Density of states and phonon-induced relaxation of electrons in semiconductor quantum dots

To understand the energy relaxation of electrons interacting with both longitudinal-optical (LO) and longitudinal-acoustic (LA) phonons in a semiconductor quantum dot, the electron density-of-states $D(E)$ is calculated using the Green's-function method taking into account interactions of all orders and self-consistent level broadening. The $D(E)$ calculated for a GaAs dot exhibits sharp peaks (width 0.1 meV ) at $T=77$ K, indicating the absence of fast relaxation in the usual sense. For level separation near, but not necessarily too close to, the LO-phonon energy, the peaks are equally narrow but split by the coherent mixing of electron levels (Rabi splitting). The LA phonons are much too weak to destroy this coherence. In the time domain, the electron undergoes rapid $(<$ ps) Rabi flopping between levels.