137 research outputs found
The influence of steps on the island distribution function in thin solid film formation
No full textThe gamma distribution has been shown to be the simplest function for describing the universal size distribution function of InAs quantum dots on GaAs(001) substrate (Fanfoni et al 2007 Phys. Rev. B 75 245312), although there is no reason to believe that it could not be applied to any film growth where the principal feeding of the islands occurs through surface diffusion as proposed, after numerical simulations in the two-dimensional case, by Mulheran and Blackman (1995 Phil. Mag. Lett. 72 55). As far as InAs/GaAs(001) quantum dots are concerned, by fitting the data of Ebiko et al (1999 Phys. Rev. B 60 8234) and Krzyzewski et al (2002 Phys. Rev. B 66 201302(R)) to the gamma function, beta = 4.5 and 2.9 are the respective returned values. The latter value appears anomalous because for a Poissonian distribution of points (centers of islands), beta = 3.5-3.6. Moreover, the greater the spatial correlation the greater the beta value. We prove that the presence of steps alters the distribution of nucleation centers throughout the substrate in such a way that its variance increases with respect to the substrate without steps and, as a consequence, beta decreases
Kinetics of island density in thin film growth in the framework of statistical mechanics of rigid disks
No full textThe paper centers on the evaluation of the function n(Theta)=N(Theta)/N-0, that is the normalized number of islands as a function of coverage Theta is an element of[0,1], given N-0 initial nucleation centers (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, and 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, and M. Volpe, Phys. Rev. B 62, 11300 (2000)]
Effect of the impingement on the kinetics of island aggregation in the post-nucleation stage of film growth at solid surfaces
No full textThe kinetics of island aggregation in the post-nucleation stage, for a model case system where the impingement mechanism among the islands dominates the film growth, has been measured using scanning electron microscopy (SEM). A theoretical model previously developed is found to be in accordance with the experimental kinetics [M. Fanfoni, M. Tomellini, Appl. Surf. Sci,, 136 (1998) 338.]. (C) 1999 Elsevier Science B.V. All rights reserved
Dirac delta nucleation in the framework of Avrami's model: The case of diamond growth on deformed Si(100)
No full textThe nucleation and growth kinetics of diamond deposited by hot-filament chemical vapour deposition (HFCVD) on Si(100) substrates, previously deformed by uniaxial compression dong the [100] direction, have been investigated Although the nucleation density at saturation (0.04-0.06 mu m(-2)) was similar to those measured on virgin, as-received Si(100) wafers, the kinetics of stable nucleus formation resembled the fast kinetics observed for substrates which were mechanically abraded prior to CVD in order to enhance diamond nucleation. The results definitely indicate that diamond nucleation occurs randomly with a rate that is a Dirac delta function. The time dependence of the substrate fraction which is covered by islands was measured, and a good agreement with Avrami's kinetics for 2D phase transitions was found. The total island perimeter has also been measured as a function of the covered surface, and is well described by the analytical model recently developed [M. Tomellini and M. Fanfoni, Surf Sci. 349 (1996) L191]. The observed fast nucleation has been attributed to stress-induced defects pre-existing at the surface and which provides suitable sites for diamond growth. (C) 1997 Elsevier Science B.V
Avrami's kinetic approach for describing Volmer Weber growth mode at solid surfaces studied via PES and AES
No full textA model is presented for describing the time dependence of the photoelectron and/or Auger signals during the overlayer formation in the case of Volmer Weber growth mode, i.e. 3D island formation. The impingement among clusters has been taken into account in the framework of Avrami's statistical approach. A first system has been considered in which nucleation occurs at a given number of preexisting sites randomly distributed throughout the whole surface. The results obtained by numerical computations indicate that particular conditions can be indeed realized for which the PES signal is chiefly related to the kinetics of the surface fraction that is covered by islands. A more involved system has been also modeled where nucleation does not occur at preexisting sites but through the formation of stable dimers. Under this circumstance, Avrami's treatment of island impingement can be still retained although now a system of integral differential equations has to be solved to get the kinetics. Such a modelling should be suitable for describing the metallic film growth studied by PES
Comparative study of approaches based on the differential critical region and correlation functions in modeling phase-transformation kinetics
No full textThe statistical methods exploiting the “Correlation-Functions” or the “Differential-Critical-Region” are both
suitable for describing phase transformation kinetics ruled by nucleation and growth.We present a critical analysis
of these two approaches, with particular emphasis to transformations ruled by diffusional growth which cannot
be described by the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. In order to bridge the gap between
these two methods, the conditional probability functions entering the “Differential-Critical-Region” approach
are determined in terms of correlation functions. The formulation of these probabilities by means of cluster
expansion is also derived, which improves the accuracy of the computation. The model is applied to 2D and 3D
parabolic growths occurring at constant value of either actual or phantom-included nucleation rates. Computer
simulations have been employed for corroborating the theoretical modeling. The contribution to the kinetics of
phantom overgrowth is estimated and it is found to be of a few percent in the case of constant value of the actual
nucleation rate. It is shown that for a parabolic growth law both approaches do not provide a closed-form solution
of the kinetics. In this respect, the two methods are equivalent and the longstanding overgrowth phenomenon,
which limits the KJMA theory, does not admit an exact analytical solution
Perché il logaritmo della somma non è uguale alla somma dei logaritmi: gli operatori lineari
No full textQuesto articolo vuole offrire uno spunto di riflessione su come alcune regole matematiche possano essere comprese ad un livello concettuale più alto e dunque più generale. Tra le molteplici possibilità abbiamo scelto le funzioni logaritmiche come esempio paradigmatico
Film growth viewed as stochastic dot processes
No full textIn this article some results regarding film growth considered as a stochastic process of dots are reviewed. The central concept of the theory described in the initial part of the article is the evaluation of the exclusion probability, i.e. the probability that no dots are found in a given region of the surface. This is reviewed to a certain extent for both correlated and uncorrelated dots and, moreover, for distinguishable classes of dots. This theoretical framework allows one to tackle the nucleation and growth of films ruled by diffusion of adspecies. In this specific instance the theory has been employed for computing the coverage dependent characteristic times for monomer capture from islands and for island collision, in the case of impingement and/or coalescence mechanisms. The ultimate aim is to model, by means of rate equations, the kinetics of film formation over the whole range of coverage. © 2005 IOP Publishing Ltd
Mean field approach for describing thin film morphology
No full textA mean field approach is employed for determining the kinetics of two main quantities for film morphology, namely the number of islands and the film perimeter. These two quantities have been computed for both coalescence and impingement growth regimes. For each case the growth of two- and three-dimensional islands has been considered. In addition, the effect of the spatial correlation among nuclei has been taken into account on the grounds of the hard core interaction. Analytic formulae have been derived for each case
Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws
No full textThe 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
- …
