Burson, Kristen M.Graphene has attracted a great deal of attention for its exceptional electronic and mechanical properties. As graphene, a two-dimensional lattice of carbon atoms, is an `all surface' material, its interactions with the underlying substrate play a crucial role in determining graphene device behavior. In order to tailor graphene device properties, the interaction between graphene and the underlying substrate must be clearly understood. This thesis addresses the question of the relationship between graphene and graphene substrates by considering both the substrate topography and the impact of charged impurities in the substrate. Utilizing scanning tunneling microscopy and high-resolution atomic force microscopy, we measure the topography of silicon dioxide (SiO₂) supported graphene and the underlying SiO₂(300nm)/Si substrates. We conclude that the graphene adheres conformally to the substrate with 99% fidelity and resolve finer substrate features by atomic force microscopy than previously reported. To quantify the density of charged impurities, simultaneous atomic force microscopy (AFM) and Kelvin probe microscopy are used to measure the potential and topographic landscape of graphene substrates, SiO₂ and hexagonal boron nitride (h-BN). We find that the surface potential of SiO₂ is well described by a random two-dimensional surface charge distribution with charge densities of ~10<super>11</super> cm<super>-2</super>, while BN exhibits charge fluctuations that are an order of magnitude lower than this. Charged impurities in the substrate present a scattering source for transport through graphene transistors, and the difference in magnitude in measured substrate charged impurities densities for SiO₂ and BN is consistent with the observed improvement in charged carrier mobility in graphene devices on h-BN over graphene devices on SiO₂. Finally, this thesis presents a theoretical model elucidating the challenges of imaging corrugated substrates by non-contact AFM and an experimental work using Kelvin probe microscopy to characterize the electrostatic potential steps at interfaces of small-molecule organic heterojunctions.DissertationPhysicsAtomic Force MicroscopyGrapheneKelvin Probe Force MicroscopyNanotechnologySubstratesSurface Science