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.