Pattern Formation in Fe on Fe Homoepitaxy

The morphology of films grown by molecular beam epitaxy varies widely depending largely on how effectively the roughness induced by the random nature of the impinging atom flux is counterbalanced by a smoothing process resulting from the mobility of the atoms diffusing on the surface. To better understand the processes that control roughness in epitaxial growth, we investigated multilayer homoepitaxial growth of Fe on a Fe(001) surface at room temperature. Surprisingly, the films do not exhibit the scaling properties postulated by a number of theories, but rather they consist of mounds with a characteristic size and separation. The size and separation increase as growth proceeds with an initial separation determined by the coalescence into islands of the first atoms deposited on the surface. Since the initial density of islands is somewhat uniform, the mounds that develop subsequently are also somewhat uniform. Mounding occurs because the energy barriers at the island step edges inhibit the downward transport of atoms to the next terrace compared to diffusion of atoms on a flat terrace. Thus, the atoms tend to remain on the terrace on which they were deposited and a wedding-cake island structure develops. Eventually the slope of the islands saturates and the larger islands grow at the expense of the smaller islands, a process called coarsening.

We measured the homoepitaxial growth of Fe(001) at room temperature using STM and RHEED. The mosaic of mounds can be seen in the STM image of Fig. 1 which corresponds to a 10 monolayer film Fe. The characteristic mound separation was determined 1) from the height-height correlation function obtained from STM images and 2) independently from the splitting of RHEED intensity peaks. The characteristic separation was found to increase (coarsen) with power-law behavior with a coarsening exponent of 0.16 ± 0.04 for thicknesses greater than or equal to 20 monolayers and less than or equal to 600 monolayers [see Fig. 2(a)]. This is in contrast to the t^1/4 behavior predicted for capillary-induced coalescence events that eliminate smaller mounds in favor of larger mounds. The feature separation increases slowly as the film thickness increases but the slope that the mounds make with respect to the surface plane rapidly saturates, as growth proceeds, to a "magic" slope corresponding to an angle of 13°±3°. An additional characteristic of the surface morphology is the absence of reflection symmetry in the plane defined by the mean height. This is clearly seen in the contour plot shown in Fig. 1(b) where channels are observed to run through the collection of mounds.

Figure 2. (a) Feature separation and ratio of RMS height to feature separation versus film thickness.
The solid line is the result of a least squares fit to the STM (squares) and RHEED (diamonds) measurements
of the feature separation for thicknesses greater than 20 monolayers, with a slope of 0.16 ± 0.04. The dashed line is the initial separation of the islands. The characteristic slope, as determined from STM measurements (circles), saturates to a value corresponding to 13° ± 3°.
(b) Feature separation and characteristic slope from numerical simulation of continuum equations to model the growth. The solid line shows the least squares fit to the data for thicknesses greater 150 giving a slope of 0.18 ± 0.02.

We performed a numerical study of a phenomenological, continuum equation of motion to help interpret our experimental results. This approach has the great virtue that it focuses attention on general thermodynamic and kinetic features of the problem rather than on atomistic details that distinguish one material from another. To get qualitative agreement with the experimental data required significant modifications of the standard models used to describe growth. The term that describes diffusion induced smoothing of the surface had to be left out or the coarsening exponent would be significantly different than that observed. Omission of this term is consistent with the lack of such smoothing in the experimental results. In addition, terms had to be introduced to saturate the slope, and to break the up-down symmetry of the surface. The growth is significantly more complicated than that assumed in simple models. The numerical simulations show the coarsening behavior quite dramatically.

Simulation (533 K: May not open with some older mpeg players such as Windows 95 Media Player)
Movie 1. The surface profile for one realization of the numerical simulation of the growth by integration of continuum equations. Green corresponds to low points on the surface, and red to high points. In the initial phases, the surface is up-down symmetric and has a characteristic length scale. As growth proceeds, the symmetry is broken, and the characteristic length scale increases as larger islands grow at the expense of smaller islands.

Supported in part by the Office of Naval Research

Online: May 1996
Last Updated: February 2008

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