A thin film semiconductor transistor structure has a substrate with a dielectric surface, and an active layer made of a semiconductor thin film exhibiting a crystallinity as equivalent to the single-crystalline. To fabricate the transistor, the semiconductor thin film is formed on the substrate, which film includes a mixture of a plurality of crystals which may be columnar crystals and/or capillary crystal substantially parallel to the substrate. The resultant structure is then subject to thermal oxidation in a chosen atmosphere containing halogen, thereby removing away any metallic element as contained in the film. This may enable formation of a mono-domain region in which the individual columnar or capillary crystal is in contact with any adjacent crystals and which is capable of being substantially deemed to be a single-crystalline region without presence or inclusion of any crystal grain boundaries therein. This region is for use in forming the active layer of the transistor.