Variable-period oscillations in optical spectra in sub-bandgap long wavelength region: signatures of new dispersion of refractive index?

Abstract

Variable-period oscillations (VPOs) in various optical spectra in sub-bandgap long wavelength region, including reflection, transmission, absorption, and even luminescence spectra, are a frequently observed phenomenon in various semiconducting and dielectric films. These functional films include nitrides, oxides, silicides, sulfides, and perovskites. Although the phenomenon is widely known to be caused by optical interference, a generalized analytical model for it has not yet been established, probably due to both varying oscillation period and amplitude. In this article, we attempt to develop such a model by introducing a new concise dispersion of the sub-bandgap refractive index, i.e. containing a frictional component. In particular, we show that the VPOs in the reflectance and corresponding transmission shall have reverse maxima and minima in intensity, giving a self-consistent explanation to the existing experimental results in literature. Furthermore, the present analytical method is proven to be accurate for finding optical constants and thicknesses of films. Finally, the rationality of the new dispersion is further argued in terms of a generalized refractive index of crystal with lattice anomalies (e.g. defected and strained lattice), which was derived by Gonçalves et al from the fractional Drude–Lorentz model. In addition, the equivalency between the VPOs and Newton’s rings in energy space is discussed based on the present model.