Silicon oxide reaches its limit as dielectric material in future MOSFET devices. Reduced device dimensions demand for advanced characterization methods, applicable in the nanometer regime. Here, conductive atomic-force microscopy (C-AFM) is used to study different high-k dielectric materials with regard to their dielectric properties and homogeneity. Materials like ZrO2 and HfO2 have been investigated by C-AFM under ultra-high vacuum. Local current-voltage measurements are performed to obtain statistical information on the leakage current depending on the voltage applied. From the results, the influence of the amorphous or crystalline structure of these films depending on their thickness and heat treatment is deduced. Further, two-dimensional current scans are performed to obtain information on the lateral distribution of leakage currents. It is found that crystallite growth of ZrO2 in comparison to HfO2 starts at lower film thickness. For both films increasing crystallinity results in inhomogeneous dielectric properties. In a second part, C-AFM was used to study CaF2 films on Si(111). A reduced current in the vicinity of steps was observed in agreement with enhanced film growth due to relaxation at steps.