Impact of Faddeeva–Voigt broadening on line-shape analysis at critical points of dielectric functions

Abstract

Faddeeva–Voigt broadening (FVB) couples the physical characteristics of both Lorentzian and Gaussian profiles as a combined analytic function shaping the dielectric response. Accurate extraction of the Gaussian and Lorentzian broadening contents in line-shape analysis is essential for reliable optical characterization of semiconductors and dielectrics. By adding the Gaussian-broadening width to each Lorentzian width, we investigate how FVB affects critical-point (CP) analysis. We revisit a selection of earlier work based on classical Lorentz broadening in modulation spectroscopy and spectral ellipsometry. To generalize CP analysis, we derive the FVB’s analytical representation in terms of fractional derivatives of the Faddeeva function and apply the twenty-pole Martin–Donoso–Zamudio approximation for its precise and efficient computation of the FVB of model dielectric functions and derivatives. We investigate the FVB of the electroreflectance line shape of HgCdTe for three-dimensional M0 transitions and of the photoreflectance line shape of InP excitonic E0 transitions. Furthermore, we explore how FVB affects the dielectric functions of three-dimensional excitonic and two-dimensional M0 transitions vs Tanguy’s analytical two-dimensional exciton E1 and E1+Δ1 fits of GaAs to the second-order derivatives. We use the Akaike information criterion to quantitatively estimate the goodness of fit that statistically penalizes overfitting due to extraneous parameters. By consolidating both Gaussian and Lorentzian broadenings, the FVB significantly affects the CP analysis of modulation-spectroscopy line shapes and second-order derivatives of the dielectric function.