Structures for laterally-diffused metal-oxide-semiconductor devices and drain-extended metal-oxide-semiconductor devices, as well as methods of forming laterally-diffused metal-oxide-semiconductor devices and drain-extended metal-oxide-semiconductor devices. A gate electrode is arranged to extend about a semiconductor fin projecting from a substrate. A drain region is arranged in the substrate, and a source region is coupled with the semiconductor fin. The source region is arranged over the semiconductor fin. A drift region is arranged in the substrate between the drain region and the semiconductor fin. The drain region, source region, and drift region have a given conductivity type. The drift region has a lower electrical conductivity than the drain region.