Kinetics of monolayer growth

The kinetics of a monolayer growth is studied using the two-dimensional lattice gas model by means of the path-probability method (PPM) for nonequilibrium phenomena. Kinetic equations for the combined processes of relaxation (adsorption and desorption) and diffusion are derived analytically and solved for the first time in the square approximation of the PPM. Comparison of the square approximation with the point and pair approximations along with Monte Carlo simulation shows the effect of using a larger basic cluster than in the previous studies. When the square approximation is used, the growth rate results are much improved in both cases with and without diffusion and agree well with the Monte Carlo simulations results, except for very small values of the driving forceL=/k _b T where is the chemical potential difference between the vapor and the solid phase. In the range where the agreement is good, there exists a region where the growth rateR is proportional to exp(–c/L with a constantc. This is the feature which is characteristic of two-dimensional nucleation-limited growth.     

Surfactant-mediated growth revisited

The x-ray structure analysis of the oxygen-surfactant-mediated growth of Ni on Cu(001) identifies up to 0.15 monolayers of oxygen in subsurface octahedral sites. This questions the validity of the general view that surfactant oxygen floats on top of the growing Ni film. Rather, the surfactant action is ascribed to an oxygen-enriched zone extending over the two topmost layers. Surface stress measurements support this finding. Our results have important implications for the microscopic understanding of surfactant-mediated growth and the change of the magnetic anisotropy of the Ni films.     

Sb-mediated growth of high-density InAs quantum dots and GaAsSb embedding growth by MBE

Self-assembled InAs quantum dots (QDs) with high-density were grown on GaAs(0 0 1) substrates by antimony (Sb)-mediated molecular beam epitaxy technique using GaAsSb/GaAs buffer layer and InAsSb wetting layer (WL). In this Sb-mediated growth, many two-dimensional (2D) small islands were formed on those WL surfaces. These 2D islands provide high step density and suppress surface migration. As the results, high-density InAs QDs were achieved, and photoluminescence (PL) intensity increased. Furthermore, by introducing GaAsSb capping layer (CL), higher PL intensity at room temperature was obtained as compared with that InGaAs CL.     

Layer-by-layer growth of metal overlayers

We have used plots of the Auger amplitudes versus deposition time to investigate the growth mode of 3d-transition metals on noble metal (100) surfaces. The systems considered are Fe/Cu(100), Fe/Au(100), Co/Cu(100), and Cr/Ag(100). We find that: 1. The Auger plots consist of a succession of straight lines of constant length with sharp breaks in between, i.e. the growth mode is essentially layer-by-layer. 2. From the experimental data points a slight rounding off in the vicinity of the break points cannot be excluded, although a numerical analysis shows that the deviation from perfect layer-by-layer growth is less than 10% of a monolayer for all systems considered.     

Multi-cut solutions of Laplacian growth

A new class of solutions to Laplacian growth (LG) with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls in viscous fingering experiments in Hele-Shaw cells. Integrals of motion for the multi-cut LG solutions in terms of singularities of the Schwarz function are found, and the dynamics of densities (jumps) on the cuts are derived. The subclass of these solutions with linear Cauchy densities on the cuts of the Schwarz function is of particular interest, because in this case the integral equation for the conformal map becomes linear. These solutions can also be of physical importance by representing oil/air interfaces, which form oil fjords with a constant opening angle, in accordance with recent experiments in a Hele-shaw cell.     

Quasi-steady-state modeling of dendritic growth

A new method of the moving-boundary problem analysis is developed. After proposed coordinate transformation, the quasi-steady-state differential equation was reduced to equivalent Laplace equation. Transformed boundary conditions of a rescaled field distribution reflect the presence of rate-dependent sources on interface. Taking into account the local rate-dependence of the Neumann's boundary conditions, non-equilibrium pattern formation was considered. The problem of dendrite fractal growth was reduced to one of interaction of conformal to tips charged particles. Conditions of the quasi-steady growth and the recurrence formula for k-order dendrite spacing were derived. Theoretically obtained scaling laws for interface shape, dendrite spacing, critical sidebranch distance are confirmed by available experimental data.     

Shear-flow suppression of hotspot growth

We consider the role of fluid shear in maintaining anomalous “hotspot” solutions reported for a chaotically stirred bistable chemical reaction model [S.M. Cox, Persistent localized states for a chaotically mixed bistable reaction, Phys. Rev. E 74 (2006) 056206]. In the well-mixed regime, the chemical concentration is governed by a single autonomous ordinary differential equation with two stable equilibria. Whether the reaction goes to extinction or to an excited state depends on whether the initial concentration lies below or above some unstable threshold. By contrast, when the concentration varies spatially, and the chemical is stirred, the interplay between advection, diffusion and reaction is much more complicated, and the fate of the reaction depends sensitively on the initial conditions. It has previously been shown that, if the stirring is temporally periodic, a localised hotspot may form, and so the system never becomes fully extinct, nor fully excited. In this work, we first demonstrate that hotspots are in some sense generic, in that they are easily found by trial and error, by choosing reaction parameter values between those giving rise to global extinct and excited states. We also show that hotspots may be associated with hyperbolic, elliptic or even parabolic orbits associated with the underlying stirring. We observe that fluid shear is an important mechanism in localising a hotspot, and derive a reduced ordinary differential equation model which can predict the fate of a chemical stripe in a shear flow accurately.     

Macroscopic dynamics of cancer growth

Macroscopic modeling is used to describe various aspects of cancer growth. A recently proposed “dysnamical exponent” hypothesis is critically examined in the context of the angiogenic development. It is also shown that the emergence of necroses facilitates the growth of avascular tumors; the model yields an excellent fit to available experimental data, allowing for the determination of growth parameters. Finally, the global effects of an applied antitumoral immunotherapy are investigated. It is shown that, in the long run, the application of a therapeutical course leads to bigger tumors by weakening the intraspecific competition between surviving viable cancer cells. The strength of this model lies in its simplicity and in the amount of information that can be gleaned using only very general ideas.     

Epitaxial growth of organic heterostructures: Morphology, structure, and growth mode

For organic molecular materials the definition of the condition of epitaxial growth has been subjected to several misconceptions and a great debate, leading in any case to less restrictive requirements than for inorganic materials. Here, the deposition of oligothiophene films by molecular beam epitaxy on properly grown organic single crystals is discussed and all-organic rigorous epitaxy demonstrated for both sub-monolayer and several-monolayer thick films. The possibility of growing all-organic nanostructures directly follows from these results.