Analytic representations of the complex dielectric function, which describe various types of materials, are needed for the analysis of optical measurements, in particularly, ellipsometric data. Here, we examine an improved multi-oscillator Tauc-Lorentz (TL) model with a constraint on the band-gap parameter E_g, which forces it to be common for all TL oscillators, and possibility to represent reasonably weak absorption features below the bandgap by inclusion of additional unbounded Lorentz and/or Gaussian oscillators with transition energies located below E_g. We conclude that the proposed model is the most appropriate for the characterization of various materials with sub-band absorption features and provides meaningful value for the energy bandgap. A few examples to illustrate the use of modified model have been provided.

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