Kinetic Size Selection Mechanisms in Heteroepitaxial Quantum Dot Molecules

Heteroepitaxial growth of $\mathrm{S}{\mathrm{i}}_{\mathrm{0.7}}\mathrm{G}{\mathrm{e}}_{\mathrm{0.3}}/\mathrm{Si}(001)$ films under kinetically limited conditions leads to self-assembly of fourfold quantum dot molecules. These structures obtain a narrowly selected maximum size, independent of film thickness or annealing time. Size selection arises from efficient adatom trapping inside the central pit of the quantum dot molecule when the surrounding islands cojoin to form a continuous wall. Self-limiting growth of nanostructures has significant implications for novel nanoelectronic device architectures such as quantum cellular automata.

Figure 1

Atomic force microscope images, $2\mu \mathrm{m}$ wide, showing morphology for $\mathrm{S}{\mathrm{i}}_{\mathrm{0.7}}\mathrm{G}{\mathrm{e}}_{\mathrm{0.3}}$ films (a) $50\AA$ thick; (b) $200\AA$ thick; (c) $300\AA$ thick; (d) $300\AA$ thick annealed for 1 h at $550°\mathrm{C}$. Gray scale is optimized for showing edges and is not a true height scale. The arrows show the $⟨100⟩$ in-plane directions, and lines indicate where topographic data in Fig. 2 were obtained.

Figure 2

Line scans of the samples shown in Fig. 1. Traces are offset for clarity. The data for Fig. 1a are magnified $2\times$ relative to the other samples. The arrow shows how lateral size of a QDM is defined.

Figure 3

A percentile plot summary of the size distributions for $\mathrm{S}{\mathrm{i}}_{\mathrm{0.7}}\mathrm{G}{\mathrm{e}}_{\mathrm{0.3}}$ films of different thicknesses, with and without 1 h anneals. Each open box encloses the inner $90\%$ of the data, each filled box encloses the inner 50% of the data, and the white bar represents the mean. For each sample, between 39–45 islands were measured.

Figure 4

Results of finite element calculations for (a) compact QDMs and (b) mature QDMs, showing contours of elastic strain energy. The perspective view shows one-fourth of the structure. Lighter shadings represent lower energy, and the darkest contour represents $5.81\times {10}^{+11}\mathrm{J}/{\mathrm{m}}^3$. In (a) the arrows illustrate easy diffusion paths enabling QDM enlargement, while in (b) the triangle and arrow show the optimal facet nucleation and growth process.