A multilayer model for describing hardness variations of aged porous silicon low-dielectric-constant thin films

This paper reports on the micro-instrumented indentation of a porous silicon structure obtained by anodization of a highly p⁺-doped (100) silicon substrate aged over 1 week. The three-layer structure obtained consists of oxidized porous silicon (cap-layer), porous silicon (inner-layer) and silicon substrate. The hardness curve has the typical “U shape” of low-dielectric-constant films when the indentation depth rises: the early decrease in hardness, due to the soft inner layer, is followed by an increase, due to the hard substrate. A multilayer model is developed to account for hardness variation with respect to the applied load. This model considers the crumbling of the cap-layer and of the inner porous structure. As a result, it is shown that considering the minima in the U shape gives an over-estimated value when it comes to assessing the coating hardness. In our experiment, this minimum depends on both the hardness and the thickness of the oxidized cap layer, but not on the mechanical properties of the substrate, even for indentation depths slightly lower than the film's thickness.