A nanometer-size quantum thin line is formed on a semiconductor substrate of a Si substrate or the like by means of the general film forming technique, lithographic technique and etching technique. By opportunely using the conventional film forming technique, photolithographic technique and etching technique, a second oxide film that extends in the perpendicular direction is formed on an Si substrate. Then, by removing the second oxide film that extends in the perpendicular direction, a second nitride film located below the film and a first oxide film located below the film by etching, a groove for exposing the Si substrate is formed. Then, a Si thin line is made to epitaxially grow on the exposed portion of the Si substrate. The quantum thin line is thus formed without using any special fine processing technique. The width of the groove can be accurately controlled in nanometers by controlling the film thickness of the second oxide film that is formed by oxidizing the surface of the second nitride film.