Properties of Graphene

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis provides the study of graphene’s electrostatic interaction with the substrate surround-ing it. Mathematical models based on current experimental configurations of graphene field-effect transistors (FET) are developed and analyzed. The conductivity and mobility of charge carriers in graphene are examined in the presence of impurities trapped in the substrate near graphene. The impurities encompass a wide range of possible structures and parameters, including different types of impurities, their distance from graphene, and the spatial correlation between them. Furthermore, we extend our models to analyze the influence of impurities on the fluctuations of the electrostatic potential and the charge carrier density in the plane of graphene. The results of our mathematical models are compared with current experimental results in the literature. ii