The technique of scanning tunneling microscopy (STM) has been used to study the spatial variation of the electric potential on thin film surfaces. Topography and potential distribution of the film surface are measured simultaneously. A lateral voltage gradient is obtained by applying a DC voltage bias to a metal film. With our experimental arrangement potential differences of a few my V can be distinguished. On the lateral scale, potential drops of about 500 my V can be localized within a distance of 2 nm. On uncovered parts of the high resistive carbon film a homogeneous drop of the potential can be measured. In the vicinity of the gold islands on the carbon surface this smooth distribution is heavily disturbed. Due to their large conductance, the islands correlate well with plateaus of the measured potential. In order to identify gold and carbon on the surface, additional spectroscopic STM-measurements have been performed.