and magnetic fields,21,22 and mechanical strain.23–25 GNRs are predicted to be more potentially applicable in future nanodevices. In this work, a

Department of Physics, National Cheng Kung University, 701 Tainan, Taiwan. E-mail: [email protected], [email protected] b National Center for High-Performance Computing, 741 Tainan, Taiwan

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first-principle calculations are used to investigate the diversified electronic properties and the reconstructed boundary structures due to adatoms on non-passivated edges of GNRs. Pristine GNRs, without passivation, possess a flat structure with open edges that provide a reactive chemical environment. The intrinsic dangling bonds associated with edge carbon atoms are highly unstable and tend to adsorb atoms,13,26–30 molecules13,31,32 or radical groups.13,31 The essential electronic properties and geometric structures can be significantly altered by the type and concentration of the adsorbed adatoms.27,29 Some adatom-terminated GNRs, other than the H-terminated one, are predicted to be stable in theoretical calculations, such as K,27 F,20,28 O,19,24 B,29 Mg,29 Ru,33 Te,34 and transition-metalterminated GNRs (X-GNRs, X: adatoms).26 These studies, based on planar configurations, are mainly focused on the modulation of electronic properties under specific configurations. These edge-decorated systems may be 1D metals or semiconductors. Specially, the K-passivated GNR is a metal, independent of the concentration of K atoms. However, only a few investigations have been carried out on the most stable configurations of the edge-decorated GNRs.30,35 For instance, the armchair O-GNR possesses a non-planar edge geometry which is more energetically stable than the planar one. Elements from the first three rows of the periodic table are generally chosen as edge-decorated atoms since they tend to form the most stable configurations.

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Based on the edge structure, GNRs can be classified into three types, namely armchair, zigzag, and chiral ones. This research only focuses on armchair GNRs (AGNRs). The width of an AGNR is characterized by the number of dimer lines (Ny) along the transverse y-direction. All pristine AGNRs are indirect-gap semiconductors, with their energy gap associated with the edge carbon atoms. This phenomenon originates from the quantum confinement effect.36 In general, the energy gaps gradually decrease with the ribbon width; furthermore, these gaps could be classified into three groups (Ny = 3n, 3n + 1, and 3n + 2). A simple relation, Eg(3n + 1) 4 Eg(3n + 2) 4 Eg(3n), is present for Ny Z 7.37 However, in the case of H-passivation,38 Eg(3n + 2) is smaller than Eg(3n), and the smallest band gap is for Ny = 3n + 2. It should be noted that the onedimensional parabolic bands induced by the quantum confinement effect have been verified by angle-resolved photoemission spectroscopy (ARPES).9 The energy gaps of semiconducting GNRs have been identified from experimental scanning tunneling spectroscopy (STS) measurements, e.g., for armchair,9,39 zigzag,39,40 and chiral ones.41 However, the specific dependence of Eg on Ny needs to be further verified experimentally. In this paper, the geometric and electronic properties of armchair graphene nanoribbons passivated by adatoms with atomic numbers lower than twenty in the periodic table are investigated via the density functional theory. The calculations of adatom–carbon bond length, charge transfer, planar or nonplanar structures, adsorption energy, energy gaps, energy bands, and density of states are given in detail. This work shows three types of most stable geometric structures associated with various adatoms, i.e., a planar hexagon structure, a heptagon–pentagon or triangle-pentagon structure at the edges, and non-planar structures with different adatom arrangements and stackings. The predicted edge-structures can be further verified by STM measurements. We pursue the full understanding of how the adatoms–carbon bonds and spatial charge distributions can diversify the electronic properties, such as the complicated energy dispersions, adatomdominated bands, and semiconducting or metallic behavior. All the predicted band structures are further reflected in feature-rich density of states; these could be further identified by ARPES and STS, respectively. Moreover, how the monotonous relationships between energy gaps and Ny are affected by the various adatoms is carefully examined, an observed change that often correlates to the semiconductor–metal transition. As expected, these passivated graphene nanoribbons with special physical properties are potential materials for application in electronic devices.

