Irradiation of metallic surfaces using ultra-short pulse laser results in a dual-scale structure. While metallic surfaces are superhydrophilic immediately after laser irradiation, prolonged exposure to air renders surfaces superhydrophobic due to surface reactions and deposition of carbonaceous materials onto the surface. In this work, we have fabricated a paraboloid microstructure, which is analyzed thermodynamically through the use of the Gibbs free energy to obtain the equilibrium contact angle and contact angle hysteresis. The effects of the geometrical details on maximizing the superhydrophobicity of the nanopatterned surface are also discussed in an attempt to design surfaces with desired and/or optimum wetting characteristics.