This thesis describes experiments to characterize defects in two-dimensional materials and understand their effect on electrical conductivity. Defects limit the electrical conductivity through a material by scattering electrons. Understanding the physics of defects is therefore essential to building materials and structures with novel electronic properties. This dissertation has focused on low dimensional materials because they are simple thereby allowing for more advanced theory and they will act as a foundation for understanding higher dimensional systems.

High resolution x-ray photoelectron spectroscopy (XPS) and near edge x-ray absorption fine structure spectroscopy (NEXAFS) were used to determine the character of vacancy defects in graphene. Vacancies were induced in graphene on a thermally oxidized silicon substrate using argon ion bombardment. XPS of the carbon 1s core level of pristine graphene shows a C 1s spectrum consistent with a single C 1s peak broadened both instrumentally and by a Doniach-Sunjic type effect. As defects are created, the resulting spectrum is deconvolved into two peaks. The first retains the same spectral width as that for the pristine graphene but with a reduced intensity. The broader second peak at higher binding energy (~200 meV), increases in intensity with increasing defect concentration. This second peak is identified as the experimental XPS signature of defective graphene. The observation is somewhat at odds with theoretical calculations of XPS spectra for graphene with various vacancy arrangements, which generally produce C 1s peaks shifted to lower binding energy. Instead, the emergence of this second peak, together with the emergence of a single sharp resonance seen near the vacuum level in the NEXAFS spectra, is interpreted as a distribution of molecular-like states forming on the surface.

Preliminary efforts were made to characterize defects in semiconducting monolayer MoS2 using scanning tunneling microscopy (STM) and spectroscopy (STS). Techniques for obtaining a clean MoS2 surface suitable for ultra-high vacuum STM were developed, and preliminary characterization of the single layer tungsten disulfide surface by STM and STS was carried out. The local density of states of MoS2, as measured by STS, shows the semiconducting bandgap as well as signatures of donor and acceptor states within the gap.