Evolution of thermodynamic potentials in closed and open nanocrystalline systems: Ge-Si:Si(001) islands

An open (closed) system, in which matter is (not) exchanged through surface diffusion, was realized via growth kinetics. Epitaxially grown Si-Ge:Si (001) islands were annealed in different environments affecting the diffusivity of Si adatoms selectively. The evolution of the driving forces for intermixing while approaching the equilibrium was inferred from Synchrotron x-ray measurements of composition and strain. For the open system, intermixing due to the Si inflow from the wetting layer (reservoir) caused a decrease in the Ge content, leading to a lowering of the elastic energy and an increase in the mixing entropy. In contrast, for the closed system, while keeping the average Ge composition constant, atom rearrangement within the islands led to an increase in both elastic and entropic contributions. The Gibbs free energy decreased in both cases, despite the different evolution paths for the composition profiles.