Dynamics of the pump-probe reflectivity spectra in GaAs and GaN

Abstract

The pump-probe reflectivity (PPR) technique is a quick way to characterize the short carrier lifetime in materials which may be potentially good terahertz (THz) emitters or detectors. Here, we study the PPR signal in semiconductors theoretically in the frequency domain (at various energies above and below the band gap) as a function of pump-probe delay. We consider two conditions of carrier relaxation. In one, the carriers are assumed to form a hot, thermalized energy distribution during excitation itself and then to cool via phonon emission, as is expected in the case of high density excitation in GaAs. In the other case, the carriers essentially remain in a nonequilibrium, nonthermal state even as they relax. This can happen when the carrier-longitudinal optical phonon interaction is stronger than carrier–carrier scattering, as is likely in GaN even at moderately high densities. In addition, effects of carrier trapping and recombination determining the carrier lifetime are included. The calculation takes into account the effect of Sommerfeld factor and pump induced modulation of the probe reflectivity due to band filling (BF), band gap renormalization (BGR), and free carrier absorption. Signatures of carrier cooling and decay can be identified from the delay dependence of the PPR signal at high enough carrier densities (⩾1×1018 cm−3) when the carrier cooling rate is comparable with the decay rate. In that case, carrier cooling shows up in the reflectivity signal as a rise in the time evolution whereas the signal decay is mainly related to carrier decay, albeit in a nonexponential way. However, at lower densities, the signal evolution with delay is rather complex. There, it is not possible to identify the signature of carrier cooling and the decay of the signal is not governed simply by the carrier decay rate. We point out that in general, the magnitude and signature of the PPR signal at different delays are governed by an interplay between the BGR and BF effects. The delay dependence of the signal is a very sensitive function of the form of BGR used to describe its density dependence at low densities. We find that the delay and frequency dependence of the PPR signal is different for a thermalized, cooling distribution from that for the relaxing, nonthermalized distribution. Thus, PPR experiments may be able to distinguish rapid carrier relaxation via a cascade emission of longitudinal optical phonons due to stronger Fröhlich coupling in GaN from cooling of hot, thermalized carriers in GaAs.