GaN epitaxially grown on Si is a material for power electronics that intrinsically shows a high density of dislocations. We show by Conductive Atomic Force Microscopy (C-AFM) and Defect Selective Etching that even for materials with similar total dislocation densities substantially different subsets of dislocations with screw component act as current leakage paths within the AlGaN barrier under forward bias. Potential reasons are discussed and it will be directly shown by an innovative experiment that current voltage forward characteristics of AlGaN/GaN Schottky diodes shift to lower absolute voltages when such dislocations are present within the device. A local lowering of the Schottky barrier height around conductive dislocations is identified and impurity segregation is assumed as responsible root cause. While dislocation related leakage current under low reverse bias could not be resolved, breakdown of AlGaN/GaN Schottky diodes under high reverse bias correlates well with observed conductive dislocations as measured by C-AFM. If such dislocations are located near the drain side of the gate edge, failure of the gate in terms of breakdown or formation of percolation paths is observed for AlGaN/GaN high electron mobility transistors.