A technique has been developed for growing single-crystal germanium films in situ on a dielectric substrate. An electron beam is used to melt a small zone of a polycrystalline germanium film. Single-crystal growth is induced by electrically scanning the beam in a preferred manner over a selected region of the film. An additional heat source maintains the surrounding film at elevated temperatures in order to avoid excessive temperature differentials. The scanning pattern employed permits a randomly nucleated crystallite to seed the surrounding growth. In this manner, a single-crystal the order of a millimeter across can be grown in a chosen location. Larger crystals should be possible with larger beam deflections. This work has been largely confined to film thicknesses of 3–10 μ and to substrates of sapphire. Sapphire was used because its coefficient of thermal expansion closely matches that of germanium and because of other desirable properties. All films were deposited by vacuum evaporation. The technique is logically extendable to other materials that can be grown in vacuum. It is anticipated that the technique will find applications in microelectronics and in the fabrication of special device structures.