Witten—Sander growth

The mechanism of growth of columnar structure ZnO layers assumes the presence of nanosized clusters in the reagent flow and that the formation of ZnO layers can be described by a model close to the one of Witten-Sanders. Increase of target-to-substrate distance leads to the decrease of the number of aggregates in the flow near the substrate and to the improvement of the structural perfection of ZnO layers. 

The idea that disorderly growth can lead to scale invariance was first pointed out by Witten and Sander (33) who were attempting to explain earlier observations of Forrest and Witten (34) of smoke aggregates. Computer simulations (33, -M) have also suggested that the resultant structures exhibit scale invariance and can be described as fractals. Two general classes of irreversible aggregation have emerged from the simulations. 

We discuss below the DLA model in detail which was proposed by Witten and Sander [16, 18]. The DLA is a particular model of a random irreversible growth. The growth process starts from a seed particle. A second particle is launched far enough from the seed and makes a random walk. If it visits a position next to the seed, it is stuck to it and both form a two-particle cluster extending the initial seed. Then a third particle is launched and moves randomly around this cluster. It may join the two-particle... 

The DLA model has been investigated in 1981, by Witten and Sander [112]. This was catching the attention of researchers due to property of various levels of crystal patterns especially in non-equilibrium state can be simulated instantly. The standard DLA model includes some basic terminologies which are conceptually helpful to describe complexity of the growth process. 

Monomer-cluster or cluster-cluster growth can be limited by diffusion or by reaction. In diffusion-limited monomer-cluster aggregation (DLMCA), simulated by the Witten and Sander model (25) in Fig. 5.11, it is assumed that monomers are released one by one from sites arbitrarily far from a central cluster. The monomers travel by a random walk diffusion mechanism and stick irreversibly at first contact with the growing cluster. Because of this trajectory, the monomers cannot penetrate deeply into a cluster without intercepting a cluster arm and the arms effectively screen the interior of the cluster from incoming monomers. Growth occurs preferentially at exterior sites, resulting in objects in which the density decreases radially from the center of mass (in three dimensions dm = 2.45). 

In 1981 the diffusion limited aggregation (DLA) model was introduced by Witten and Sanders [96]. In this model particles are added, one at a time, to a cluster or aggregate of particles via random walk trajectories. According to this model, there is competing growth of polymer chains from a surface, which leads to the formation of independent clusters. 

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