Formation and evolution of multimodal size distributions of InAs/GaAs quantum dots

Self-organized formation and evolution of quantum dot (QD) ensembles with a multimodal size distribution is reported. Such ensembles form after fast deposition near the critical thickness during a growth interruption (GRI) prior to cap layer growth and consist of pure InAs truncated pyramids with heights varying in steps of complete InAs monolayers, thereby creating well-distinguishable sub-ensembles. Ripening during GRI manifests itself by an increase of sub-ensembles of larger QDs at the expense of sub-ensembles of smaller ones, leaving the wetting layer unchanged. The dynamics of the multimodal QD size distribution is theoretically described using a kinetic approach. Starting from a broad distribution of flat QDs, a predominantly vertical growth is found due to strain-induced barriers for nucleation of a next atomic layer on different facets. QDs having initially a shorter base length attain a smaller height, accounting for the experimentally observed sub-ensemble structure. The evolution of the distribution is described by a master equation, which accounts for growth or dissolution of the QDs by mass exchange between the QDs and the adatom sea. The numerical solution is in good agreement with the measured dynamics.