Electron and hole puddles in monolayer graphene on SiO$_{2}$

We have performed spatially resolved scanning tunneling spectroscopy measurements on single layer graphene. The graphene was prepared on SiO$_{2}$ by the mechanical exfoliation technique and an electrode was attached by electron beam lithography. Atomically resolved topography images over 40 nm areas show that the graphene conforms to the SiO$_{2}$ surface as well as having intrinsic ripples. In addition to the topography measurements, we have mapped the local density of states as a function of position and energy. We observe a spatially varying Dirac point which leads to electron and hole puddles at low energy. These puddles have a characteristic size scale of about 5 nm. The puddles arise due to curvature in the graphene film which induces shifts in the chemical potential as well as long range scattering from charged impurities.