Time-resolved pump–probe spectroscopic ellipsometry of cubic GaN. I. Determination of the dielectric function

An ultra-fast change of the absorption onset for zincblende gallium-nitride (zb-GaN) (fundamental bandgap: 3.23 eV) is observed by investigating the imaginary part of the dielectric function using time-dependent femtosecond pump–probe spectroscopic ellipsometry between 2.9 and 3.7 eV. The 266 nm (4.66 eV) pump pulses induce a large electron–hole pair concentration up to 4×1020cm−3, which shift the transition energy between conduction and valence bands due to many-body effects up to ≈500 meV. Here, the absorption onset increases due to band filling while the bandgap renormalization at the same time decreases the bandgap. Additionally, the absorption of the pump-beam creates a free-carrier profile within the 605 nm zb-GaN layer with high free-carrier concentrations at the surface, and low concentrations at the interface to the substrate. This leads to varying optical properties from the sample surface (high transition energy) to substrate (low transition energy), which are taken into account by grading analysis for an accurate description of the experimental data. For this, a model describing the time- and position-dependent free-carrier concentration is formulated by considering the relaxation, recombination, and diffusion of those carriers. We provide a quantitative analysis of optical experimental data (ellipsometric angles Ψ and Δ) as well as a plot for the time-dependent change of the imaginary part of the dielectric function.