Statistical Properties of Exciton Fine Structure Splittings and Polarization Angles in Quantum Dot Ensembles

We propose an effective model to describe the statistical properties of exciton fine structure splitting (FSS) and polarization angle of quantum dot ensembles (QDEs). We derive the distributions of FSS and polarization angle for QDEs and show that their statistical features can be fully characterized using at most three independent measurable parameters. The effective model is confirmed using atomistic pseudopotential calculations as well as experimental measurements for several rather different QDEs. The model naturally addresses three fundamental questions that are frequently encountered in theories and experiments: (I) Why the probability of finding QDs with vanishing FSS is generally very small? (II) Why FSS and polarization angle differ dramatically from QD to QD? and (III) Is there any direct connection between FSS, optical polarization and the morphology of QDs? The answers to these fundamental questions yield a completely new physical picture for understanding optical properties of QDEs.