Frequency dependence of the radiative decay rate of excitons in self-assembled quantum dots: Experiment and theory

We analyze time-resolved spontaneous emission from excitons confined in self-assembled InAs quantum dots placed at various distances to a semiconductor-air interface. The modification of the local density of optical states due to the proximity of the interface enables unambiguous determination of the radiative and nonradiative decay rates of the excitons. From measurements at various emission energies, we obtain the frequency dependence of the radiative decay rate, which is only revealed due to the separation of the radiative and nonradiative parts. It contains detailed information about the dependence of the exciton wave function on quantum dot size. We derive the quantum optics theory of a solid-state emitter in an inhomogeneous environment and compare this theory to our experimental results. Using this model, we extract the frequency dependence of the overlap between the electron and hole wave functions. We furthermore discuss three models of quantum dot strain and compare the measured wave-function overlap to these models. The observed frequency dependence of the wave-function overlap can be understood qualitatively in terms of the different compressibility of electrons and holes originating from their different effective masses and binding energies.