Alloying mechanisms for epitaxial nanocrystals

Atomic structure and composition distribution in wetting layers and islands of germanium grown on silicon (001) substrates

We present a comprehensive structural investigation of the Ge wetting layer (WL) and island growth on Si(001) substrates by a combination of AFM, high resolution transmission electron microscopy and the energy-differential coherent Bragg rod analysis (COBRA) x-ray method. By considering the influence of the initial Si surface morphology on the deposited Ge, these techniques provide quantitative information on the Ge content and its distribution, in particular within the WL which plays a crucial role in the formation of epitaxial nanostructures. In the WL, the Ge content was found to be above 80% for our growth conditions. Furthermore, from the digital analysis of high-resolution transmission electron microscope images, quantitative information on the strain relaxation is obtained, which complements the COBRA analysis of the Ge distribution and content in these nanostructures.

Ordering mechanisms in epitaxial SiGe nanoislands

We investigate and elucidate the surprising observation of atomically ordered domains in dome-shaped SiGe nanoislands. We show, through atomistic Monte Carlo simulations, that this ordering is a surface-related phenomenon, and that is driven by surface equilibrium rather than by surface kinetics. The ordering depends on facet orientation. The main source of ordering is the {15 3 23} facet, while the {105} and {113} facets contribute less. Subsurface ordered configurations self-organize under this facet and are frozen-in and buried during island growth, giving rise to the ordered domains. Ordering mechanisms based on constrained surface kinetics, requiring step-mediated segregation at the island facets, are shown to be much less likely.

Enhanced quantum confinement due to nonuniform composition in alloy quantum dots

Strain and nanoscale variations in composition can significantly alter the electronic and optical properties of self-assembled alloy quantum systems. Using a combination of finite element and first-principles methods, we have developed an efficient and accurate technique to study the influence of strain and composition on the quantum confinement behavior in alloy quantum dots. Interestingly, we find that a nonuniform distribution of alloy components can lead to an enhanced confinement potential that allows a large quantum dot to behave electronically in a manner similar to a much smaller dot. The approach presented here provides a general means to quantitatively predict the influence of strain and composition variations on the performance characteristics of various small-scale alloy systems.

A fast computational method for determining equilibrium concentration profiles in intermixed nanoislands

An efficient computational method for finding the equilibrium concentration profiles which minimize the free energy of intermixed heteroepitaxial islands of assigned shape and average composition is described. A combination of a Monte Carlo method and continuum elasticity theory solved by a finite element method is shown to provide the desired profiles allowing for a significant computational gain with respect to atomistic approaches. The role played by dimensionality (ridges versus islands) and by entropy is discussed.

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.

Three-dimensional composition profiles of single quantum dots determined by scanning-probe-microscopy-based nanotomography

Scanning probe microscopy combined with selective wet chemical etching is employed to quantitatively determine the full three-dimensional (3D) composition profiles of single strained SiGe/Si(001) islands. The technique allows us to simultaneously obtain 3D profiles for both coherent and dislocated islands and to collect data with large statistics. Lateral and vertical composition gradients are observed, and their origin is discussed. X-ray scattering measurements performed on a large sample area are used to validate the results.

Composition maps in self-assembled alloy quantum dots

Nanoscale variations in composition arising from the competition between chemical mixing effects and elastic relaxation can substantially influence the electronic and optical properties of self-assembled alloy quantum dots. Using a combination of finite element and quadratic programming optimization methods, we have developed an efficient technique to compute the equilibrium composition profiles in strained quantum dots. We find that the composition profiles depend strongly on the morphological features such as the slopes and curvatures of their surfaces and the presence of corners and edges as well as the ratio of the strain and chemical mixing energy densities. More generally, our approach provides a means to quantitatively model the interplay among the composition variations, the temperature, the strain, and the shapes of small-scale lattice-mismatched structures.