Nucleation of colloids and macromolecules: does the nucleation pathway matter?

A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in spatially-extended, low-amplitude density fluctuations. In this paper, it is shown how the formalism can be used to determine the maximum probability of observing \emph{any} proposed nucleation pathway, thus allowing one to address the question as to their relative likelihood, including of the newly proposed pathway compared to classical scenarios. Calculations are presented for the nucleation of high-concentration bubbles in a low-concentration solution of globular proteins and it is found that the relative probabilities (new theory compared to classical result) for reaching a critical nucleus containing $N_c$ molecules scales as $e^{-N_c/3}$ thus indicating that for all but the smallest nuclei, the classical scenario is extremely unlikely.Comment: 7 pages, 5 figure

Quantum box energies as a route to the ground state levels of self-assembled InAs pyramidal dots

A theoretical investigation of the ground state electronic structure of InAs/GaAs quantum confined structures is presented. Energy levels of cuboids and pyramidal shaped dots are calculated using a single-band, constant-confining-potential model that in former applications has proved to reproduce well both the predictions of very sophisticated treatments and several features of many experimental photoluminescence spectra. A connection rule between their ground state energies is found which allows the calculation of the energy levels of pyramidal dots using those of cuboids of suitably chosen dimensions, whose solution requires considerably less computational effort. The purpose of this work is to provide experimentalists with a versatile and simple method to analyze their spectra. As an example, this rule is then applied to successfully reproduce the position of the ground state transition peaks of some experimental photoluminescence spectra of self-assembled pyramidal dots. Furthermore the rule is used to predict the dimensions of a pyramidal dot, starting from the knowledge of the ground state transition energy and an estimate for the aspect ratio Q. © 2000 American Institute of Physics

Classification of Ge hut clusters in the arrays formed by molecular beam epitaxy at low temperatures on the Si(001) surface

Morphological investigations and classification of Ge hut clusters forming the arrays of quantum dots on the Si(001) surface at low temperatures in the process of the ultrahigh vacuum molecular beam epitaxy have been carried out using in situ scanning tunnelling microscopy. Two main species of Ge hut clusters composing the arrays - pyramidal and wedge-shaped ones - have been found to have different atomic structures. The inference is made that shape transitions between pyramids and wedges are impossible. The nucleation probabilities of pyramids and wedges equal 1/2 at the initial stage of the array formation. The wedges become the dominating species as the amount of the deposited germanium is increased. A fraction and a density of the pyramids in the arrays are rapidly decreased with the growth of Ge coverage. The derivative types of the clusters - obelisks (or truncated wedges) and accreted wedges - have been revealed and investigated for the first time, they have been found to start dominating at high Ge coverages. The obelisks originate from the wedges as a result of their height limitation and further growth of trapezoid facets. The apexes of the obelisks are formed by sets of the parallel (001) ridges. The uniformity of the cluster arrays have been evidenced to be controlled by the length of the wedge-like clusters. At low growth temperatures (360C) nucleation of new clusters is observed during the array growth at all values of Ge coverage except for a particular point at which the arrays are more uniform than at higher or lower coverages. At higher (530C) temperatures cluster nucleation has not been observed after the initial stage of the array formation.Comment: 27 pages, 11 figures. A brief review of literature is added. Final version accepted to Physics-Uspekhi. Typos are correcte

Stability of strained heteroepitaxial systems in (1+1) dimensions

We present a simple analytical model for the determination of the stable phases of strained heteroepitaxial systems in (1+1) dimensions. In order for this model to be consistent with a subsequent dynamic treatment, all expressions are adjusted to an atomistic Lennard-Jones system. Good agreement is obtained when the total energy is assumed to consist of two contributions: the surface energy and the elastic energy. As a result, we determine the stable phases as a function of the main ``control parameters'' (binding energies, coverage and lattice mismatch). We find that there exists no set of parameters leading to an array of islands as a stable configuration. We however show that a slight modification of the model can lead to the formation of stable arrays of islands.Comment: 11 pages, 14 figures, submitted to Physical Review

Effect of the lattice misfit on the equilibrium shape of strained islands in Volmer-Weber growth

