Self-Limiting Growth Kinetics of 3D Coherent Islands

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reveal another important and fascinating feature, the self-limiting behavior of 3D strained island growth, which is highly relevant to the fabrication of monosized quantum dots. Over the past three years, several groups 3 -5 have reported a remarkably narrow size distribution of 3D islands, which were observed after molecular beam epitaxy (MBE) deposition of a few monolayer coverage of a highly strained InAs film on a GaAs substrate (7% mismatch). However, the mechanism responsible for this narrow size distribution has not been well understood. A few energetic models 6-8 have been proposed to explain this feature. In all of these models, a global thermodynamic equilibrium state was assumed for the growth of either twodimensional (2D) strained islands, or 3D coherent islands, somewhat contrary to the nonequilibrium nature of MBE growth processes. To reveal the mechanism responsible for the sizeuniformity, we investigate 3D island growth from a metastable 2D strained film, which is induced by a post-deposition annealing. This approach emulates equilibrium surface conditions, at least locally, as close as possible. Our results determine that the high size-uniformity can result from a self-limiting behavior during the growth stage, i.e. well before a global equilibrium state is reached. EXPERIMENTAL OBSERVATIONS We began with a flat 2 nm thick Ge 0 .5 Si0 .5 strained film (2% mismatch) which was deposited on Si(100) substrate at low temperature of 400'C. The flat film surface was unstable to the formation of 3D islands upon post-deposition annealing for temperatures above a transition temperature region around 570'C. Since the chemical potential of a stable 3D island is lower than that of a 2D film, the planar strained film can be treated as an atom reservoir for 3D island 271 Mat. Res. Soc. Symp. Proc. Vol. 399 0 1996 Materials Research Society

nucleation and growth. The islands at this growth stage were examined by atomic force microscopy (AFM) after quenching samples from different annealing stages. Taking advantage of the existence of a temperature gradient across the sample surface (20±5'C difference from the sample center to edge), we can obtain information about the growth evolution from AFM measurements of islands at different temperature regions of one sample wafer. Fig. Ia and b show the typical AFM images of islands at the edge and center regions, respectively. Most of the islands have strain-stabilized (501 ) facet planes. The number density of strained 3D islands in (b) is much higher than that in (a), consistent with the thermally activated nature of 3D island formation. 8,9 A surprising feature revealed in fig.lb is the uniformity of island sizes, which can be clearly seen from the remarkably narrow distribution shown in fig.2. Comparing the size distributions between (a) and (b), we find that the size distribution is rather broad at initial stage of 3D island formation, but narrows upon further annealing. More surprisingly, however, is that the maximum sizes in both distribution curves are almost unch