Computational methods For the geometric and electronic properties of the edge-adsorbed AGNRs, first-principle density functional theory calculations are performed using the Vienna ab initio simulation package.42 The generalized gradient approximation, within the Perdew–Burke– Ernzerhof functional,43 is applied to describe the exchange– correlation energy of interacting electrons. Projector-augmented wave pseudopotentials44 are employed to characterize the electron– ion interactions. The wave functions are built from the plane waves

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with a maximum energy cutoff of 500 eV. The first Brillouin zone is sampled along the one-dimensional periodic direction by 22  1  1 and 100  1  1 k points in a Gamma scheme for structure relaxation and band-structure calculations, respectively. The convergence criterion for one full relaxation is determined by setting the Hellmann–Feynman forces to less than 0.01 eV Å 1, and the total energy difference to less than 10 5 eV. Regarding Gaussian smearing, the width is set at 0.02 eV for the density of states (DOS). The Ny = 8 AGNR is chosen as a representative system with an adatom concentration of 25%; the unit cell contains 4 adatoms and 16 carbon atoms. The vacuum distance between a ribbon and its replica is set to at least 15 Å. The charge transfer between the edge carbon atoms and the adatoms is obtained by the Bader analysis method.45 Moreover, the adsorption energy DE, characterizing the reduced energy owing to the adatoms adsorbed on the ribbon edges, is defined as DE = 14(Esys

EGNR

4Ead),

(1)

where Esys, EGNR, and Ead are the total energies of the edge-adsorbed AGNR, pristine AGNR, and a single adatom, respectively. It is noticed that the strain energy is part of the total energy. In addition, a valid comparison among these total energies has to be obtained inside the same unit cell.

Results and discussion Geometric structures Most of the symmetric configurations are examined for distinct edge atoms belonging to the first three rows of the periodical table. The most stable structure corresponding to each adsorbed element in the state of the lowest total energy is shown in Fig. 1(a)–(c). According to the plane distortion and the edge-atom arrangement, there are three types of optimal geometric structures, denoted type I, type II, and type III, respectively. Adatoms in type I systems, based on the planar structures in Fig. 1(a), include H, N, Be, and B. The H-AGNR possesses the well-known hexagonal plane, in which the H–C single bond length is 1.08 Å. A tiny electric charge of about 0.02 e is transferred from H towards the outermost C atom, indicating a covalent H–C bond. As for the N-AGNR, a series of repeated heptagon–pentagon structures is formed at the edges. Nevertheless, a significant reconstruction occurs, and the C–C bond length in the middle of the ribbon agrees well with that of pristine graphene (i.e., 1.42 Å). The N–C bond lengths in the heptagons and pentagons are, respectively, 1.30 Å and 1.28 Å. The higher electronegativity of N in comparison to C causes charges to be transferred from the latter to the former; that is, each N atom gains an extra 3.13 e in the heptagon and 2.77 e in the pentagon parts, respectively. This high carrier concentration is clearly illustrated by the charge density distribution in Fig. 2(a) (red region), which also indicates a strong covalent bonding. The Be-AGNR exhibits a series of triangle-pentagon structures devoid of an obvious reconstruction edges. The Be–C bond length is 1.73 Å in the trilateral part and 1.85 Å in the pentagonal one. The atomic interactions between the Be adatoms

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Fig. 1 Geometric structures of edge-decorated graphene nanoribbons: (a) type-I, (b) type-II, and (c) type-III configurations.

Fig. 2 Charge density distribution for (a) N-, (b) S-, (c) Li-, and (d) Si-AGNR systems.

and AGNR are highly ionic since the former contributes all valence electrons to the latter during the full charge transfer (2 e). The B-AGNR has pentagonal edges where a weak B–B bond of the length 2.00 Å is formed. Each B adatom shares about half its valence charge (B1.6 e) with the neighboring one and the AGNR; therefore, the interaction of B and C is classified as a covalent bond. These particular adatom-dependent edge morphologies are strongly related to the atomic radii and the number of valence electrons. Type II systems possess two stable configurations, namely, Xsame-AGNR and Xopp-AGNR, both of which are more energetically favorable than a planar configuration. These two structures have been predicted previously for an oxygen-decorated system.30 The Xsame-AGNR system represents a scenario where the adatoms opposingly placed across the nanoribbon plane are located on the same side, while the opposing adatoms in Xopp-AGNR systems are on opposite sides. X is used to indicate the adatom species. However, these two configurations only have a small total energy difference of a few meVs; furthermore, Xsame-AGNR systems possess a lower total energy. We only focus on Xsame-AGNR systems without magnetism in this work. In the case of O-AGNR, the short O–C bond length is 1.22 Å, with a high charge distribution in a strong covalent bond. These are almost the same as what has been demonstrated in

