Weibull function to describe the cumulative size distribution of clumps formed by two-dimensional grains randomly arranged on a plane.

Many manifestations of natural processes give rise to interesting morphologies; it is all too easy to cite the corrugation of the Earth's surface or of planets in general. However, limiting ourselves to 2D cases, the morphology to which crystal growth gives rise is also intriguing. In particular, it is interesting to study some characteristics of the cluster projection in 2D, namely the study of the shapes of the speckles (fractal dimension of their rims) or the distribution of their areas. Recently, for instance, it has been shown that the size cumulative distribution function (cdf) of "voids" in a corrole film on Au(111) is well described by the well known Weibull distribution. The present article focuses on the cdf of cluster areas generated by numerical simulations: the clumps (clusters) are generated by overlapping grains (disks) whose germs (disk centers) are chosen randomly in a 2000×2000 square lattice. The obtained cdf of their areas is excellently fitted to the Weibull function in a given range of surface coverage. The same type of analysis is also performed for a fixed-time clump distribution in the case of Kolmogorov-Johnson-Mehl-Avrami (KJMA) kinetics. Again, a very good agreement with the Weibull function is obtained.

Electronic structure of the Ge/Si(1 0 5) hetero-interface: an ARPES and DFT study.

We present a joint experimental and theoretical study of the electronic properties of the rebonded-step reconstructed Ge/Si(1 0 5) surface which is the main strained face found on Ge/Si(0 0 1) quantum dots and is considered a prototypical model system for surface strain relaxation in heteroepitaxial growth. Using a vicinal surface as a model system for obtaining a stable single-domain film structure with large terraces and rebonded-step surface termination, we realized an extended and ordered Ge/Si planar hetero-junction suitable for direct study with angle-resolved photoemission spectroscopy. At the coverage of four Ge monolayers photoemission spectroscopy reveals the presence of 2D surface and film bands displaying energy-momentum dispersion compatible with the 5 × 4 periodicity of the system. The good agreement between experiment and first-principles electronic structure calculations confirms the validity of the rebonded-step structural model. The direct observation of surface features within 1 eV below the valence band maximum corroborates previously reported analysis of the electronic and optical behavior of the Ge/Si hetero-interface.

A novel eye drop application monitor to assess patient compliance with a prescribed regimen: a pilot study.

PURPOSE: To assess the ability of a novel imaging device to allow physicians to personalize therapeutic regimens based on objective patient drop administration data. METHODS: A novel imaging system was used to record video of the drop technique of subjects in clinic (n=25) or at home (n=17) for 1 week. Video assessment by a reading center was compared with patient reporting and their prescribed regimen with respect to how many drops were applied and how many landed in the eye. RESULTS: Reading center assessment of both drops dispensed and drops landing in the eye was significantly different from the prescribed regimen in the clinic (Pd=0.005, Pi<0.001, respectively) and at-home arms (Pd=0.003, Pi<0.001, respectively). CONCLUSIONS: This imaging system is a powerful tool to help physicians tailor patient therapy more accurately, to help researchers evaluate new drop therapies with objective rather than subjective data, and to potentially facilitate better patient training for improved drug delivery.

Irreversible order-disorder transformation of Ge(0 0 1) probed by scanning tunnelling microscopy.

We investigate the surface structure of Ge(0 0 1) during the (2 × 1)-(1 × 1) phase transition occurring at T > 1130 K by high-resolution scanning tunnelling microscopy. We find a drastic size reduction of dimerized domains in line with substantial dimer breakup accompanied by surface roughening. Completing the picture provided by previous spectroscopic observations, probing with high spatial resolution reveals the nucleation of several nanodomains with distinct vicinal orientations and reconstructions. The structural transformation is irreversible and is not observed for other singular faces of Ge.

Heteroepitaxy of Ge on singular and vicinal Si surfaces: elastic field symmetry and nanostructure growth.

Starting with the basic definition, a short description of a few relevant physical quantities playing a role in the growth process of heteroepitaxial strained systems, is provided. As such, the paper is not meant to be a comprehensive survey but to present a connection between the Stranski-Krastanov mechanism of nanostructure formation and the basic principles of nucleation and growth. The elastic field is described in the context of continuum elasticity theory, using either analytical models or numerical simulations. The results are compared with selected experimental results obtained on GeSi nanostructures. In particular, by tuning the value of quantities such as vicinality, substrate orientation and symmetry of the diffusion field, we elucidate how anisotropic elastic interactions determine shape, size, lateral distribution and composition of quantum dots.

The entangled role of strain and diffusion in driving the spontaneous formation of atolls and holes in Ge/Si(111) heteroepitaxy.

We investigate the interdependent processes of strain and diffusion in the formation of holes and atolls obtained by rapid annealing of Ge/Si(111) islands at T ≈ 970 °C. We show that the shape evolution from islands to atolls and holes is closely captured by an analytical model including strain-driven diffusion. In the model, strain profiles obtained by finite element solutions of continuum elasticity equations are introduced in the diffusion equation as the source of a diffusion flux driven by the strain gradient. When the shape of the elastic field in Ge/Si(111) islands is coupled to diffusion, the morphology of the SiGe nanostructures observed after annealing is reproduced.

Size-dependent reversal of the elastic interaction energy between misfit nanostructures.

By exploiting a fully three-dimensional finite-element modeling of strain fields, we investigate the spatial dependence of the elastic interaction energy between misfitting nanostructures beyond the point-dipole approximation. When interacting islands are finite in size, the detailed shape of the elastic strain field around and under the islands may convert the repulsive interactions, usually experienced between equal-sized islands, into an attractive basin between a large island and a population of neighboring clusters smaller than a critical size. The results of the simulations applied to large Ge islands grown on a Si(111) substrate have significant implications for the understanding of the strain-mediated coarsening of quantum dots around the islands.

Breaking elastic field symmetry with substrate vicinality.

We present a novel approach to engineer the growth of strained epitaxial films based on tailoring the elastic-interaction potential between nanostructures with substrate vicinality. By modeling the island-island interaction energy surface within continuum elasticity theory, we find that its fourfold symmetry is broken at high miscuts, producing directions of reduced elastic-interaction energy. As a consequence, it is possible to direct the Ge island growth on highly misoriented Si(001) substrates towards desired pathways.

Ge growth on vicinal si(001) surfaces: island's shape and pair interaction versus miscut angle.

A complete description of Ge growth on vicinal Si(001) surfaces is provided. The distinctive mechanisms of the epitaxial growth process on vicinal surfaces are clarified from the very early stages of Ge deposition to the nucleation of 3D islands. By interpolating high-resolution scanning tunneling microscopy measurements with continuum elasticity modeling, we assess the dependence of island's shape and elastic interaction on the substrate misorientation. Our results confirm that vicinal surfaces offer an additional degree of control over the shape and symmetry of self-assembled nanostructures.

Shaping Ge islands on Si(001) surfaces with misorientation angle.

A complete description of Ge growth on vicinal Si(001) surfaces in the angular miscut range 0 degrees -8 degrees is presented. The key role of substrate vicinality is clarified from the very early stages of Ge deposition up to the nucleation of 3D islands. By a systematic scanning tunneling microscopy investigation we are able to explain the competition between step-flow growth and 2D nucleation and the progressive elongation of the 3D islands along the miscut direction [110]. Using finite element calculations, we find a strict correlation between the morphological evolution and the energetic factors which govern the {105} faceting at atomic scale.