  The chemical modification of graphene with adatoms is of importance for
nanoelectronics applications. Based on first-principles density-functional
theory calculations with including van der Waals interactions, we present a
comparative study of the diffusion characteristics of oxygen (O) and fluorine
(F) atoms both on graphene and between the layers of bilayer graphene. We find
that O and F atoms have lower binding energies between the layers of bilayer
graphene compared to on graphene. Interestingly, the calculated diffusion
barrier for the O atom slightly increases from 0.81 eV on graphene to 0.85 eV
within bilayer graphene, while that for the F atom significantly decreases from
0.30 eV on graphene to 0.18 eV within bilayer graphene. Such contrasting
behaviors of the O and F diffusions within bilayer graphene can be traced to
their different bonding natures: i.e., the O adatom that has a strongly
covalent C$-$O$-$C bonding on the bridge site of the C$-$C bond diffuses on one
graphene layer with a slight interference of the other layer, while the F
adatom that has a weakly ionic F$-$C bonding on top of a C atom easily diffuses
by hopping between two graphene layers with accepting more electron charges
from the two layers. The present findings have important implications for
understanding the diffusion processes of F and O atoms on graphene and within
bilayer graphene.
