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Publication# Self-organized growth of cluster arrays

Abstract

We present a novel method for the fabrication of well-ordered, two-dimensional nanocluster arrays. The method is based on the confined nucleation of adatoms within the superstructure cells of periodic surface dislocation networks, which form in many heteroepitaxial systems. Sire show how quantitative understanding of adatom diffusion and heterogeneous nucleation on such surfaces can be obtained through kinetic Monte-Carlo simulations and discuss the potential of this approach.

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Related concepts (26)

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Well-order

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the well-order relation is then called a well-ordered set. In some academic articles and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering. Every non-empty well-ordered set has a least element.

Partially ordered set

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, transitive and antisymmetric.

Well-ordering theorem

In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn's lemma are the most important mathematical statements that are equivalent to the axiom of choice (often called AC, see also ). Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle" to prove the well-ordering theorem.

Learn the fundamentals of microfabrication and nanofabrication by using the most effective techniques in a cleanroom environment.

Learn the fundamentals of microfabrication and nanofabrication by using the most effective techniques in a cleanroom environment.

Learn the fundamentals of microfabrication and nanofabrication by using the most effective techniques in a cleanroom environment.

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