Spontaneous Emission from Semiconductors After Ultrafast Pulse Excitation: Theory and Simulation
In this chapter, we review the recent progress in the theoretical description of ultrafast phenomena in the spontaneous emission of pulse-excited semiconductors. The theory of femtosecond pulse excitation, intraband energy relaxation, and interband luminescence processes in semiconductors is outlined within the framework of two different nonequilibrium techniques, namely, density-matrix theory and Green’s functions. In contrast to the well-established theory of semiconductor absorption, both approaches are found to yield inequivalent results for the luminescence signal if excitonic effects, i.e., Coulomb interactions between the excited electrons and holes, are taken into account. While the method of photon-assisted density matrices contains spurious effects such as negative luminescence, the Green’s function theory fulfills all physical requirements and allows the calculation of PL signals for arbitary nonequilibrium situations. In combination with quantum-kinetic simulations of electron--hole-pair generation and relaxation, this theory is then applied to the calculation of hot-luminescence signals from pulse-excited semiconductors. The numerical simulations for bulk GaAs show how the luminescence intensity is transferred within about 2 ps from the initial signal at the pump frequency towards the excitonic resonance via step-by-step emission of LO phonons. Finally, the PL theory is extended to a first-principles description of PLE experiments under nonequilibrium conditions. For small time intervals between pulse excitation and luminescence detection, we find significant differences between PLE and absorption signals, in contrast to the usually assumed equivalence of both spectra in thermal equilibrium. From our numerical simulations of ultrafast PL and PLE experiments, predictions are made as to how one may study hot-carrier phenomena including quantum-kinetic and bottleneck effects by means of spontaneous-emission spectroscopy. With the experimental confirmation of these predictions still to be achieved, the outcome of such PL and PLE experiments in the ultrafast regime would be highly important and interesting, both for experimentalists and theorists.
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