Ultimate carrier mobility in graphene

Since its isolation in monolayer sheets, graphene has emerged as an ideal two-dimensional (2D) material with exotic physical properties. For electronics applications, graphene is attractive because of the linear energy-momentum dispersion, by which all charge carriers move with the same velocity vf approximately equal to 10^8 cm/s, much greater than in conventional semiconductor materials, anticipating faster device time response. As a gapless material, graphene has an overlap between its valence and conduction bands of just a single point, the so-called Dirac point around the K and K' symmetry points of the Brillouin zone. For this reason, the graphene conductivity exhibits a minimum value around the Dirac point varying between 2Gsub0 and 10Gsub0, where Gsub0 = 2e^2=h is the quantum conductance, regardless of temperature or static impurity scattering. Several theories including charged impurity scattering have been developed to explain this invariance of the minimum conductivity. In this paper, we present our new theory that takes into account the surface corrugation of graphene sheets, which results in a landscape of inhomogeneous electron and hole puddles in the sheet. We postulate the existence of an intrinsic quantum transmission rate to explain the existence of the minimum conductivity. By comparing our quantum results with the classical de nition of carrier mobility, we derive the expression of the ultimate mobility in 2D graphene.U of I OnlyUndergraduate senior thesis not recommended for open acces