Scaling of Island Size Distributions in Fe Growth
Understanding the processes of nucleation and growth is central to growing
high-quality materials by molecular-beam epitaxy. On a microscopic scale, we
would like to know how atoms diffuse on a surface, after being deposited at
random from an impinging flux, and how they are incorporated in the growing
material. Random deposition of atoms drives a system into non-equilibrium, with
an initial higher than equilibrium concentration of adatoms. An adatom, or
monomer, then undergoes a random walk and has two alternatives that determine
its fate: (1) the monomer may find an existing island and become
incorporated leading to growth, or (2) it may find one or more other
diffusing atoms and nucleate a new island. This new island may be stable or
unstable against dissociation depending on the binding energy of the cluster
and the surface temperature. In traditional growth theories, the size i
at which an island consisting of i or less atoms is unstable, but
i+1 atoms is stable, is labeled the critical size. In general the
critical nucleus size i will depend on temperature.
In our experiments on the initial stages of growth of Fe on Fe(001), an
analysis of the Fe island size and separation distributions show scaling
properties recently predicted by Bartelt and Evans (see references below), for
distributions as a function of the ratio of the diffusion to deposition rate.
The resulting scaling functions closely resemble predictions for a critical
nucleus size i=1 in the temperature range of 20-250° C.
Measurements of the island density and size distributions at temperatures above
250° C show a change from the initial scaling function to a second
scaling relation, which can be interpreted as an increase in the critical size
for nucleation in this temperature range.
Figure 1 shows a selection of STM images of the initial stages of growth of
single-atom-high Fe islands as a function of substrate temperature. A number of
features are apparent from the images in Fig. 1. First the propensity
towards island growth versus nucleation increases with increasing temperature.
Growth and nucleation are competing processes, and since the adatom diffusion
increases with temperature, the probability for an atom to find an existing
island instead of nucleating a new one increases. The second feature to notice
is the self-similarity of the island distributions with change in temperature;
this can be seen qualitatively by comparing Figs. 1(a)-1(c) with 1(d)-1(f)
and noticing the change in scale.
Figure 1: STM images, 100 nm x 100 nm2,
of single-layer Fe islands (white) on the Fe(001) surface (black). Sample
temperatures during growth are (a) 20° C,
(b) 108° C, (c) 163° C, (d) 256° C,
(e) 301° C, and (f) 356° C. Fe was deposited for
a fixed time for all measurements, yielding a coverage of 0.07 ML.
The self-similarity of the island size distributions seen in Fig. 1 is demonstrated more quantitatively by analyzing the size distributions obtained from the STM images. Figure 2 shows the scaled island size distributions for the temperature range of 20-356° C, where the ratio of hopping rate to deposition rate ranges from 106 to 1010. For temperatures below 250° C [Fig. 2(a)] one observes a collapse of the island size distributions onto a single curve, in excellent agreement with the predictions by Bartelt and Evans (see references below). The resulting scaling function closely resembles the prediction for a critical size of 1 (see inset). At higher growth temperatures, deviation from the scaling function in Fig. 2(a) is observed, as shown in Fig. 2(b). However, we observe that the distributions still collapse onto one curve, albeit a different scaling function than observed for the low temperature growth. The change to a different scaling function for the island size distribution at higher growth temperature is suggestive of a change in critical size for nucleation. Comparing to simulations, the measured scaled size distribution resembles the scaling function for a critical nucleus size of 3. Further measurements of the island density as a function of deposition rate would be useful to corroborate these critical island size determinations.
Figure 2: Scaled island size distributions as a function of growth
temperature from the STM measurements in Fig. 1. Ns is
the island density per lattice site of islands with s atoms and
sav is the average island size, and
Θ is the total coverage.
(upper panel) Lower temperature data from 20° C to 207° C,
and ratio of hopping to diffusion rate from 106 - 109.
(lower panel) Higher temperature data; 301° C and 356° C,
hopping to diffusion rate, 8x109 and 2x1010,
respectively.
Scaling of Diffusion-Mediated Island Growth in Iron on Iron Homoepitaxy
The Growth of Iron on Iron Whiskers
Homoepitaxial Growth of Iron and a Real Space View of Reflection-High-Energy-Electron-Diffraction
Joseph A. Stroscio
Daniel T. Pierce
Robert J. Celotta
Supported in part by the Office of Naval Research
Online: May 1996
Last Updated: February 2008
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