Wet-etching mechanism of a semi-sphere pattern on sapphire substrate

A semi-spherical pattern can be converted to a triangular pyramid comprising three r-planes using chemical wet etching with a mixture of sulfuric and phosphoric acids. The apex Al atom on the triangular pyramid with numerous dangling bonds can be subject to etching with prolonged exposure. After removing the apex Al atoms, Al atoms underneath the r-plane can be readily etched and low incline-angle, side-facet planes are developed. The concentrations of SO₄2- and PO₄^3- ions in the mixed etching solution greatly affect the etching rate on the patterns on the sapphire surface. The SO₄^2- and PO₄^3- etchant ions in the etching solution will react with the etching site (surface Al atoms) and form Al₂(SO₄)₃ and AlPO₄. The molar ratios of the reactants (surface Al etching sites and acid molecules) are different. Given the size of the SO₄^2- radicals (the average bond length of the sulfate ion is 1.49 Å), the other surface Al atoms next to the Al atoms engaging with the SO₄^2- radicals cannot be close to any free SO₄^2- radicals in the etching solution. This effect is called the “screening effect” or “spatial barrier effect.” For forming AlPO₄, one PO₄^3- ion can bond with one etching Al site without being limited by the spatial screening effect. There is no spatial screening effect for the phosphoric acid etching of a sapphire surface. Thus, phosphoric acid would have a higher etching rate of a sapphire surface than sulfuric acid. In this study, the bottom of the triangular pyramid is not an equilateral triangle. Instead, the sides of the bottom triangular of the triangular pyramid are curved. The availability of etching Al sites on the etching side-facet surface and ridges of the triangular pyramid can explain the curved sides of the bottom triangle of the triangular pyramid.