Thermodynamic model of metal-induced self-assembly of Ge quantum dots on Si substrates

We have investigated the nucleation thermodynamics and kinetics of the Ge quantum dot (QD) self-assembly on the Au-patterned Si substrates based on the surface chemical potential theory. It is find that the minimum chemical potential on the substrate surface is located at the center site of the square lattice constructed by Au islands, which indicates that the nucleation of QD is thermodynamically favorable at the center site. The nucleation probability of QD at the center site is kinetically calculated by the mechanochemical potential-based approach. The influence of the surface orientation of Si substrates on the QD shape is addressed by the surface chemical potential theory.