  The charge carrier density in graphene on a dielectric substrate such as
SiO$_2$ displays inhomogeneities, the so-called charge puddles. Because of the
linear dispersion relation in monolayer graphene, the puddles are predicted to
grow near charge neutrality, a markedly distinct property from conventional
two-dimensional electron gases. By performing scanning tunneling
microscopy/spectroscopy on a mesoscopic graphene device, we directly observe
the puddles' growth, both in spatial extent and in amplitude, as the Dirac
point is approached. Self-consistent screening theory provides a unified
description of both the macroscopic transport properties and the
microscopically observed charge disorder.
