Effective refractive index and composition of oxidized porous silicon films

Abstract

The relationship between the refractive index of porous silicon, its porosity and oxidation degree has been calculated in the framework of the three-component Bruggeman effective medium model (silicon, SiO 2 and pores). It takes into account the fact that the gain of SiO 2 volume fraction, occurring in the course of oxidation, takes place with sacrifice in the silicon component, and the enhanced volume of the solid phase results in the decrease of porosity. Dependence of porosity on the effective refractive index for oxidized films with various initial porosity p in is limited by the curves for the two-component media: silicon and pores (Si+V) and porous oxide (SiO 2+V). Films with p in>56% remain porous even after the 100% oxidation of silicon carcass, and those with lower p in become poreless at a certain value of oxidation degree and form another two-component system: Si+SiO 2. It has been shown how the SiO 2 content in the oxidized porous silicon is obtained by using the calculated relations and graphs, when the experimental values of the refractive index and porosity (or the refractive index alone before and after oxidation) are known, and, vice versa, how the refractive index and the oxidation degree are determined from porosity variation resulting from oxidation. It has been found by ellipsometry in stain etched porous films that, as oxidation proceeds, the refractive index, the extinction coefficient and the optical thickness of the film decrease gradually, whereas the film thickness grows. Analysis of the film thickness dependence on the oxidation degree revealed that it obeys the law valid for a silicon film without pores.