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

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

Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional islands on top of the wetting layer in Stranski-Krastanov mode of growth is considered in a model in 1+1 dimensions accounting for the anharmonicity and non-convexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than in expanded overlayers beyond a critical lattice misfit. In the latter case the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is the incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. The latter explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after exceeding the corresponding critical sizes. The rearrangements are initiated by nucleation events each next one requiring to overcome a lower energetic barrier. The model is in good qualitative agreement with available experimental observations.Comment: 12 pages text, 15 figures, Accepted in Phys.Rev.B, Vol.61, No2

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

Communication: Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules.

We study the nucleation of model two-dimensional crystals formed from anisotropically interacting molecules using kinetic Monte Carlo simulations and the forward flux sampling algorithm. The growth probability P(n) of a cluster of n molecules is measured while the supersaturation s and interaction anisotropy of the molecules are varied, in order to gain insight into the nucleation mechanism. It is found that with increasing degree of interaction anisotropy the nucleus size (defined as the cluster size at which P(n) = 0.5) can increase with increasing s, with sharp jumps at certain s values. Analysis of the cluster shape reveals that nucleation in the system studied is of a non-standard form, in that it embodies elements of both the classical nucleation theory and the density functional theory frameworks

Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy

We study the energetics of island formation in Stranski-Krastanow growth within a parameter-free approach. It is shown that an optimum island size exists for a given coverage and island density if changes in the wetting layer morphology after the 3D transition are properly taken into account. Our approach reproduces well the experimental island size dependence on coverage, and indicates that the critical layer thickness depends on growth conditions. The present study provides a new explanation for the (frequently found) rather narrow size distribution of self-assembled coherent islands.Comment: 4 pages, 5 figures, In print, Phys. Rev. Lett. Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Quantum-coupled single-electron thermal to electric conversion scheme

Thermal to electric energy conversion with thermophotovoltaics relies on radiation emitted by a hot body, which limits the power per unit area to that of a blackbody. Microgap thermophotovoltaics take advantage of evanescent waves to obtain higher throughput, with the power per unit area limited by the internal blackbody, which is n2 higher. We propose that even higher power per unit area can be achieved by taking advantage of thermal fluctuations in the near-surface electric fields. For this, we require a converter that couples to dipoles on the hot side, transferring excitation to promote carriers on the cold side which can be used to drive an electrical load. We analyze the simplest implementation of the scheme, in which excitation transfer occurs between matched quantum dots. Next, we examine thermal to electric conversion with a lossy dielectric (aluminum oxide) hot-side surface layer. We show that the throughput power per unit active area can exceed the n2 blackbody limit with this kind of converter. With the use of small quantum dots, the scheme becomes very efficient theoretically, but will require advances in technology to fabricate