Study of optical properties of porous silicon by DFT, comparison to experimental and effective medium approximation methods

In this study, the optical properties of porous silicon (PSi), such as the dielectric function, absorption coefficient, bandgap, reflectivity and refractive index, were studied as a function of porosities ranging from 3% to about 40% by using a supercell model in an ab-initio pseudo-potential plane wave (PP-PW) method based on density functional theory (DFT). To validate these theoretical results, various PSi samples were prepared by varying the etching parameters to achieve similar porosities. The PSi samples were subjected to UV–vis spectrophotometry in order to measure their reflectivity. The refractive indexes predicted by DFT were compared to those obtained by the Fresnel equation and the effective medium approximation methods (EMA), particularly Bruggeman’s, Looyenga’s and del Rio's model (dRZW). These studies showed that the PSi dielectric constant decreases with increasing porosity, which is consistent with a decrease in the refractive index. In addition, as the porosity of PSi rises, the bandgap energy values increase, which is closely related to the decrease in the refractive index. For low porosity, DFT and Looyenga refractive indexes fit better than dRZW or Bruggeman. Furthermore, when the porosity is increased, DFT gives similar results as dRZW and is better than the Bruggeman method. Moreover, at medium porosity (28 or 40%), DFT and EMA models agree well with the experimental refractive indexes of PSi.