We present a theoretical model for capture, inter-level relaxation and recombination of excitons to describe time-resolved experiments on (uncoupled) semiconductor quantum dots. Such zero-dimensional system is fundamentally different from any other higher dimensional semiconductor structure (bulk, quantum wells, quantum wires) because the properties of individual dots are independent of the ensemble average. Master equations for the transitions between micro-states provide an adequate modeling, while conventional rate equations for the ensemble averaged occupation probabilities fail. We apply our theory to two types of real quantum dots with fast and slow inter-level relaxation constant, respectively.
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Grundmann et al. (1997) studied this question.