Fractal structure can explain the increased hydrophobicity of nanoporous silicon films

Nano porous silicon (NPSi) films were fabricated via a process of Si anodic dissolution. An apparent contact angle as large as 140°was measured. Atomic force microscopy (AFM) was used for deriving the surface roughness profile and imaging the topography of the porous layer. A power spectrum was conveniently derived and used to deconvolute the fractal dimension of the surface as D _f ∼ 2.8, thus strictly larger than the topological or Euclidean dimension D = 2. Due to its fractal nature, the NPSi surface would be self affine, thus containing details at arbitrarily small scales. The apparent contact angle was accordingly derived in terms of a recursive function wherewith hydrophobicity increases with the scale factor n. The right size of the problem (that is, the degree to which one should enlarge the system to gain sufficient insight of the problem) would strictly depend upon the fractal dimension and thus on an accurate measurement of the profile of the NPSi surface. The values derived for the apparent contact angle according to the procedure above are in good agreement with the observations, thus demonstrating that the model here proposed is both consistent and predictive in nature.