Structural and Morphological Transformations in Self-assembled Sn Quantum Dots in Si matrix

The thermodynamics of misfitting precipitates provide reasonable explanations for structural and morphological transformations of Sn (rich) quantum dots in Si matrix that were observed by means of atomic resolution Z-contrast scanning transmission electron microcopy. Morphological transformations (within the diamond structure) from tetrakaidecahedrons to octahedrons with the precipitate size are explained by an increasing contribution of the elastic mismatch energy to the Gibbs free energy. A simple estimate shows that an excess Gibbs free energy of approximately 0.4 eV per atom, corresponding to a hydrostatic pressure of about 19 GPa, can be released by a structural transformation from a quantum dot with diamond structure to a precipitate with beta-Sn structure and a lattice mismatch strain minimizing orientation relationship with the surrounding Si matrix.