a previous study.30 It should be noted that the planar heptagon– pentagon edges in N-AGNR can also form in O-AGNR, but a higher energy of 1.26 eV per unit cell is estimated as compared to the Xsame-AGNR structure. For S-, F-, and Cl-AGNR systems, it is impossible to form the planar configurations, mainly owing to the high repulsive interaction of these larger adatoms. In addition, F- and Cl-AGNRs have their adatoms in a periodic arrangement where the first two adatoms lie above the ribbon plane while the following two lie below the plane, and so on. Their adsorption energies are a bit lower than those of the XsameAGNR and Xopp-AGNR. When adatoms are selected from the third-row elements of the periodic table, the bond lengths increase; that is, S–C 4 O–C and Cl–C 4 F–C. With higher electronegativities, O and F adatoms attract 1.73 and 0.78 of electrons, respectively. The cross section of the charge distribution clearly illustrates the bonding properties in sulfur dimers and S–C bonds. The total energy reduction in type II systems, resulting from adatom bonding, competes against the energy increase due to the distorted ribbon edges. However, the lower adsorption energy means that the latter is effectively suppressed by the former. Type III, consisting of much bigger adatoms (X = Li, Na, K, Ca, Mg, Al, Si, and P), has an arrangement where the adatoms symmetrically stack up at the edges as shown in Fig. 1(c).

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Distorted pentagons are revealed by the adatom bonding to the ribbon, while the carbon hexagons have no distortion even near the edges. For alkali metal adatoms (Li, Na, and K), the electronegativity is much larger than that of carbon, by a factor of about 1.6, reflecting the rather low carrier charge density between them. An example is the Li-AGNR shown in Fig. 2(c). The atomic interactions in these X–C bonds are highly ionic, especially for Li–C, in which a valence charge of 0.83 e is transferred to the two edge C atoms from each Li atom. The attractive Coulomb interactions in the X–C bonds compete with the repulsive Coulomb interactions in the stacked adatoms; these interactions determine the associated bond lengths. Among type III systems, Li-AGNR exhibits the strongest Coulomb interactions and thus has the shortest bond lengths, as indicated in Table 1. The competitive Coulomb interactions also dominate the Na-, K-, Ca-, and Mg-AGNR systems, and even the type I Be-AGNR. On the other hand, the Al-, Si-, and P-AGNR systems, in which the adatoms have more valence electrons, possess covalent charge distributions in the X–X and X–C bonds, as shown for the Si charge densities in Fig. 2(d). The two bond lengths decrease with increasing atomic number. The shorter covalent bond lengths result in stronger atomic interactions. Thus, the strongest adatom–adatom coupling occurs in the P-AGNR. Whether the edge-decorated graphene nanoribbons can exist or not is determined by the adsorption energy. DE’s are respectively, 5.881 eV, 5.776 eV, 5.500 eV, and 4.795 eV for the N-, O-, B-, and F-AGNR systems. The first one displays the lowest adsorption energy found in theoretical calculations to date. Furthermore, the four systems possess a lower DE, as compared to that ( 4.359 eV) of the H-AGNR frequently used in experimental measurements. This suggests that they can easily be produced in experimental growth. On the other hand, it is relatively difficult to create Na- and Ca-AGNR systems, since they have higher adsorption energies of DE’s = 0.732 eV and 0.819 eV, respectively. To date, theoretical researchers have used DFT calculations to conduct investigations on the surface adsorption and the

edge passivation of 2D graphene and 1D graphene nanoribbons with elements such as hydrogen,38 oxygen,19,24 and nitrogen.29,46 On the other hand, recent experiments show that some atoms, which are as stable as a diatomic gas, can be applied to passivate the ribbon edge in a monatomic form, such as H,10 Br,10 and O.6 Moreover, H,47,48 O,49 and F50 atoms can be adsorbed on a graphene surface as a single atom. As for the realization of the N-passivated nanoribbon, nitrogen can be manipulated through some special chemical processes, such as the catalytic method.6 The STM experimental measurements, which are capable of revealing the local nano-structures, have been successfully applied to GNRs,8,10,40,41,51 carbon nanotubes,52,53 graphene,54–57 graphene compounds,47 and graphite.58,59 The chiral arrangements of the hexagons on the planar boundary41 and the cylindrical surface,52,53 the adatom bonding at the open edges,10,51 the rippled and buckled structures,54,55 the adatom distributions on the graphitic surface,58 and the local defects59 are clearly identified through these atomic-scale observations. The unique edge structures of passivated AGNRs, including triangular, pentagon, hexagon, or heptagon edges in planar systems, and edge-bucked and adatom-stacked-up configurations in non-planar systems, are worthy of further experimental verification. Also, such measurements are useful in understanding the chemical bonding between adatoms and edge carbons. Band structures The complex chemical bonding between adatoms and edge carbon atoms competes with the quantum confinement effect, which determines the essential electronic properties. The X-AGNR systems exhibit rich electronic structures, as shown in Fig. 3(a)–(d). There are a lot of 1D energy bands, in which the occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level (EF = 0). Most of the energy bands have parabolic dispersions, while some possess linear or partial-flat dispersions. For each energy dispersion, the band-edge states are located at G and X points (kx = 0 and 1), with extra ones located elsewhere

