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

Abstract

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 ≈ 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 ( ≈ 0.21 ps), recombination time ( ≈ 25 ps), and diffusion coefficient ( ≈ 1 cm 2 /s).