X-ray scattering profiles: revealing the porosity gradient in porous silicon

Porous silicon layers with different porosities were prepared by adjusting the anodization current density of the electrochemical etching process, starting from highly doped p-type crystalline silicon wafers. The microstructural parameters of the porous layers were assessed by high-resolution X-ray diffraction, total external reflection, scanning electron microscopy and nitrogen adsorption–desorption analysis. Furthermore, both the surface porosity and the mean porosity for the entire volume of the samples were estimated by employing total external reflection measurements and X-ray reciprocal-space mapping, respectively. The results clearly indicate that the surface porosity is different from the mean porosity, and the presence of a depth porosity gradient is suggested. To evaluate the porosity gradient in a nondestructive way, a new laboratory method using the grazing-incidence X-ray diffraction technique is reported. It is based on the analysis of the X-ray scattering profiles of the porous layers to obtain the static Debye–Waller factors. In this way, a description of the porosity gradient in a quantitative framework becomes possible, and, as a result, it was shown that the porosity increases exponentially with the X-ray penetration depth. Moreover, a strong dependence between the porosity gradient and the anodization current was demonstrated. Thus, in the case of the lowest anodization current (e.g. 50 mA cm−2) a variation of only 15% of the porosity from the surface to the interface is found, but when applying a high anodization current of 110 mA cm−2 the porosity close to the bulk interface is almost three times higher than at the surface.