The formation and electrical properties of discrete islands in discontinuous Au films on Si(111) were studied with a scanning tunneling microscope (STM). Ohmic electrical contact between the STM tip and isolated gold islands was established and I-V characteristics of the Au-Si junctions were measured. A typical Schottky diode behaviour with ideality factor close to 1 was observed. The STM appears to be an appropriate probe for electrical measurements of nano-scale diodes.