Application of the Martin-Donoso-Zamudio multipole approximation for generalized Faddeeva/Voigt broadening of model dielectric functions

Abstract

Faddeeva/Voigt broadening of dielectric functions (DFs) couples the physical properties of mutual Lorentzian and Gaussian broadening as a combined unit. This work investigates accurate computations for the general Faddeeva/Voigt broadening of complex analytic DFs and their derivatives. The paper builds on the multipole approximation for broadening profiles and exploits the reduction of the approximation into a finite sum of Lorentzian profiles. Using a two-point Padé approximant for the Faddeeva function, we computed this study's twenty-pole Martin-Donoso-Zamudio (MDZ20) approximation. First, we evaluated the accuracies of the MDZ20 approximation relative to high-precision evaluation of the Faddeeva function and its first three derivatives. Second, we applied the MDZ20 approximation to derive the general approximation formula for the Faddeeva/Voigt broadening of Kramer-Kronig-consistent complex analytic DFs. Third, we assessed the accuracy of Voigt broadening in two theoretical applications: the universal-dispersion model through piecewise polynomial elements and the three-dimensional (3D) M0 critical point and derivatives by using the MDZ20 approximation. Finally, we developed formulas for the Faddeeva/Voigt broadening of Tanguy's 3D excitons and the Tauc-Lorentz models. The Faddeeva/Voigt-broadened Tanguy model is investigated within Gilliot's dielectric model of sol-gel ZnO. The Faddeeva/Voigt-broadened Tauc-Lorentz model is applied to amorphous silicon (a-Si). Specifically, we evaluated the impact of adding a Gaussian component to each Lorentzian width on the agreement of the Voigt-broadened DF to experimental data.