Abstract
The implementation of graphene-based electronics requires fabrication processes that are able to cover large device areas, since the exfoliation method is not compatible with industrial applications. The chemical vapor deposition of large-area graphene represents a suitable solution; however, it has an important drawback of producing polycrystalline graphene with the formation of grain boundaries, which are responsible for the limitation of the device’s performance. With these motivations, we formulate a theoretical model of a single-layer graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the charge carrier transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach, and represents per se an important enrichment of the scattering theory of polycrystalline graphene. Moreover, the outcomes of the theory can contribute to understanding and limiting the detrimental effects of graphene grain boundaries, while also providing a benchmark for more elaborate techniques.
Highlights
Graphene (G) is a two-dimensional honeycomb lattice that is constituted by carbon atoms.Its reciprocal lattice determines a hexagonal Brillouin zone that has six corners (K/K’ points) where the low-energy part of the band’s structure is well described by a linear energy–momentum dispersion relation, defining the so-called Dirac cone
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The model provides a description of the grain boundary based on a Dirac Hamiltonian written in a rotated side-dependent reference frame describing crystallographic axes mismatching at a grain boundary junction
Summary
Graphene (G) is a two-dimensional honeycomb lattice that is constituted by carbon atoms. The mentioned approach provides a continuous model to study transport properties in the presence of selected linear defects, whose atomic arrangement determines the boundary conditions of the scattering problem. We provide an alternative method and develop a continuous model of polycrystalline graphene in which general boundary conditions are derived without specifying the microscopic structure of the linear defect. With these motivations, we formulate a theoretical model of the graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. Generalization of the ideas exposed hereafter to spinful particles having two-valley degrees of freedom is in principle immediate
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