Contributions to the work function: A density-functional study of adsorbates at graphene ribbon edges

In the present computational study, we focus on graphene ribbons with zigzag edge atoms with their unsaturated bonds either dangling or terminated by various adsorbates ~H, O, or Cs!. Using this system as a test case, we discuss the two important contributions to the work function—the first one being an anisotropic bulk property related to the electron affinity of the material, and the second one being directly related to the surface dipole moment caused by the spill over of electronic charge into the vacuum. The latter contribution, which tends to increase the work function, can to a large extent be minimized by a judicious choice of adsorbates ~typically, adsorbates that are more electropositive than the surface !. The former face-dependent contribution turns out to be the minimum possible work function achievable for a given surface. Our calculations are based on density-functional theory within the local density approximation using nonlocal pseudopotentials and a plane wave basis set. @S0163-1829~99!03632-2# tion of species at a surface alters the work function of the surface in an understandable manner, with adsorbates having higher electronegativities than the surface increasing the work function while those with lower electronegativities having the opposite effect. 5-7 In the present study, we quantify the above anticipated trends for the test case of graphene ribbon edges with various adsorbates. We also address an appealing—although not unanticipated—correlation between the edge dipole moment and the work function perpendicular to the edge ~and along the ribbon plane!. This correlation points to an interesting way of viewing the work function, viz., by partitioning it into an anisotropic ~face-dependent! bulk cohesive ~electron af- finitylike! part and a part entirely due to the surface or edge dipole moment. The latter, which is a positive contribution to the work function, is due to the spill over of the electron gas into the vacuum region, and can to a large extent be reduced by a judicious choice of adsorbates. In fact, this analysis indicates that there is a minimum possible work function associated with a particular surface or edge that can be at- tained when the surface or edge dipole moment can be made to vanish. Our choice of an allotrope of carbon as a test case in the present study is motivated by the fact that recent attention has focused on carbon-based materials due to their promise as potential candidates for cold-cathode field emission applications. 8 Among the allotropes of carbon, nanotubes seem to be active field emitters, although other forms—like fragments of graphene and diamond-like carbon—are also known to be active. 9 One possible reason the nanotubes are active may be because they display special electronic states localized at the tip atoms. 10,11 It has also been pointed out that the nanotubes may be quite defective, with one such defect being similar to a graphene edge. 12,13 While the car- bon atoms in a cylindrical defect-free nanotube are all three- fold coordinated ~just as in graphite!, those in defected tu- bules may be two-fold coordinated, with an entirely different p-electron network in its vicinity ~as in fragments of graphene!. A recent tight-binding study of graphene ribbons 14 with the edge carbon atoms passivated with H has demonstrated that graphene ribbons with zigzag edges dis- play special localized states near the Fermi level arising pri- marily due to the topology of the p electron networks at the edges. Here, we use density-functional methods and consider zigzag graphene edges with unsaturated bonds either dan- gling or passivated with H, O, or Cs, and assess the impor- tance of such terminations on the edge dipole moment and the work function perpendicular to the edge—quantities which are key to the electron emission properties of these confined systems. In the next section, we give details of the method and models used in this study. We comment about the specifics of the work function and dipole moment calculations and formally relate the former to the latter in Sec. III. In Sec. IV, we present electronic and geometric structure results, calcu- lated work functions and dipole moments for the unpassi- vated and H-, O-, and Cs-terminated zigzag ribbons. We fi- nally conclude with Sec. V.