Semiconductor crystal films on a dielectric substrate are advantageously made by a zone melting method. Single-crystal structure is initiated at a seed surface, and made to extend across a dielectric surface by melting and resolidifying.Melting is effected upon irradiation with optical radiation which is focused onto an elongated zone; the zone is moved so as to locally melt successive portions of a layer of precursor material which may be amorphous or polycrystalline. The use of incoherent radiation is convenient, and focusing is typically by using a reflector.The process is conveniently effected under a controlled atmosphere and the layer being crystallized may be encapsulated so that no free semiconductor surface is exposed to an atmosphere.