Quantum dots (QDs) have been receiving considerable attention lately due to the unique properties, which arise due to the confinement of the electron and holes in a lower band gap material. The InAs on GaAs material system is one of the most studied combinations in which quantum dots form during epitaxy. These QDs form in a Stranski Krastanov manner via a self-assembly process in which the dots nucleate at a critical adatom coverage on a wetting layer of InAs. QDs may be vertically aligned by using the residual strain above a buried dot layer to enhance the nucleation of the second layer of dots. In this work, we show the formation of QDs, which are composed of multiple materials, can be formed through a marriage of these two concepts. In particular, we have fabricated a composite dot formed of an initial core of one material which result from normal self-assembly followed by the epitaxy of a crown composed of a similarly strained material. Finally the entire dot structure can be capped with a barrier material closely lattice matched with the substrate. In this particular demonstration, we formed InAs dots on GaAs and crowned the QDs with GaSb and encapsulated the entire structure with GaAs.