We have studied the effect of the misfit on the equilibrium shape of three-dimensional pyramidal islands grown on a foreign substrate in the case of incomplete wetting (Volmer-Weber mode of growth). We have found that tensile islands have smaller aspect ratios compared with compressed islands owing to its better adhesion to the substrate. The average strains of consecutive layers decrease faster with thickness in compressed than in tensile islands. The strains decrease rapidly with thickness, with the consequence that above a certain height, the upper layers of the pyramid become practically unstrained and does not contribute to a further reduction in the upper base. As a result, the truncated pyramids are not expected to transform into full pyramids. Our results are in good agreement with experimental observations in different systems.Comment: 6 pages, 7 figures. Accepted version, minor change

Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots

We have studied the monolayer-bilayer transformation in the case of the coherent Stranski-Krastanov growth. We have found that the energy of formation of a second layer nucleus is largest at the center of the first-layer island and smallest on its corners. Thus nucleation is expected to take place at the corners (or the edges) rather than at the center of the islands as in the case of homoepitaxy. The critical nuclei have one atom in addition to a compact shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with i>1 an integer. When the edge of the initial monolayer island is much larger than the critical nucleus size, the latter is always a rectangle plus an additional atom, adsorbed at the longer edge, which gives rise to a new atomic row in order to transform the rectangle into the equilibrium square shape.Comment: 6 pages, 4 figures. Accepted version, minor change

Some electronic and optical properties of self-assembled quantum dots: asymmetries in a lens domain

The self-assembled quantum dot with lens domain has rotational symmetry but it is intrinsically asymmetric when the electron moves perpendicularly to its circular base, {\it i. e.} along the rotational axis. To characterize this asymmetry, an external electric field is applied along the positive or negative direction of the rotational axis. We report the different Stark shifts appearing in the spectra as a function of the field intensity for different lens domains. It is shown that for a flat lens domain the asymmetry effects decrease, but even for very flat lenses they can not be approximated by a cylindrical domain. Finally, some optical properties such as the dielectric constant and electroabsorption are studied. Signatures of the energy spectrum reveal in these quantities. The importance of considering the proper lens domain as long as the magnitude and direction field to tune a specific level transition is stressed

Critical Strain Region Evaluation of Self-Assembled Semiconductor Quantum Dots

A novel peak finding method to map the strain from high resolution transmission electron micrographs, known as the Peak Pairs method, has been applied to In(Ga) As/AlGaAs quantum dot (QD) samples, which present stacking faults emerging from the QD edges. Moreover, strain distribution has been simulated by the finite element method applying the elastic theory on a 3D QD model. The agreement existing between determined and simulated strain values reveals that these techniques are consistent enough to qualitatively characterize the strain distribution of nanostructured materials. The correct application of both methods allows the localization of critical strain zones in semiconductor QDs, predicting the nucleation of defects, and being a very useful tool for the design of semiconductor device

Self-organization on surfaces: foreword

After decades of work, the growth of continuous thin films, i.e., two-dimensional structures, is progressively becoming a technological issue more than a field of fundamental research. Incidentally self-organization of nanostructures on surfaces is now an important field of research, i.e., structures of dimensionality one or zero, with a steep rise of attention in the past five years. Whereas self-organization was initially motivated by potential applications, it has up to now essentially contributed to the advancement of fundamental science in low dimensions, as model systems could be produced that could not have been fabricated by lithography. This Special Issue aims at giving a cross-community timely overview of the field. The Issue gathers a broad panel of articles covering various self-organization mechanisms, specific structural characterization, physical properties, and current trends in extending the versatility of growth. The materials mostly covered here are semiconductors and magnetic materials.Comment: Foreword of the Editor to Special Issue on Self-organization on surface

Homogeneous nucleation near a second phase transition and Ostwald's step rule

Homogeneous nucleation of the new phase of one transition near a second phase transition is considered. The system has two phase transitions, we study the nucleation of the new phase of one of these transitions under conditions such that we are near or at the second phase transition. The second transition is an Ising-like transition and lies within the coexistence region of the first transition. It effects the formation of the new phase in two ways. The first is by reducing the nucleation barrier to direct nucleation. The second is by the system undergoing the second transition and transforming to a state in which the barrier to nucleation is greatly reduced. The second way occurs when the barrier to undergoing the second phase transition is less than that of the first phase transition, and is in accordance with Ostwald's rule.Comment: 11 pages, 5 figure