Study On The Structure Of Graphene By Sub-Entiredomain Basis Function Method

Graphene has recently attracted a great amount of attention both in academia and industry because of its remarkable properties.One of the most favorable properties of graphene is the tunability of its electric conductivity.Since graphene is a real two-dimensional material,the thickness of graphene is much smaller than lateral dimensions and the wavelength of millimeter wave.SED basis function method is introduced to solve the EM scattering problem of largescale finite-sized periodic structures,in which the unite cell comprises graphene.The main contents and research works in this paper include the following part:1?In this thesis,some basic principles,including the establishment of the surface electric field integral equation(EFIE)for PEC objects,the PMCHW equations for homogeneous dielectric objects,the EFIE-PMCHW equations for the composite of homogeneous dielectric and PEC objects.The principle and implementation of the method of moments(MOM)are introduced.2?The thickness of freestanding graphene is nanoscale and is the orders of magnitude smaller than other geometrical dimensions,hence it is considered as a sheet structure with zero thickness and is modeled with surface integral equation(SIE)method combined with the impedance boundary condition(IBC).3?For a substrate-supported graphene device,the thickness of the graphene is taken into account.The PMCHW equation is established on the substrate surface,and the volume electric field integral equation(V-EFIE)is built inside the graphene.Since the thickness of graphene is very small,the V-EFIE can be rewritten as surface electric field integral equation(S-EFIE).Various numerical results are presented to demonstrate the accuracy.4?The SED basis function performs well in dealing with large scale finite-sized periodic arrays.In this thesis,the SED basis function is employed to solve the periodic structure of graphene,and the EFIE-PMCHW-SED method is proposed.The IBC-EFIE-SED method is used to solve the freestanding graphene periodic structures,while the EFIE-PMCHW-SED method is employed to solve the substrate-supported graphene periodic structures.Various numerical results are provided to prove the accuracy of our method.