Electrical transport of zig-zag and folded graphene nanoribbons
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Electrical transport of zig-zag and folded graphene nanoribbons Watheq Elias1,2 , M. Elliott1 and C. C. Matthai1 1 School of Physics and Astronomy Cardiff University, The Parade, Cardiff, UK CF24 3AA 2 Dept of Physics, Koya University, Erbil, Iraq. E-mail: [email protected] ABSTRACT In recent years, there has been much interest in modelling graphene nanoribbons as they have great potential for use in molecular electronics. We have employed the NEGF formalism to determine the conductivity of graphene nanoribbons in various configurations. The electronic structure calculations were performed within the framework of the Extended Huckel Approximation. Both zigzag and armchair nanoribbons have been considered. In addition, we have also computed the transmission and conductance using the non-equilibrium Greens function formalism for these structures. We also investigated the effect of defects by considering a zigzag nanoribbon with six carbon atoms removed. Finally, the effect of embedding boron nitride aromatic molecules in the nanoribbon has been considered. The results of our calculations are compared with that obtained from recent work carried out using tight-binding model Hamiltonians.
INTRODUCTION Graphene is a two-dimensional sheet of graphite in which the sp2 hybridization leads to a trigonal planar structure with strong bonds connecting the C-atoms with an equilibrium separation, a, of 1.42 . It is the strength of these bonds that result in such a robust structure. This crystal structure also gives rise to a unique electronic band structure and a whole range of interesting electronic properties [1]. The high electron mobility and good thermal conductivity of graphene makes it a useful and promising material for use in next generation electronic devices. In particular, their mechanical and electronic properties have enhanced the prospect of graphene nanoribbons (GNR) being used as nanowires in miniaturized electronic devices. GNR, which are sheets of graphene cut to make ribbons, have two basic edge shapes. The corresponding ribbons are termed zigzag nanoribbons (ZNR) or armchair nanoribbons (ANR). The width of a GNR is defined in terms of the number of C-atoms across the ribbon (N). The same number N for both types of ribbons does not mean that the ribbons have the same width. The width is related to N through the relations: 1 N+ 1 W A= a for the ANR and W Z = ¥ 3N+ a 2 ¥ 3 for the ZNR.
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self-consistent with the ionization potentials. Conductance calculations The current I across a molecular wire is given by I=
2e T ( E )[ f ( Eí ȝ 1 )í f ( Eí ȝ2 ) ] dE h
(4)
where T ( E ) is the transmission function across an electrode-molecule-electrode system, f ( E) is the Fermi function. μi are the electro-chemical potentials of the two electrodes at bias voltage VB such that ȝ1 í ȝ2 = eV B . T ( E ) is determined by applying the non-equilibrium Greens function (NEGF) formalism with the molecular wave functions obtained from the SCEHT calculations. In the transport calculations on the GNR, th
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