A thick column is formed by masking and etching a substrate, and the column is thinned to a very small diameter (e.g., .ltoreq.5 nm) by oxidizing the column and removing the oxide layer. A metal layer is deposited on the surface of the substrate, and the column and substrate are etched to form a pit. The backside of the substrate is etched to form an aperture surrounded by the metal layer. Alternatively, the metal layer is removed and a dopant layer is implanted into the substrate, followed by the etching of the backside, leaving an aperture surrounded by the dopant layer. In a second alternative, the oxidized column is broken from the substrate, and the backside is etched, leaving an aperture surrounded by an oxide layer. These processes can be used to fabricate apertures of very small and reproducible dimensions for such instruments as near field scanning optical microscopes and scanning ion conductance microscopes.