It is well known that the close-packed CF3-terminated solid surface is among the most hydrophobic surfaces in nature. Molecular dynamic simulations show that this hydrophobicity can be further enhanced by the atomic-scale roughness. Consequently, the hydrophobic gap width is enlarged to about 0.6 nm for roughened CF3-terminated solid surfaces. In contrast, the hydrophobic gap width does not increase too much for a rough CH3-terminated solid surface. We show that the CF3-terminated surface exists in a microscopic Cassie-Baxter state, whereas the CH3-terminated surface exists as a microscopic Wenzel state. This finding elucidates the underlying mechanism for the different widths of the observed hydrophobic gap. The cage structure of the water molecules (with integrated hydrogen bonds) around CH3 terminal assemblies on the solid surface provides an explanation for the mechanism by which the CH3-terminated surface is less hydrophobic than the CF3-terminated surface.