Edge-functionalized and substitutionally doped graphene nanoribbons: Electronic and spin properties

F. Cervantes-Sodi, G. Csányi, S. Piscanec, and A. C. Ferrari

Phys. Rev. B 77, 165427 – Published 25 April 2008

Abstract

Graphene nanoribbons are the counterpart of carbon nanotubes in graphene-based nanoelectronics. We investigate the electronic properties of chemically modified ribbons by means of density functional theory. We observe that chemical modifications of zigzag ribbons can break the spin degeneracy. This promotes the onset of a semiconducting-metal transition, or of a half-semiconducting state, with the two spin channels having a different band gap, or of a spin-polarized half-semiconducting state, where the spins in the valence and conduction bands are oppositely polarized. Edge functionalization of armchair ribbons gives electronic states a few eV away from the Fermi level and does not significantly affect their band gap. N and B produce different effects, depending on the position of the substitutional site. In particular, edge substitutions at low density do not significantly alter the band gap, while bulk substitution promotes the onset of semiconducting-metal transitions. Pyridinelike defects induce a semiconducting-metal transition.

Received 14 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.165427

Authors & Affiliations

F. Cervantes-Sodi, G. Csányi, S. Piscanec, and A. C. Ferrari^*

Department of Engineering, University of Cambridge, Cambridge CB3 OFA, United Kingdom

^*acf26@eng.cam.ac.uk

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Vol. 77, Iss. 16 — 15 April 2008

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Images

Figure 1
Scheme of H-terminated (a) zigzag and (b) armchair nanoribbons. Periodic boundary conditions are assumed in the $x$ direction. $N$ and $M$ are the numbers of columns and rows of atoms used to label the $M \times N$ ribbon.Reuse & Permissions
Figure 2
(Color online) Spin density of states of $α$ (red/gray solid line) and $β$ (blue/black solid line) for functionalized ZGNRs in comparison with a clean ribbon (black dotted line). [(a)–(f)] $6 \times 2 Z$ (i.e., $M = 6$ , $N = 2$ ZGNR) functionalized with (a) $N H_{2}$ , (b) OH, (c) COOH, (d) stable- $N O_{2}$ , (e) metastable- $N O_{2}$ , and (f) O radicals in one of the ribbon edges, resulting in [(a)–(f)] lifting of the spin degeneracy, [(a)–(d)] spin-selective band gap, or [(e) and (f)] semiconductor-metal transition. (g) Oxygen edge substitutional atom favoring a semiconductor-metal transition. (h) $6 \times 5$ zigzag ribbon with a nitrogen bulk substitution in the center of the ribbon. (i) Nitrogen bulk substituted ribbon shown in (h) with an extra single $N H_{2}$ at the edge of the opposite carbon sublattice, with the maximum distance between N and $N H_{2}$ in the periodic direction, resulting in a semiconductor-metal transition.Reuse & Permissions
Figure 3
(Color online) Spin density of states of $α$ (red/gray solid line) and $β$ (blue/black solid line) for functionalized AGNRs in comparison with a clean ribbon (black dotted line). (a) Single edge $N H_{2}$ functionalized $12 \times 3$ AGNR. (b) N and (c) B edge substitutional atoms on the $12 \times 3$ AGNR. N and B bulk substitutions for the $12 \times 3$ AGNR are shown in (d) and (e), where a semiconductor-metal transition occurs. [(f) and (g)] Two pyridinelike substitutional doping in the bulk of $2 \times 3 A$ and $12 \times 6 A$ , resulting in a metallic behavior. Arrows indicate impurity levels due to substitutional atoms. The DOS of the clean ribbon is shifted for the bulk N and B substitutions, so that the edges of the valence band of clean and doped ribbons coincide.Reuse & Permissions
Figure 4
(Color online) Change in spin band gap [ $β$ channel (blue dotted line) and $α$ channel (red solid line)] as a function of [(a) and (c)] edge density $(N)$ and [(b) and (d)] width of ribbon $(M)$ for different sets of [(a) and (b)] single-edge functionalized ZGNRs, and $N H_{2}$ double-edge antisymmetric functionalized ZGNRs [triangles in (c) and (d)].Reuse & Permissions
Figure 5
(Color online) Band structure of the $N H_{2}$ [(a)–(c)] $2 \times 2 Z$ and [(d)–(f)] $4 \times 8 Z$ [(a) and (d)] single-edge and [(b), (c), (e), and (f)] double-edge functionalizations. Single-edge functionalization [(a) and (d)] breaks spin degeneracy, whereas this is nearly recovered for double-edge [(b) and (e)] antisymmetric and [(c) and (f)] symmetric functionalizations. $α (β)$ spins are represented by red/gray (blue/black) solid lines. The folded band structures of the pristine ZGNRs are plotted with black dotted lines. On the right of each BS are the corresponding spin density maps [ $β$ (blue) and $α$ (red)] of the total SD and spin density of the HOMO and LUMO bands. The image shows the relaxed structure in the $x y$ projection and a close-up of the edges in the $y z$ projection.Reuse & Permissions
Figure 6
(Color online) Spin density maps [ $β$ (blue) and $α$ (red)] of the ground (right) and metastable states (left) of clean $6 \times 5 Z$ (top) and $N sub − N H_{2} − 6 \times 5 Z$ (bottom). For each ribbon, we show the small difference in total energy between the [(a) and (d)] antiferromagnetic and [(b) and (c)] ferromagnetic configurations.Reuse & Permissions

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