Ab initio study of dopant-defect interactions in graphene sheets and graphene nano-ribbons

Theoretical studies of nanostructured systems, such as doped, defective and pristine graphene and graphene nanoribbons, present a major challenge to conventional computational methods. This thesis presents ab initio calculations based on density functional theory (DFT) to study the structural and electronic properties of doped and defective graphene and graphene 'nanoribbons. Our calculations are carried-out using density-functional pseudopotential approximations combined with the generalized gradient approximation (GGA) for the exchange-correlation functional. Structural optimizations are executed by iterative force minimization using the conjugate gradient algorithm. We investigate the effect of dopants and point defects on graphene and graphene nanoribbons and study the interactions between the two. Binding energies, equilibrium geometries, charge transfer, and exchange-splitting-induced magnetism are calculated. The dependence of dopant-defect separation distance on interaction energy and interaction energy is examined in detail. We find that the interaction energy for on-defect dopant sites is dominated by how well defect geometry accommodates the dopant-carbon interatomic distance. Depending on the site dopant-defect interaction is either attractive or repulsive. Stone-Wales defect-nitrogen pairing was found to induce exchange splitting and magnetism in certain configurations. Nitrogen was also found to passivate single-vacancy dangling bonds and eliminate exchange-splitting induced magnetism; vacancy-nitrogen interactions were found to be mostly attractive. Boron-vacancy pairing can result in a favorable symmetric sp3 configuration, this is the only vacancy-boron pairing were dangling bonds are passivated and magnetism is eliminated; other favorable boron-vacancy pairings maintain exchange splitting and can in some cases enhance it. We found that the effect of dopant-defect separation distance follows a simple inverse power law. Our results indicate that, when the supercell is made sufficiently large, the interaction energy will vanish with increasing separation distance. However, in the case of nitrogen-vacancy and -divacancy interaction the interaction energy will reach a non-zero minimum below which it does not decrease. This minimum is a believed to be proportional to defect concentration and inversely proportional to supercell size.