This thesis covers the nanoscale electron transport in thin films of bismuth selenide (Bi2Se3) and bismuth telluride (Bi2Te3) on Si(111). Bi2Se3 and Bi2Te3 belong to the new material class of topological insulators (TI). These materials are insulating in their bulk while they provide a metallic, spin-polarized surface state. The surface state is protected by the material’s topology which leads to a high robustness against non-magnetic defects. The local electron transport of the TI films was studied by scanning tunneling potentiometry (STP), an extension of the scanning tunneling microscope (STM) which gives access to the microscopic topography and the corresponding electrochemical potential μ_ec of the surface simultaneously. The local (nm-scale) STP measurements are supported by global (µm-scale) multi point probe studies. The STP analysis shows that the local electron transport in the TI film is dominated by a constant gradient of μ_ec. In addition, μ_ec drops suddenly at step edges and domain boundaries on the Bi2Se3 and Bi2Te3 surface. Therefore, these morphological structures are transport barriers for conduction electrons. For some samples thermovoltage signals were observed as well. Additionally, the influence of adsorbates on the transport properties of the TI films is studied. While Bi islands on Bi2Se3 films lead to an increased sheet conductance, additional iron islands on Bi2Te3 films have no significant influence on the electron transport.