Limited Aggregation Model Research Articles

Electrodeposited Thin Film ZnTe Semiconductors for Photovoltaic Applications

The electrodeposition of zinc telluride thin films on tin conductive oxide substrates in aqueous solution containing TeO2 and ZnCl2 was studied. The electrodeposition mechanism was investigated by cyclic-photovoltammetry. The appropriate potential region where formation of stoichiometric ZnTe semiconductor occurs, was found to be close to -0.75 V vs. SCE. Annealing of the as-deposited films was carried out at 400°C to obtain a crystalline phase. The crystallographic structure and film morphology were studied by XRD and SEM analyses, respectively. ZnTe films have the hexagonal structure of wurtzite and they are characterized by good homogeneity. A direct energy gap of 2.25 eV was determined by NIR-VIS-UV spectroscopy, in close agreement with the energy gap of ZnTe single crystals. A fractal dimension of 2.4 was determined by AFM analysis of ZnTe films. The mechanism of the thin film growth has been interpreted in terms of diffusion limited aggregation model.

Modelling of the Structural and Dynamical Properties of Porous Silicon

ABSTRACTThe changes in the radial distribution function (RDF) and vibrational density of states (DOS) of porous silicon (p-Si) with change of porosity are studied within a modified diffusion limited aggregation model and molecular dynamics simulations. By decomposing the first peak of the radial distribution function of p-Si on to partial RDFs, for atoms having different coordinations, and partial RDFs, for bonds connecting atoms with different coordinations, we show that appearance of the structure in the first peak of the RDF in p-Si is stipulated by bonds between undercoordinated surface atoms. The vibrational DOS projected on surface atoms are also shown to be different from that corresponding to crystalline phonons. It is characterised by the relative increase of the intensity of vibrations in the acoustic region and by appearance of surface-like vibrations split from the optical band.

Multiparticle aggregation model for dendritic growth applied to experiments on amorphous Co-P alloys.

We introduce a multiparticle biased diffusion limited aggregation model for dendritic growth. Its most relevant feature is that it includes the overall effect of strong applied electric fields and therefore applies to nonequilibrium situations. We compare simulations of a two species version of our model to actual experiments on preparation of amorphous Co-P alloys with very good agreement: The model accurately reproduces the dependence of composition, morphology, and growth time of the alloy on the current. We conclude with a discussion of specific predictions and possible generalizations of the model.

SANS study of the aging of xTiO2-SiO2 gels

Silica-titania gels, prepared in acidic conditions, with contents of TiO2 up to 6 mol%, have been studied by small angle neutron scattering (SANS) as wet gel with increasing aging times. In all samples, small primary particles have been found with a diameter of about 3 nm. At the gel point, cylindrical clusters, ca. 10 nm long, were observed as well. These grow with aging time, becoming branched. The cluster-cluster diffusion limited aggregation model is found to be consistent with the SANS results. The growth process is independent of the TiO2 content. It is mainly influenced by the ratio of the aging time to the gelation time.

The microgel formation by crosslinking reaction of primary polymer

Abstract The crosslinking reaction of primary polymers under the influence of potentials was studied by computer simulation. Under the predominant action of repulsive potential, macrogelation did not appear and the products remained as a sol (microgel). With increasing repulsive potential, the particle size descended and the final size distribution became narrow (Pw/Pn = 1·06; Pw, weight average degree of polymerization; Pn, number average degree of polymerization). By the simulation according to a diffusion limited aggregation model with distant repulsive potential and short distant weak attractive potential, round and dense particles were obtained. In the crosslinking reaction of partially quaternized poly (4-vinylpyridine) (q-P4VP), the size of the particles declined and the size distribution became narrow with the quaternization degree of q-P4VP. This result agrees with that of the simulation.

FRACTAL DIMENSION ANALYSIS OF YBaCuO THIN FILM CLUSTERS

In a recent paper, we reported the observation of the growth of YBaCuO thin film clusters on SiTi 3 O substrate. These clusters were formed in the sputter-deposited YBaCuO thin film with strong composition variation. Here we will give an auto-correlation function analysis of the fractal dimension of these clusters at different growth stages. The results will be compared with diffusion limited aggregation model, and implications of the cluster growth of the YBaCuO thin film will be discussed.

Electrode-electrolyte interface impedance: experiments and model.

The impedance of the junction between a solid or aqueous electrolyte and a metal electrode at which no charge transfer processes occur (blocking contacts) follows closely the constant phase angle form, Z = A(j omega)-n, over a wide frequency range, where A is a constant, and the frequency exponent n is typically in the range of 0.7 to 0.95. Several models have been proposed in which the magnitude of the frequency exponent n is related by a simple expression to the fractal dimension d of the rough electrode surface. But experiments with aqueous H2SO4 and roughened platinum and silicon electrodes show that there is no simple relationship, if any at all, between n and d when d is determined from the analysis of one dimensional surface profiles. Moreover, n is not a simple function of the average roughness of the electrode. In order to gain some insight into the effect of electrode topography and the interface impedance, a model for the response of the interface to a constant voltage pulse was constructed. This model is based on the idea that, following a pulse, locally concentrated regions of ions accumulate rapidly at the tips of large protrusions on the electrode surface which screens deeper regions of the electrode from the field driven flux of mobile ions. After this rapid charging, ions are able to reach the deeper, screened regions of the electrode by diffusion, and it is this diffusive process that gives rise to the observed t1-n dependence of the charge collected. Computer simulations, similar to the diffusion limited aggregation model, using measured profiles as fixed (non-growing) clusters, gave exponents n in good agreement with experiment.

