Beyond the Kolmogorov Johnson Mehl Avrami kinetics: inclusion of the spatial correlation

The Kolmogorov-Johnson-Mehl-Avrami model, which is a nucleation and growth poissonian process in space, has been implemented by taking into account spatial correlation among nuclei. This is achieved through a detailed study of a system of distinguishable and correlated dots (nuclei). The probability that no dots be in a region of the space has been evaluated in terms of correlation functions. The theory has been applied to describe nucleation and growth in two dimensions under constant nucleation rate, where correlation among nuclei depends upon the size of the nucleus. We propose a simple formula for describing the phase transition kinetics in the presence of correlation among nuclei. The theory is applied to the constant nucleation rate process when correlation depends upon the nucleus-birth time. It is shown that the random sequential adsorption and Tobin process can be analyzed in the framework of the simultaneous nucleation case, admitting a common rationale that is apart from an appropriate re-scaling they represent the same process from the mathematical point of view.Comment: 28 pages, no figure

Eliminating overgrowth effects in Poisson spatial process through the correlation among actual nuclei

It has been shown that the KJMA (Kolmogorov-Johnson-Mehl-Avrami) solution of phase transition kinetics can be set as a problem of correlated nucleation [Phys.Rev.B65, 172301 (2002)]. In this paper the equivalence between the standard solution and the approach that makes use of the actual nucleation rate, i.e. that takes into account spatial correlation among nuclei and/or grains, is shown by a direct calculation in case of linear growth and constant nucleation rate. As a consequence, the intrinsic limit of KJMA theory due to the phenomenon of phantom overgrowth is, at last, overcome. This means that thanks to this new approach it is possible, for instance, to describe phase transition governed by diffusion.Comment: 9 pages, 3 figure

Ripple-to-dome transition: the growth evolution of Ge on vicinal Si(1 1 10) surface

We present a detailed scanning tunnelling microscopy study which describes the morphological transition from ripple to dome islands during the growth of Ge on the vicinal Si(1 1 10) surface . Our experimental results show that the shape evolution of Ge islands on this surface is markedly different from that on the flat Si(001) substrate and is accomplished by agglomeration and coalescence of several ripples. By combining first principle calculations with continuum elasticity theory, we provide an accurate explanation of our experimental observations

Hug-like island growth of Ge on strained vicinal Si(111) surfaces

We examine the structure and the evolution of Ge islands epitaxially grown on vicinal Si(111) surfaces by scanning tunneling microscopy. Contrary to what is observed on the singular surface, three-dimensional Ge nanoislands form directly through the elastic relaxation of step-edge protrusions during the unstable step-flow growth. As the substrate misorientation is increased, the islands undergo a shape transformation which is driven by surface energy minimization and controlled by the miscut angle. Using finite element simulations, we show that the dynamics of islanding observed in the experiment results from the anisotropy of the strain relaxation.Comment: 4 figure

How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: the case of InAs/GaAs(001)

The two- to three-dimensional growth transition in the InAs/GaAs(001) heterostructure has been investigated by atomic force microscopy. The kinetics of the density of three dimensional quantum dots evidences two transition thresholds at 1.45 and 1.59 ML of InAs coverage, corresponding to two separate families, small and large. Based on the scaling analysis, such families are characterized by different mechanisms of aggregation, involving the change of the critical nucleus size. Remarkably, the small ones give rise to a wealth of "monomers" through the erosion of the step edges, favoring the explosive nucleation of the large ones.Comment: 10 pages, 3 figures. Submitted to Phys. Rev. Let

Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws

The theory of Kolmogorov-Johnson-Mehl-Avrami (KJMA) for phase transition kinetics is subjected to severe limitations concerning the functional form of the growth law. This paper is devoted to side step this drawback through the use of correlation function approach. Moreover, we put forward an easy-to-handle formula, written in terms of the experimentally accessible actual extended volume fraction, which is found to match several types of growths. Computer simulations have been done for corroborating the theoretical approach.Comment: 18 pages ;11 figure

Kinetic theory of cluster impingement in the framework of statistical mechanics of rigid disks

The paper centres on the evaluation of the function n(theta)=N(theta)/N0, that is the normalized number of islands as a function of coverage 0<theta<1, given N0 initial nucleation centres (dots) having any degree of spatial correlation. A mean field approach has been employed: the islands have the same size at any coverage. In particular, as far as the random distribution of dots is concerned, the problem has been solved by considering the contribution of binary collisions between islands only. With regard to correlated dots, we generalize a method previously applied to the random case only. In passing, we have made use of the exclusion probability reported in [S. Torquato, B. Lu, J. Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics of surface coverage in the case of correlated dots, improving our previous calculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].Comment: 10 pages, 3 figure

Islanding, growth mode and ordering in Si heteroepitaxy on Ge(001) substrates structured by thermal annealing

Si/Ge heteroepitaxial dots under tensile strain are grown on nanostructured Ge substrates produced by high-temperature flash heating exploiting the spontaneous faceting of the Ge(001) surface close to the onset of surface melting. A very diverse growth mode is obtained depending on the specific atomic structure and step density of nearby surface domains with different vicinal crystallographic orientations. On highly-miscut areas of the Ge(001) substrate, the critical thickness for islanding is lowered to about 5 ML, in contrast to the 11 ML reported for the flat Ge(001) surface, while on unreconstructed (1x1) domains the growth is Volmer-Weber driven. An explanation is proposed considering the diverse relative contributions of step and surface energies on misoriented substrates. In addition, we show that the bottom-up pattern of the substrate naturally formed by thermal annealing determines a spatial correlation for the dot sites