The electronic semiconductor component has a crystalline wafer substrate with an active surface and a semiconductor layer coating the active surface. So that the semiconductor layer has a few surface defects the crystalline wafer substrate is a sapphire or silicon carbide single crystal and the active surface has a pit density of less than 500 pit/cm.sup.2, preferably less than 100 pit/cm.sup.2. The polishing method for obtaining the active surface with these pit densities includes polishing with a polishing agent, such as a silicon suspension, and a polishing tool, which is pressed on the active surface with a pressure of preferably from 0.05 to 0.2 kg/cm.sup.2 and moved over the active surface with polishing motions distributed statistically and uniformly over a 360.degree. angle during polishing.