A packaged semiconductor device (200) with a substrate (220) having, sandwiched in an insulator (221), a flat sheet-like sieve member (240) made of a non-linear material switching from insulator to conductor mode at a preset voltage. Both member surfaces are free of indentations; the member is perforated by through-holes, which are grouped into a first set (241) and a second set (242). Metal traces (251) over one member surface are positioned across the first set through-holes (241); each trace is connected to a terminal on the substrate top and, through the hole, to a terminal on the substrate bottom. Analogous for metal traces (252) over the opposite member surface and second set through-holes (242). Traces (252) overlap with a portion of traces (252) to form the locations for the conductivity switches, creating local ultra-low resistance bypasses to ground for discharging overstress events.