Disclosed is a method for forming a nano-crystal. In the above method, there is prepared a substrate having a metal film or a semiconductor film formed thereon. A focused-ion beam is irradiated onto a plurality of positions on a surface of the metal film or the semiconductor film, whereby the metal film or the semiconductor film is removed at a focal portion of the focused-ion beam but an atomic bond in the metal film or the semiconductor film is broken at an overlapping region of the focused-ion beams due to an radiation effect of the focused-ion beam to form the nano-crystal. The method allows a few nm or less-sized nano-crystals to be formed with ease and simplicity using the focused-ion beam. As a result, the formed nano-crystals come to have a binding energy capable of restraining thermal fluctuation phenomenon at room temperature and thereby it becomes possible to fabricate a tunneling transistor capable of being operated at room temperature. Further, the invention contributes largely to a development of next generation ultra high density memory device with a memory capacitance of tera byte level or more.