Physically realistic, parametric model for excitonic critical point parabolic band oscillators

Critical point parabolic band (CPPB) oscillators are often useful to model the optical response of semiconductor materials, such as hybrid organic–inorganic lead halide-based perovskites, to incident photons in the form of the complex dielectric function (ε=ε1+iε2) spectra. Some models of ε using CPPB oscillators are not guaranteed Kramers–Kronig (KK) consistent (and therefore not physically realistic), may have excess or arbitrary parameter values, or may require prohibitively long computational time when used to fit ellipsometric spectra. For excitonic CPPBs, commonly used to describe the optical response of hybrid organic–inorganic lead halide-based perovskite materials, a physically realistic, parametric model of ε is developed from the KK relationship between ε1 and ε2 for a number of CPPB oscillators with an Urbach tail below the lowest direct transition. This parametric model is shown to produce the same line shape reported from previous works accurately and more quickly than other available KK-consistent CPPB models.