Thermodynamic control of germanium quantum dot growth on silicon

Strained epitaxial growth of Ge on Si(0 0 1) produces self-assembled, nanometer scale islands, or quantum dots. We study this growth by atomistic simulation, computing the energy of island structures to determine when and how islanding occurs. The distribution of island sizes on a surface is determined by the relation of island energy to size. Applying the calculated energy per atom to the Boltzmann-Gibbs distribution, we predict size distributions as functions of coverage and temperature. The peak populations around 86,000 atoms (35 nm wide) compare favorably with experiment.