A method of fabricating semiconductor devices and, particularly, an art for forming thin-film semiconductor elements on a substrate. The fabrication method comprises a step for forming a conductor layer having a step on at least a portion on one main surface of the substrate, and a step for forming a semiconductor thin film on the substrate under the condition where a dc potential is being given to the conductor layer. The low-temperature process of the invention makes it possible to easily form a single- crystal semiconductor layer of high quality on any insulating substrate. Therefore, very high-speed semiconductor devices and high-performance flat panel displays can be manufactured.