A thermodynamic theory of the self-assembly of quantum dots

We establish a general thermodynamic model to address the self-assembly of quantum dots (QDs) in heterogeneous epitaxial systems by taking into account the size-dependent surface and interface energies and the interactions between QDs. The proposed thermodynamic theory not only elucidates the growth mechanisms of the QD formation at a critical coverage and the physical origins of the narrow size distribution of QDs, but also predicts two important critical sizes in the QD growth: one is the critical size of the QD formation and the other is the critical size of the stable array of QDs. The theoretical results are in good agreement with the experimental observations, which implies that the established thermodynamic theory could be expected to be a general approach to pursue the physical mechanisms of self-assembly of QDs.