Abstract
Graphene antidot lattices constitute a novel class of nano-engineered graphene devices with controllable electronic and optical properties. An antidot lattice consists of a periodic array of holes that causes a band gap to open up around the Fermi level, turning graphene from a semimetal into a semiconductor. We calculate the electronic band structure of graphene antidot lattices using three numerical approaches with different levels of computational complexity, efficiency and accuracy. Fast finite-element solutions of the Dirac equation capture qualitative features of the band structure, while full tight-binding calculations and density functional theory (DFT) are necessary for more reliable predictions of the band structure. We compare the three computational approaches and investigate the role of hydrogen passivation within our DFT scheme.
Highlights
Sheet causes a band gap to open up around the Fermi level [22], changing graphene from a semimetal to a semiconductor with corresponding clear signatures in the optical excitation spectrum [25]
The Tight binding (TB) calculations agree well with qualitative features of the band structure calculations based on density functional theory (DFT), some differences are found on a quantitative level
In our original proposal for graphene antidot lattices, we focused on the possibility of fabricating intentional ‘defects’ by leaving out one or more holes in the otherwise periodic structure [22]
Summary
Sheet causes a band gap to open up around the Fermi level [22], changing graphene from a semimetal to a semiconductor with corresponding clear signatures in the optical excitation spectrum [25]. Rodriguez-Manzo and Banhart [32] created individual vacancies in carbon nanotubes using a 1 Å diameter e-beam These advances suggest that fabrication of nano-scale graphene antidot lattices with desired hole geometries may be possible in the near future. The aim of this paper is to study the band structure of graphene antidot lattices using three numerical approaches of different computational complexity, efficiency and accuracy. We first develop a computationally cheap scheme based on a finite-element solution of the DE This method gives reasonable predictions for the size of the band gap due to the antidot lattice, but has limited accuracy in predicting the full band structure. We discuss hydrogen passivation along the edges of the holes in a graphene antidot lattice and study the influence on the electronic properties using DFT.
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