A Study of the Structural Properties of Porous Silicon

AbstractWe have implemented a modified diffusion limited aggregation model to simulate the porous silicon structure obtained by electro-chemical dissolution. The fractal structures thus obtained have been used as starting configurations from which a fully equilibrated structure was determined by the method of molecular dynamics.

Fractal analysis of a discotic texture

Abstract The dendritic-type texture displayed by low molar mass discotic charge transfer systems possessing a columnar hexagonal ordered phase has been subjected to a fractal analysis. The diffusion limited aggregation approach was used to simulate the growth of the texture. The results are that the texture displays a fractal geometry and that the prominent features of the discotic texture are correctly reflected by the simulated clusters, including the fractal dimension. The conclusion is that the texture is conditioned by the lattice structure of the discotic phase and the kinetic processes, the sticking rules in the terms of diffusion limited aggregation model, responsible for the growth of the texture.

A theoretical model of the formation morphologies of porous silicon

In this paper a qualitative theoretical model describing the mechanism and formation morphology of porous silicon is presented. The model is based on the diffusion limited aggregation models of Witten and Sanders. The validity of this model is verified by performing small scale computer simulations to construct various porous silicon structures. These structures are compared with the known properties of bulk silicon and morphologies of porous silicon. The postulates of the model are sufficiently rich to explain the relationship between pore density, pore diameter, porosity as well as crystallographic etch selectivity and electropolishing.

A new approach to generalized diffusion limited aggregation models. The coherent anomaly method

We analyzed the generalized diffusion limited aggregation model, the η-model, applying the coherent anomaly method. Fractal dimensions of the growth patterns are estimated from a set of mean densities, { n( L)}, which are defined in a modified η-model with a screened potential (Δ− 1 L 2 )φ=0 .

Surface topography and electrical response of metal-electrolyte interfaces

The small-signal impedance of chemical cells with “blocking” electrodes is dominated at low frequencies ( f < 100 Hz ) by the impedance of the metal-electrolyte interfaces, which is accurately represented by Z rmi = A (j ω ) − n . The frequency exponent n , n <1, is sensitive to the texture of the interface, and several recent theories have been proposed that relate n to the fractal dimension d of the rough interface. However, we have found no correlation between n and d from experiments using aqueous electrolytes and metal and semiconductor electrodes. A new model for the transient response of a rough electrode-electrolyte interface to a constant voltage pulse is proposed. Computer simulations, similar to the diffusion limited aggregation model, using measured profiles as fixed (non-growing) clusters, gave exponent n in good agreement with experiments.

Theory of Laplacian fractals: Diffusion limited aggregation and dielectric breakdown model

We describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the Laplace equation and a stochastic field. This new theory provides a systematic method for the calculation of the fractal dimension D and of the multifractal spectrum of the growth probability (ƒ(α)). A detailed application to the dielectric breakdown model and diffusion limited aggregation in two dimensions is presented. Our approach exploits the scale invariance of the Laplace equation that implies that the structure is self-similar both under growth and scale transformation. This allows one to introduce a Fixed Scale Transformation (instead of coarse graining as in the renormalization group theory) that defines a functional equation for the fixed point of the distribution of basic diagrams used in the coarse graining process. For the calculation of the matrix elements of this transformation one has to consider an infinite, but rapidly convergent, number of processes that occurs outside a considered diagram.

Topics in the physics of electrochemistry

We describe recent progress in the theory of electrochemical systems which makes important use of concepts and techniques of solid state physics. In particular we describe models of the microscopic layer between the solvent and the metal-ion cores at an electrode-electrolyte interface. These studies make heavy use of the density functional techniques which are widely used in surface physics. As a second example, we describe how the process of alloy dissolution at an electrode-electrolyte interface can be mapped in one limit onto a planar version of the diffusion limited aggregation model.

Fractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon

What happens when one attempts to push water through a fluid of higher viscosity? Under appropriate experimental conditions, the water breaks through in the form of highly branched patterns called viscous fingers. Water was used to push a more viscous but miscible, non-newtonian fluid in a Hele-Shaw cell. The resulting viscous finger instability was found to be a fractal growth phenomenon. Reproducible values of the fractal dimension df were found and were interpreted using a modification of the diffusion limited aggregation model.

Hierarchical model for irreversible kinetic cluster formation

A model is proposed to describe the growth of clusters by a mechanism of irreversible clustering of clusters. The fractal exponent is extracted by means of numerical simulations on small systems, both directly and in the form of a renormalisation-group analysis. The results are in excellent agreement with previous Monte Carlo simulations. The numerical precision is better due to the simpler (hierarchical) formulation of the model. In the present form the model looks like the diffusion limited aggregation model, which for the sake of comparison is treated by the same renormalisation-group method.