Disclosed is a method of forming a large number of monocrystalline silicon regions, of uniform orientation, on the surface of an insulator material. Initially, a large number of island regions of amorphous or polycrystalline silicon, thermally connected to one another in a predetermined direction by connecting regions, are provided. Then such island regions are sequentially melted and regrown in such predetermined direction so as to form the monocrystalline semiconductor regions, with such regions having a uniform orientation. Thereafter, such connecting regions can be removed in order to isolate the island regions. The connecting regions can be formed with gaps, whereby such connecting regions need not be removed. The connecting regions can be formed of materials having a higher heat conductivity than that of the material of the island regions, and/or the connecting regions can have a smaller cross-sectional area at right angles to the predetermined direction than that of the island regions. Such island regions can be utilized for forming semiconductor elements, such as MOS FETs, therein.