Time-resolved pump-probe spectroscopic ellipsometry of cubic GaN II: Absorption edge shift with gain and temperature effects

We recently published a study concerning femtosecond pump-probe absorption edge spectroscopy of cubic GaN (fundamental bandgap: 3.23 eV), resulting in the transient dielectric function. In the present study, we continue our investigations of those pump-probe measurements by determining the time-dependent transition energy at the Fermi-vector between the conduction and valence bands. The generation of electron-hole pairs by the 266 nm pump-beam (4.66 eV) shifts the absorption edge by approximate to 500 meV within 1 ps due to many-body effects like band-filling and bandgap renormalization. Modeling this ultra-fast change is achieved by converting the transition energies into free-carrier concentrations, assuming the electron contributions to be dominant. We consider the relaxation, recombination, and diffusion of those free-carriers as well as either an additional gain-recombination or temperature effects. This allows for describing the transition energies on short time scales. Both models yield similar values for the characteristic relaxation time (similar to 0.21 ps), recombination time (similar to 25 ps), and diffusion coefficient (similar to 1 cm(2)/s).