First-principle study of nanostructures of functionalized graphene

We present first-principle calculations of 2D nanostructures of graphene functionalized with hydrogen and fluorine, respectively, in chair conformation. The partial density of states, band structure, binding energy and transverse displacement of C atoms due to functionalization (buckling) have been calculated within the framework of density functional theory as implemented in the SIESTA code. The variation in band gap and binding energy per add atom have been plotted against the number of add atoms, as the number of add atoms are incremented one by one. In all, 37 nanostructures with 18C atoms, 3 × 3 × 1 (i.e., the unit cell is repeated three times along x-axis and three times along y-axis) supercell, have been studied. The variation in C–C, C–H and C–F bond lengths and transverse displacement of C atoms (due to increase in add atoms) have been tabulated. A large amount of buckling is observed in the carbon lattice, 0.0053–0.7487 Å, due to hydrogenation and 0.0002–0.5379 Å, due to fluorination. As the number of add atoms (hydrogen or fluorine) is increased, a variation in the band gap is observed around the Fermi energy, resulting in change in behaviour of nanostructure from conductor to semiconductor/insulator. The binding energy per add atom increases with the increase in the number of add atoms. The nanostructures with 18C+18H and 18C+18F have maximum band gap of 4.98 eV and 3.64 eV, respectively, and binding energy per add atom –3.7562 eV and –3.3507 eV, respectively. Thus, these nanostructures are stable and are wide band-gap semiconductors, whereas the nanostructures with 18C+2H, 18C+4H, 18C+4F, 18C+8F, 18C+10F and 18C+10H atoms are small band-gap semiconductors with the band gap lying between 0.14 eV and 1.72 eV. Fluorine being more electronegative than hydrogen, the impact of electronegativity on band gap, binding energy and bond length is visible. It is also clear that it is possible to tune the electronic properties of functionalized graphene, which makes it a suitable material in microelectronics.     

Diffraction of Progressing Waves by a Screen

Problems of diffraction of a time-dependent wave by a planescreen of arbitrary shape are discussed. The method is basedon the progressing wave formalism which is a time-dependentversion of the geometrical theory of diffraction and yieldsapproximate solutions of diffraction problems. The diffractionproblem is formulated as an initial-boundary value problem forthe scalar wave equation. The solution is obtained by generalizinga "uniform" asymptotic solution recently found for the time-harmoniccase. These solutions are free of the anomalous singularitiesat the shadow boundaries and at the edge of the screen whichare present in the solutions constructed by the geometricaltheory of diffraction.