Growth energetics of germanium quantum dots by atomistic simulation.

Abstract

Strained epitaxial growth of Ge on Si(001) 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. We also describe experimental methods of island growth and characterization in order to understand the relevant physical processes and to interpret experimental observations for comparison with simulation. We show that pyramidal Ge islands with rebonded step {105} facets are energetically favorable compared to growth of planar Ge (2 x 8) on Si(001). We determine how the chemical potential of these islands varies with size, lateral spacing, and wetting layer thickness. We also illustrate the atomic-level structure of these islands with favorable formation energy. Intermixing can occur between the growing Ge film and the Si substrate. We show that although Ge prefers to wet the surface, entropy drives some fraction into the underlying layers. We present a simple model of intermixing by equilibration of the top crystal layers. The equilibration is performed with a flexible lattice Monte Carlo simulation. Ultimately, intermixing produces a temperature-dependent graded Ge concentration. The resulting chemical potential leads to the onset of islanding after 3--4 monolayers of deposition, consistent with experimental observations. The distribution of island sizes on a surface is determined by the relation of island energy to size. We find that there exists a minimum-energy island size due to the interaction of surface energy and bulk relaxation. Applying the calculated chemical potential to the Boltzmann-Gibbs distribution, we predict size distributions as functions of coverage and temperature. The distributions, with peak populations around 86 000 atoms, compare favorably with experiment. This work explores the driving force in growth of Ge on Si(001). The knowledge derived here explains why islanding occurs and provides guidance for the control of island self-assembly to construct useful microelectronic devices from quantum dots.