Table 1 Calculated adatom–carbon bond lengths, adatom–adatom distances, adsorption energies, and charge transfers of adatoms for various X-AGNR systems with Ny = 8. Semiconductors and metals are indicated

DE (eV)

Charge transfera (e)

Configuration

Adatom

X–C bond (Å)

X–X bond (Å)

Type I

H N Be B

1.08 1.30/1.28 1.85/1.73 1.57

1.83 2.12 2.15 2.23

4.359 5.881 3.707 5.500

0.02 3.13/ 2.77 2.00 1.48

S S M S

Type II

O S F Cl

1.22 1.75 1.34 1.71

3.03 2.03 2.58 3.21

5.776 4.274 4.795 3.276

1.73 0.09 0.78 0.16

S S S S

Type III

Li Na K Ca Mg Al Si P

2.01 2.49 2.81 2.39 2.25 2.14 2.15 1.83

2.38 3.06 3.86 3.38 2.78 2.78 2.23 2.23

2.216 0.732 1.413 0.819 2.011 3.558 3.483 3.732

0.83 0.59 0.51 0.90 1.05 1.60 1.16 0.50

M M M M M S S S

a

Metal/semiconductor

The plus or minus signs, respectively, denote that electrons are lost or gained in the adatoms.

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Furthermore, these atoms also make certain contributions to other valence bands. On the other hand, the Li adatoms can lead to semiconductor–metal transitions; that is, the Li-AGNR becomes a 1D metallic system. The lowest conduction band overlaps with the two highest valence bands near EF; the latter are closely related to the Li adatoms (green circles in Fig. 3(d)). There are some free electrons in the lowest conduction band and some free holes in the highest valence one. Such a band overlap is also found in Na-, K-, Ca-, Mg-, and Be-passivated AGNRs. The above-mentioned changes are revealed to originate from the suppressed quantum confinement effect caused by the adatom– carbon bonds. The drastic changes in semiconducting or metallic properties by the chemical decoration of adatoms on the graphene nanoribbon indicate a high potential for application in electronic devices. How electronic properties are affected by the strong adatom-induced bonding will be further examined from the projected DOS. To date, ARPES has served as a powerful experimental method to investigate the band structures of graphene-related systems, such as GNRs,9 graphenes,60 graphene compounds,47 and graphite.61 Concerning H-passivated AGNR, the parabolic energy dispersions, band-edge states of kx = 0, and energy gaps have been identified by ARPES.9 The predicted feature-rich energy spectra, including various energy dispersions, wave vectors of extra band-edge states, energy gaps, and adatom-dominated bands, could be further verified using ARPES measurements. Specifically, the band overlaps in metallic adatom-decorated AGNRs deserve a closer examination. Density of states Fig. 3 Energy bands of (a) pristine, (b) N-, (c) S-, and (d) Li-AGNR systems. The radii of the circles represent the contributions from the nonpassivated edge carbon atoms or the adatoms.

along this kx-path. Such states are expected to induce the special structures in DOS. The low-lying electronic structures for different adatoms are diverse. Pristine AGNR, without passivation, exhibits an indirect band gap of 0.473 eV, with the highest occupied state (HOS) and the lowest unoccupied state (LUS) located at kx = 0 and 1, respectively. HOS and LUS mainly come from the non-edge and edge carbon atoms, respectively (the contribution from the latter is indicated by the black circles in Fig. 3(a)). The danglingbond-induced kx = 1 LUS cannot survive in the presence of chemical bonding between edge carbons and adatoms. For the N-AGNR, both HOS and LUS are located at kx = 0 and thus determine a direct narrow gap of B0.04 eV (Fig. 3(b)). The energy dispersions near EF are drastically altered by N adatoms, and some non-monotonous ones also exist. Such atoms make much contribution to the band-edge states (blue circles in the inset), and they dominate four valence bands in the range of 1.6 eV r Ec,v r 0.9 eV. As for the low-lying bands in the S-AGNR, they present parabolic energy dispersions and a middle energy gap of B0.395 eV due to the kx = 0 HOS and LUS. The shallowest two valence bands, except for the electronic states near HOS, mainly arise from the S adatoms (yellow circles in Fig. 3(c)).

