Nucleation-Mediated Lateral Growth on Foreign Substrate

Abstract

A model is developed to deal with lateral growth of a crystalline layer on a foreign substrate, which is mediated by successive nucleation at the concave corner defined by the meeting of a crystal facet and the substrate. It is demonstrated that due to an imbalance of surface/interface tensions at the concave corner, once the embryo of a nucleus is formed, the crystallographic orientation of the nucleus is spontaneously twisted. By successive nucleation at the concave corner, the crystalline layer develops laterally on the substrate, with its crystallographic orientation continuously rotated. In this way, a regular spatial pattern with well-defined long-range order is eventually achieved. Our model provides a criterion to predict when such an effect becomes observable in the nucleation-mediated lateral growth. The theoretical expectations are consistent with the experimental observations.Thin film growth has been extensively investigated in recent decades. Previous studies concentrated mostly on vertical growth (i.e., on the increase of film thickness above a substrate). 1,2 To initiate a thin film growth, nevertheless, horizontal extension of individual crystalline islands on the substrate is an important step. It is known that the crystallographic orientation of an epitaxial film is well aligned with that of the substrate. Yet in some cases the crystallographic orientation of the film may become complicated. [3][4][5] One interesting scenario is that nucleation selectively occurs at the concave corner of an expanding crystalline island and the substrate, and the island expansion (hence the thin film growth) is a repeated nucleation process at the concave corner with the orientation of each new nucleus heavily influenced by the surface tensions at the corner site. Once an embryo of nucleus (nascent nucleus) forms at the concave corner, the asymmetric local surface tensions will apply a torque to the embryo. 6 Hence, the crystallographic orientation is rotated with respect to the previous nucleus. Indeed, it has been observed that, during lateral growth of NH 4 Cl crystallite on a glass plate, the crystallographic orientation is continuously rotated, leading to either a periodic distribution of faceted regions and roughened regions 7 or a regular zigzag branches. 8,9 The appearance of the specific morphology depends on the index of the initial crystalline facet contacting the substrate and the axis of rotation. 9 Another example is the crystallographic wing tilt commonly observed in lateral overgrowth, 10,11 which is generally ascribed to the substrate effect. The underlying mechanisms of these lateral-growth-associated phenomena, however, are still not very clear, and the relationship between the rotation of the crystallographic orientation and the longrange order in aggregating crystallites has yet to be understood. In this paper, we try to establish fundamental relationships between nucleation and the rotation of crystallographic orientation. Based on previous experimental observations, we propose a model to...

Formation of regular zigzag branch of CsCl crystallites on glass substrate: A new lateral growth mechanism leading to long-range ordering

“…Because of the asymmetric surface tensions underneath the embryo, orientation of the embryo will be twisted by a small angle Dy ¼ y n+1 Ày n . The total free energy for the formation of distorted nucleus on the concave edge can be expressed as [23] …”

“…Detail analysis indicates that Dy is usually negative and does not change the sign in crystallization [23]. This means that once crystallization is promoted by successive nucleation at the concave corner as that shown in Fig.…”

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