Influence of Gate Voltage on the diffusion of Oxygen on Graphene

We calculate the surface diffusion of Oxygen on Graphene using Density Functional Theory. We find the activation energy for diffusion to be 0.71 eV. Charging the graphene plane causes the diffusion barrier to change substantially. Electron doping graphene lowers the diffusion barrier, resulting in activation energies as low as 0.15 eV for a carrier concentration of 7.6x10$^{13}$ cm$^{-2}$. This barrier reduction yields diffusion coefficients reaching over nine orders of magnitude lower than that of diffusion on neutral graphene. After study of the change in charge density distribution and local density of states, this effect is explained by a mixture of bond weakening under the equilibrium state and bond strengthening during the transition state. With this large fluctuation in diffusivity, patterning of oxidized regions in graphene may be achieved through variation of the gate voltage.