Lateral Fractal Formation by Crystallographic Silicon Micromachining

Abstract

A novel wafer-scale silicon fractal fabrication method is presented here for forming pyramids only in the lateral direction using the crystal orientation of silicon. Fractals are fabricated in silicon by masking only the corners (corner lithography) of a cavity in silicon with silicon nitride, where the shape is determined by the crystal {111} planes of the silicon. The octahedral cavity shaped by the {111} planes was previously only used for forming octahedral fractals in all directions, but by using a planar silicon dioxide hard-mask on a silicon (100) wafer, the silicon octahedral cavity is “cut in half”. This creates a pyramid with sharper edges and vertices at its base than those determined by just the {111} planes. This allows selective corner lithography patterning at the vertices of the base while leaving the apex unpatterned, leading to lateral growing of pyramidal fractals. This selective patterning is shown mathematically and then demonstrated by creating a fractal of four generations, with the initial pyramid being 8 µm and the two final generations being of submicron size.