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Thin-film cliffhanger

Naturevolume 417pages907909 (2002) | Download Citation


Thin films are grown ideally one atomic layer at a time, but atoms can move along and between layers. The model for film growth has now been extended to describe how atoms tumble over 'cliffs' between layers.

Many modern technologies depend on our ability to grow thin films. In highly refined semiconductor technologies (such as solid-state lasers in compact-disc players or fast electronic components in mobile phones), films must be nearly perfect, grown seemingly one atom at a time, and individual layers of a composite film may be only a few atomic layers thick. In less critical technologies, films are deposited with essentially the same methods but with less need for perfection — protective coatings, decorative coatings, wear coatings and so on. Even something as simple as a potato-chip bag may have a thin-film coating that acts as a moisture barrier.

We think of film growth in terms of atoms or molecules 'raining' down on a surface, and then finding the proper sites to come to rest and form a layer. But in crystal growth in general — whether it be the formation of gems over geological timescales, the appearance of salt crystals on your skin after a dip in the ocean, or the growth of alum crystals in a school science experiment — the atomic processes that occur always follow the same rules. Writing in Applied Physics Letters, Liu et al.1 have now put in place the final piece in our understanding of the rules that govern how atoms move from one layer to another as films or crystals grow.

Consider a marble rolling off a table. It rolls over the edge, never pausing to 'think' that it might fall and break. Yet if we walk up to the edge of a cliff, we instinctively slow down, perhaps peer carefully over the edge, and draw back. There is a 'barrier' that keeps us from going forward. What would an atom do in the analogous situation?

The terrace-step-kink (TSK) model2, developed by Burton, Cabrera and Frank in the early 1950s, elegantly describes the atomic-scale morphology of the surface of a crystal (Fig. 1). When an atom lands on the surface, it diffuses along the 'terrace' formed by that film layer, trying to find the best place (from the point of view of its free energy) to settle — frequently a lower terrace. But an atom coming to the edge of a terrace behaves like a human on a cliff: it feels a barrier that prevents it going over the edge.

Figure 1: The terrace-step-kink (TSK) model of a thin-film surface.
Figure 1


The surface consists of terraces separated by steps; a kink is a step on a step. Atoms travelling over steps that are one-atomic-layer high must cross an energetic barrier, the two-dimensional Ehrlich–Schwoebel (ES) barrier. At kinks, atoms experience the 'corner-crossing' barrier, a one-dimensional version of the ES barrier. Liu et al.1 have identified a three-dimensional ES barrier for atoms travelling over steps that are four or more atomic layers high, or over the edges between two facets. The validity of the TSK model for thin films has been confirmed by the detailed imaging made possible by the scanning tunnelling microscope. The inset image shows the surface of a thin film of silicon (100 nm × 80 nm). Terraces separated by single-atom-high steps with many kinks can be seen, stepping down across the image from upper left to lower right. The white spots are atomic vacancies in the terraces.

In 1966, Gert Ehrlich performed elegant experiments3 using field–ion microscopy in which he put a single atom on an atomic terrace and observed its motion. He saw that atoms were preferentially reflected back at the edges of a terrace. He explained this behaviour in the following way. The atom on a terrace has a certain number of nearest neighbours (its coordination number) and the bonding to these neighbours provides stability for that atom. As it reaches the edge of a terrace, it suddenly has fewer neighbours, and the resulting decrease in the binding energy is manifested as a barrier for diffusion over the edge. Richard Schwoebel independently proposed4 a similar model at the same time.

But for more than 20 years this idea languished — until the advent of the scanning tunnelling microscope made it possible to observe the atomic-scale morphology of surfaces over mesoscopic regions, and provided vivid visual confirmation of the TSK model (Fig. 1). Because film-growth studies at the atomic level were now possible, the effects of barriers to atom transport between terraces in a growing crystal or film could be directly observed.

A reflective wall at the edge of a terrace, which became known as the Ehrlich–Schwoebel (ES) barrier, hinders the descent of atoms to lower levels. This increases the chance of nucleation and growth of a new film layer on top of the terrace when more atoms arrive from the deposition source. In 1991, Villain showed5 that an ES barrier (which is a two-dimensional phenomenon) creates an effective 'uphill' gradient, leading to unstable growth and the creation of roughness in the film — an undesirable feature. Thus the two-dimensional ES barrier dictates the three-dimensional morphological evolution of growing films.

But the concept of the ES barrier also extends to other dimensions. As the figure shows, a step separates one terrace from another; a kink is the one-dimensional analogue: a 'step on a step'. We have pointed out6,7 that there should also be a one-dimensional analogue to the phenomenon Villain described — that an atom moving along a step edge should feel a barrier preventing it crossing this kink because of its reduced coordination number. The ultimate kinks occur at the corners of a two-dimensional crystal (an 'island'), where two step edges meet. An atom diffusing along one edge feels a barrier to crossing to the adjacent edge: this 'corner-crossing barrier' can cause two-dimensional islands (one-atomic-layer high) to develop rough, or even fractal, shapes. This corner-crossing barrier — in fact, a one-dimensional ES barrier — can also induce growth instability in the morphology of a three-dimensional film8,9. Indeed, films may actually grow more smoothly if this barrier is large.

If a number of identical terraces were stacked on top of each other, the simple corner becomes a line or a ridge between two crystal facets. Following on from their earlier work10, Liu et al.1 propose that there is also a three-dimensional ES barrier that influences atom transport from one facet across this edge to the adjacent facet. The authors point out that the magnitude of the three-dimensional ES barrier may be quite different from that of the two-dimensional ES barrier; the latter may, in fact, be zero but the three-dimensional barrier can be quite high.

Liu et al. also show that, for transitions over a step edge between adjacent terraces, the two-dimensional barrier becomes a three-dimensional barrier as the height difference between the two terraces increases (Fig. 1). For the specific example of aluminium, the transition from two-dimensional to three-dimensional ES barrier is complete if that height is four atomic layers or more1,10.

So the picture is complete: the growth morphology and shape of every crystal — whether it is two-dimensional (a single-atomic-layer-high island), 'two-and-a-half-dimensional' (a nearly flat film with some roughness) or three-dimensional (a small nanocrystal) — is controlled by the magnitude of barriers felt by atoms as they approach a 'cliff' and decide whether they really do want to step off the edge. A proper accounting for these barriers in film growth will determine the ultimate quality, reliability and stability of films grown for a great variety of purposes.


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    Liu, S. J., Huang, H. C. & Woo, C. H. Appl. Phys. Lett. 80, 3295–3297 (2002).

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    Zhang, Z. Y. & Lagally, M. G. Science 276, 377–383 (1997).

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    Liu, S. J., Wang, E. G., Woo, C. H. & Huang, H. C. J. Comput.-Aided Mater. Design 7, 195–201 (2001).

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  1. the Department of Materials Science and Engineering, University of Wisconsin, Madison, 53706, Wisconsin, USA

    • Max G. Lagally
  2. the Solid State Division, Oak Ridge National Laboratory, Oak Ridge, 37831, Tennessee, USA

    • Zhenyu Zhang


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Correspondence to Max G. Lagally.

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