Ab-initio determination of porous silicon refractive index confirmed by infrared transmittance measurements of an omnidirectional multilayer reflector

Abstract

We report a multiscale design of omnidirectional Bragg mirrors based on dielectric multilayers by combining quantum mechanical and electromagnetic theories. This design begins with the calculation of electric permittivity for each layer using the density functional theory, followed by a transfer matrix study of light propagation along the multilayer reflector. The theoretical results were further validated by fabricating free-standing porous silicon multilayer films obtained through electrochemical etching of p+-type [100]-oriented crystalline Si wafers, alternating two anodic current densities. The measured infrared transmittance spectra confirm the position and width of the photonic bandgap predicted by the multiscale design.