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The DOS, which directly reflects the primary characteristics of the band structures, can be decomposed into distinct contributions from the carbon orbitals and the adatoms. X-AGNR systems exhibit many special structures (dashed curves), including plateaus (arrows), prominent symmetric peaks (red triangles), and square-root divergent asymmetric peaks. Such structures, respectively, originate from the linear, partial-flat and parabolic energy dispersions. Concerning pristine AGNR (Fig. 4(a)), two asymmetric peaks associated with HOS and LUS make an appearance near EF at o = 0.24 eV and 0.25 eV, respectively. According to the projected DOSs, they are exclusively contributed by the 2pz orbital (red curves) and the (2s, 2px, 2py) orbitals (blue and green curves), respectively. The 2pz orbital (p bonding) makes important contributions to the DOS in the range of 3 eV r o r 3 eV, while the other orbitals (s bonding) dominate those of o r 2.2 eV and 0.2 eV r o r 1.7 eV. The strong chemical bonding of adatoms and carbon atoms leads to drastic changes in the main features of DOS, including changes in the energy, the number and the height of the special structures. For the N-AGNR, the low-energy DOS is dominated by the carbon 2pz orbitals and the N adatoms. There exists a dip structure and two weak peaks near EF, which determine an energy gap of 0.04 meV. It should be noted that HOS and LUS mainly come from the N adatoms and the carbon 2pz orbitals, respectively. Furthermore, a wide shoulder structure is revealed at o B 0.1 eV because of the N dominance. The N adatoms also highly dominate the DOS in the range of

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The STS experimental measurements, which have been successfully applied to graphene nanoribbons,8,40 graphenes,56 graphene compounds,62 graphite,63 and carbon nanotubes,52,53 could be utilized to examine the main characteristics of DOS. The tunneling differential conductance is approximately proportional to the DOS, and the relationship between dI/dV and V is useful in identifying the form, height, number and energy of the special structures in the DOS. Whether the decorated AGNRs are semiconducting or metallic (or have the free carriers) is determined by the value of the tunneling current at zero voltage. Certain important features, dependent on the different adatoms, could be verified by the measured STS spectra in the energy range of 3 eV. Moreover, a closer experimental examination is needed for the energy gaps, discussed below, which show a complicated dependence on the ribbon width. Energy gaps

Fig. 4 The projected density of states, corresponding to carbon atoms, is shown for (a) pristine, (b) N-, (c) S-, and (d) Li-AGNR systems. The triangles and arrows indicate the prominent symmetric peaks and plateaus, respectively.

The energy gaps of AGNRs, as shown in Fig. 5(a)–(d), are enriched by various ribbon widths and adatoms. For pristine Ny Z 6 AGNRs, Eg decreases with increasing Ny, while a linearly inverse relationship between them is absent (Fig. 5(a)). The dependence of Eg on Ny can be sorted into three groups, Ny = 3n, 3n + 1, and 3n + 2, as revealed in the H-terminated AGNRs.38 The largest energy gap occurs for Ny = 3n + 1, and the smallest one for Ny = 3n at the same n value. However, the energy gap of Ny = 3n + 2 in the H-AGNRs is largely reduced by the hydrogenation, being the smallest one among the three groups. The energy gaps are changed considerably after edge passivation, mainly owing to the fact that the effect of adatoms suppresses the quantum confinement effect. There exist certain important differences among the three types of X-AGNRs, e.g.,

