We report on the electrical generation of surface acoustic waves (SAWs) on doped semiconductor substrates. This is implemented by using interdigital transducers (IDTs) placed on piezoelectric ZnO films sputtered onto evaporated thin metal layers. Two material systems are investigated, namely ZnO/Au/GaAs and ZnO/Ni/InP. The rf-field applied to the transducer is electrically screened by the highly conductive metal film underneath the ZnO film without any extra ohmic losses. As a result, absorption of the rf-field by the mobile carriers in the lossy doped region underneath the IDT is avoided, ensuring efficient SAW generation. We find that the growth temperature of the ZnO film on the metal layer affects its structure and, thus, the efficiency of SAW generation. With this technique, the SAW active layers can be placed close to doped layers, expanding the application range of SAWs in semiconductor devices.