Boundary Element Method Modification for Very Thin Films and 2D Materials

Martin Hrtoň Institute of Physical Engineering, Brno University of Technology, Brno, Czech Republic Fabrication and Characterisation of Nanostructures, CEITEC BUT - Brno University of Technology, Brno, Czech Republic Vlastimil Křápek Institute of Physical Engineering, Brno University of Technology, Brno, Czech Republic Fabrication and Characterisation of Nanostructures, CEITEC BUT - Brno University of Technology, Brno, Czech Republic Tomáš Šikola Institute of Physical Engineering, Brno University of Technology, Brno, Czech Republic Fabrication and Characterisation of Nanostructures, CEITEC BUT - Brno University of Technology, Brno, Czech Republic

With the discovery of graphene and its plasmonic properties a challenge of capturing its strictly 2D nature in 3D light scattering simulations has arisen. So far the graphene and its modifications (ribbons, discs, etc.) have been mostly treated as a very thin film of subnanometer thicknesses with an effective dielectric function derived from the 2D optical conductivity. The subnanometer thicknesses posess a difficulty for standard discretization-based methods (BEM, FDTD, FEM), since the density of discretization elements, especially near the edges of the graphene structures, must be sufficiently high.

In this study we present an extension to the existing framework of BEM with graphene treated as a conductive interface between two media. That means one can account for the presence of graphene, or any other 2D material, either by suitably adjusting the customary boundary conditions or by introducing an additional auxiliary current. The testing of our enhanced code against the standard one on a problem with a known analytical solution revealed that in the new approach the number of discretization elements necessary to obtain converging results was reduced by a factor of 4. Furthermore, the incorporation of graphene into the interface enables us to simulate the problems with non-homogeneous doping.

martin.hrton@gmail.com