Theory of carrier dynamics and time resolved reflectivity in In_xMn_1−xAs∕GaSb heterostructures

We present detailed theoretical calculations of two color, time-resolved pump-probe differential reflectivity measurements. The experiments modeled were performed on In_xMn_1−xAs∕GaSb heterostructures and have shown pronounced oscillations in the differential reflectivity as well as a time-dependent background signal. Previously, we showed that the oscillations resulted from a generation of coherent acoustic phonon wave packets in the epilayer and were not associated with the ferromagnetism. Now we take into account not only the oscillations, but also the background signal which arises from photoexcited carrier effects. The two color pump-probe reflectivity experiments are modeled using a Boltzmann equation formalism. We include photogeneration of hot carriers in the In_xMn_1−xAs quantum well by a pump laser and their subsequent cooling and relaxation by emission of confined LO phonons. Recombination of electron-hole pairs via the Schockley-Read carrier trapping mechanism is included in a simple relaxation time approximation. The time-resolved differential reflectivity in the heterostructure is obtained by solving Maxwell’s equations and by comparing the experiments. Phase space filling, carrier capture and trapping, band-gap renormalization, and induced absorption are all shown to influence the spectra.