An oxygen- or nitrogen-terminated silicon nanocrystalline structure is formed on a silicon substrate by forming a silicon film of fine silicon crystals and amorphous silicon on a substrate, and oxidizing or nitriding the formed silicon film with ions and radicals formed from an oxidizing gas or a nitriding gas. The oxidizing or nitriding step comprises substeps of disposing the substrate provided with the silicon film in an oxidizing or nitriding gas atmosphere within a plasma treatment chamber, and then plasma-oxiziding or plasma-nitriding the substrate provided with the silicon film by applying a high frequency electric field to the oxidizing or nitriding gas atmosphere. The method allows the particle diameter of the oxygen- or nitrogen-terminated silicon nanocrystals to be regulated to an accuracy of 1 to 2 nm, the density thereof per unit area to be increased, and the silicon nanocrystalline structure to be produced easily and inexpensively.