1.6 eV r o r 0.9 eV, in which the featured six peaks, corresponding to the important contributions from the (2px,2py) orbitals, clearly indicate the strong interactions among the N adatoms and the carbon (2px,2py) orbitals in a planar geometric structure. On the other hand, for the S-AGNR, the low-energy structure, a pair of asymmetric peaks with an energy spacing of 0.4 eV, is mainly determined by the carbon 2pz orbitals. The (2s,2px,2py) orbitals make contributions in a broader energy range and their featured peaks become weaker as well. The featured peaks associated with S adatoms are revealed in the wide energy ranges of o r 0.65 eV and o Z 1.3 eV; furthermore, most of them are accompanied by peaks associated with carbon 2pz orbitals. This result directly reflects the fact that the distorted geometric structure results in the strong chemical bonding among the enormous valence charges of S adatoms and the carbon 2pz orbitals. In the Li-AGNR, the special structures in DOS exhibit an obvious red shift compared to those of the pristine AGNR (Fig. 4(a) and (d)). The one valence electron in the Li adatoms only makes a partial contribution to DOS, especially for the range of 1.5 eV r o r 0 eV. Furthermore, a finite DOS is revealed at EF = 0, in which the metallic property is ascribed to the strong chemical bonding between Li and carbon atoms.

Fig. 5 Width-dependent energy gaps of (a) pristine, (b) N-, (c) S-, and (d) Li-AGNR systems.

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the fluctuation in Ny-dependence, the drastically diminished gaps, and the semiconductor–metal transition. Both N-AGNR and LiAGNR possess much smaller gaps than the pristine AGNR, as shown in Fig. 5(b) and (d), respectively. The energy gaps of the former reveal a non-monotonous width dependence, and even the severely fluctuating Ny-dependent gaps for the Ny = 3n group. That the nitrogen adatoms contribute much more to the electronic states very close to EF is the main reason for the complicated Ny-dependence. Moreover, the strong Li–C bonding results in the conduction and valence bands in Li-AGNR approaching the Fermi level simultaneously, and thus leads to a quick reduction of the energy gap, which eventually vanishes when Ny is sufficiently large, i.e., Li-AGNR becomes a metal. On the other hand, S-AGNR shows a behavior similar to pristine AGNR (Fig. 5(c)), which can be ascribed to their HOS and LUS mainly coming from the carbon atoms, with less contributed from the S adatoms. The above-mentioned full Ny-dependence needs detailed verification by future STS experiments. Their tunable gap and the semiconductor–metal transition are very useful for application in field-effect transistors and light-emitting diodes.

Conclusions The geometric and electronic properties of edge-passivated armchair graphene nanoribbons are investigated by ab initio density functional theory calculations. Adatoms with an atomic number of lower than 20 are studied systematically. Besides the geometric structures in the previous studies, we have systematically tested various adatom positions near the edge. The resulting structures in the manuscript are the most stable ones with the lowest total energy. Some of these investigated structures are really worth mentioning, since they have not been reported elsewhere before. Calculations of the adatom–carbon bond lengths, total energies, charge transfers, charge distributions, energy dispersions, and density of states are performed. Remarkably, three types of most stable geometric structures induced by various adatoms are predicted, including planar structures with a hexagon, heptagon– pentagon or triangle-pentagon structure at the edges, the edgebucked structures with adatoms located in two different patterns, and a non-planar ribbon structure with adatoms stacked up at the edges. Among them, N-AGNR is the most stable one with the lowest adsorption energy. The special edge-passivation structures can be further verified by STM measurements. These passivated systems have unique electronic properties determined by the competition between the effects of adatoms and quantum confinement. The strong chemical bonding between adatoms and edge carbons is responsible for various energy dispersions (parabolic, linear, partially flat, and non-monotonous ones), the overlap of valence and conduction bands, and adatom-dominated bands within different energy ranges. As for their DOSs, special structures are exhibited, such as energy gaps, dip structures, plateaus, symmetric peaks, and square-root divergent asymmetric peaks. The predicted energy dispersions and gaps are expected to be identifiable by ARPES and STS experiments, respectively. Moreover, adatom-dominated low-lying bands account for the change in the monotonous relationships between the energy gaps and Ny.

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Especially, Li-AGNR reveal semiconductor–metal transitions when Ny is sufficiently large, a transition that also happens in Na-, K-, Ca-, Mg-, and Be-passivated AGNRs. These rich features of the geometric structures and the electronic properties may be potentially important for the application of edge-passivated systems in nanoelectronic and nanophotonic devices.

Acknowledgements This work is supported by the NSC and NCTS (South) of Taiwan, under the grant No. NSC-102-2112-M-006-007-MY3. We are grateful to the National Center for High-performance Computing (NCHC) for computer time and facilities.

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