Theory and simulation of atomic hydrogen, fluorine, and oxygen on graphene

Graphene has generated great interest in the scientific community due to its high electron mobility and ease of reversible doping when it is part of a field effect transistor. However, several applications are limited by the lack of a gap in graphene's electronic structure. Among the methods of opening this bandgap, chemical modification has been deemed plausible theoretically and has been achieved with varying success experimentally.;In this dissertation we cover four main topics regarding graphene chemical modification: i) we model the energetics of adatom bonding with Density Functional Theory (DFT), ii) we use DFT to explore the effect of electronic and hole doping of graphene on adatom bonding and diffusion, iii) we describe the mechanisms behind the interactions between an adatom and graphene with tight-binding models that describe electron correlations beyond mean field approximations, and iv) we present a Monte Carlo model for simulating clustering behavior in partially functionalized graphene. We focus on atomic hydrogen, fluorine, and oxygen in these studies.;In the DFT study of adatom bonding energetics (Chapter 2), we find that hydrogen and fluorine attach directly above carbon atoms with chemisorption energies of -0.8 eV and -1.8 eV respectively. Hydrogen has an attachment barrier of 0.2 eV while fluorine attaches with no barrier. For both monovalent adatoms, the carbon below puckers away from the graphene plane, showing evidence of sp3 hybridization. Overlapping partial densities of states between the adatom and the underlying carbon show that the bond is covalent. A net magnetization localized around the adsorption site arises upon the adsorption of hydrogen, though no such polarization is seen for fluorine. The equilibrium position for oxygen on the surface lies above a C--C bond with both neighboring carbon atoms puckering above the plane. Diffusion calculations show energy barriers of 1.2 eV, 0.35 eV, and 0.73 eV for hydrogen, fluorine, and oxygen, respectively. Zero-point energies turn out to be non-negligible for hydrogen kinetics, though desorption is found to be more likely than diffusion both with and without these corrections.;In the study of charge effects on adatom bonding (Chapter 3), we find a drastic lowering (from 0.74 eV to 0.15 eV) of the diffusion barrier for oxygen on graphene under electron doping (7.64 x 1013 cm-2). Such a large drop in the energy barrier corresponds to an increase in diffusivity of over nine orders of magnitude. Analyzing the partial densities for the atoms involved shows a weakening of the bonds in the equilibrium position and strengthening of bonds in the transition state as evidence for the drop in the energy barrier. In the case of hydrogen, electron doping suppresses the magnetization localized around the adsorption site. Electronic charging of the graphene plane is also found to change the bonding between fluorine and graphene from largely covalent to largely ionic.;In Chapter 4, we present a Hubbard-like tight-binding model for fluorine on graphene that shows that the mechanism of the sp2-sp 3 hybridization crossover arises from a competition between electrostatic interactions and C--F hybridization. A similar model is applied to the hydrogen--graphene system; the magnetic moment formation localized around the adsorption site is explained by a balance between hybridization and intra-atomic coulomb interactions. The model is expanded to include correlations within a small cluster around the adsorption site. This Minimal Anderson Hubbard Model (MAHM) explains the dependence of the magnetization in the H--graphene system on the C--H hybridization, the H site energy, and the H Hubbard term; the model reaffirms the results gained from mean-field calculations.;A tight-binding model is proposed in Chapter 5 to explain the paramagnetic response in fluorinated graphene measured in recent experiments. Odd-numbered bare graphene clusters surrounded by fluorinated sites are hypothesized to contribute magnetic moments to the system within this model. Several adsorption models are proposed to simulate graphene fluorination from 1% to nearly 100% coverage. An Ising-like Monte Carlo model including adatom diffusion effects is found to yield odd-numbered cluster concentrations which coincide closely with experimental magnetic moment measurements.;Lastly, Chapter 6 proposes future projects on modeling the effect of a substrate on local charging of graphene and its subsequent effect on adatom diffusion. The effect of charged impurities at the SiO2--graphene interface is discussed as well as the effect of applying fields across inhomogeneous substrates with differing dielectric constants.