  We probe the local inhomogeneities of the electronic properties of graphene
at the nanoscale using scanning probe microscopy techniques. First, we focus on
the study of the electronic inhomogeneities caused by the graphene-substrate
interaction in graphene samples exfoliated on silicon oxide. We find that
charged impurities, present in the graphene-substrate interface, perturb the
carrier density significantly and alter the electronic properties of graphene.
This finding helps to understand the observed device-to-device variation
typically observed in graphene-based electronic devices. Second, we probe the
effect of chemical modification in the electronic properties of graphene, grown
by chemical vapour deposition on nickel. We find that both the chemisorption of
hydrogen and the physisorption of porphyrin molecules strongly depress the
conductance at low bias indicating the opening of a bandgap in graphene, paving
the way towards the chemical engineering of the electronic properties of
graphene.
