Reflection of Macroporous Silicon, Nanowires, and a Two-layer Structure of Silicon with an Effective Medium

A theoretical model of reflection of macroporous silicon and arrays of silicon nanowires on a monocrystalline substrate is presented. Macroporous silicon and silicon structured by nanowires are considered as a two-layer structure of silicon with an effective medium. The analytical model of the reflection from a two-layer silicon structure with an effective medium takes into account the absorption of light by the structure and the multiple reflections of light from the surfaces of the sample and the interface between the effective medium and the monocrystalline substrate. The reflection coefficient from a structured surface, which is the boundary between two media, contains the complex index of refraction of silicon. The effective index of refraction of the effective medium is found from the expression for mixing two media. The reflection of light falling on flat surfaces at different angles is calculated according to Fresnel's formulas. The frontal structured surface and the second structured surface were considered as Lambert surfaces. Total internal reflection from a flat surface between silicon and air is given by Snelius' law, and from structured surfaces between silicon and the effective medium and between the effective medium and air is accounted for by coefficients. The reflection spectra from macroporous silicon and arrays of silicon nanowires on a monocrystalline substrate are calculated according to analytically derived formulas. It is shown that the magnitude of reflection spectra from macroporous silicon and arrays of silicon nanowires on a monocrystalline substrate decreases when the volume fraction of pores increases. The reflectance begins to increase again when the pore volume fraction is high. Reflection from the surface between the effective medium and air is observed at a high volume fraction of pores.