Transient voltage suppressor semiconductor devices and other semiconductor devices having rigorous requirements for the diffusion and depth of impurities to produce P-N junctions can be fabricated at surprisingly low costs without sacrifice of functional characteristics by subjecting the substrate to a grinding process resulting in a surface short of polishing perfection, thereby to eliminate the time-consuming and hence costly conventional polishing operation, and then diffusing the desired impurity into the substrate from a solid impurity source.