While a silicon substrate is heated, gold is evaporated thereon at a thickness of 0.6 nm, whereby melted alloy droplets are formed on the substrate surface. Then, the silicon substrate is heated to 450.degree.-650.degree. C. in a silane gas atmosphere of less than 0.5 Torr. As a result, a silane gas decomposition reaction occurs with the melted alloy droplets serving as catalysts, whereby silicon wires grow on the substrate surface. Subsequently, the metal alloy droplets at the tips of the silicon wires are removed and surface portions of the silicon wires are oxidized. Resulting surface oxide films are thereafter removed. As a result, silicon quantum wires that are thinner by the thickness of the surface oxide films are obtained.