Growth Mechanisms

Most of the QDs produced using strained epitaxial growth adopt the Stranski-Krastanow (S-K) growth mode [222]. There are, however, some including InAs/GaP(001) [223], GaAs/Si(001) [224], ZnTe on ZnSe/GaAs [225], and ZnSe on ZnS/Si(00l) and ZnS/GaAs(001) [226], which have been reported to adopt the Volmer-Weber growth mode [227], that is, island growth directly without any prior wetting layer formation. In the classical S-K mode of coherent island formation, one material with a different lattice parameter and low interfacial energy is initially deposited on a substrate surface, layer by layer, forming a "wetting layer." When the wetting layer reaches a critical thickness (usually three to five monolayers for pure Ge on Si(001) [25, 228]), island growth starts to partially release the mismatch strain energy between the epitaxial layer and the substrate.

However, the classic S-K mode is too simple to explain fully the complicated experimental observations. Based on a series of TEM studies of high-temperature growth Ge(Si)/Si(001) islands, in which a trench is seen on the substrate surface around a Ge(Si)/Si(001) island and the island/substrate interface is found moving towards the substrate (see Fig. 13), Liao et al. [229] proposed a modified S-K mode for high-temperature growth of Ge islands on Si, as shown diagrammatically in Figure 14. In classical S-K growth, layer-by-layer growth takes place at the initial stage of Ge deposition, as shown in Figure 14(a). However, the layer-by-layer growth at high temperature is accompanied by an alloying process, resulting from Si transport to the wetting layer. Following the layer-by-layer growth, surface migration of both Ge and Si results in island growth (Fig. 14(b)). The formation of the small coherent island only partially releases the misfit strain. With the growth of the island, misfit strain builds up. The strain energy is further reduced by lowering the misfit between the island and the substrate, which could result from the alloying of Si into the Ge island. The transfer of Si into the island can be either through transport from the wetting layer, or directly by bulk diffusion from the bottom of island/substrate interface, or both (as in Fig. 14(c)). The lower mobility of Si than Ge [219] implies that while Ge can be transported from a longer distance, most of the Si consumed comes from areas surrounding the islands. This results in a trench around the island, as illustrated in Figure 14(c). The subsequent island expansion necessarily starts from the bottom of the trenches and the lateral Si migration process continues as the island grows, as shown in Figure 14(d).

The above-mentioned growth mode does not provide a complete picture because the composition profile is not considered. The QD islands investigated above [229] have been found to have highest Ge content at the island top and the lowest Ge content at the island/substrate interface [208, 209, 230]. On the other hand, as discussed earlier, Liao et al. [199] used EFI in the TEM to study "pure" Ge/Si(001) islands grown at a lower temperature of 575 °C.

Figure 13. A cross-section bright-field image of a coherent Ge(Si)/ Si(001) island grown at 700 °C showing a clear wetting layer. White arrows at the left and right sides of the image mark the wetting layer/substrate interface and the island/substrate interface, respectively. A white line below the wetting layer represents the depth level of the island/substrate interface. A trench with a depth of about 7 nm at the edge of the island is clearly seen. Reprinted with permission from [229], X. Z. Liao et al., Phys. Rev. B 60, 15605 (1999). © 1999, American Physical Society.

Figure 13. A cross-section bright-field image of a coherent Ge(Si)/ Si(001) island grown at 700 °C showing a clear wetting layer. White arrows at the left and right sides of the image mark the wetting layer/substrate interface and the island/substrate interface, respectively. A white line below the wetting layer represents the depth level of the island/substrate interface. A trench with a depth of about 7 nm at the edge of the island is clearly seen. Reprinted with permission from [229], X. Z. Liao et al., Phys. Rev. B 60, 15605 (1999). © 1999, American Physical Society.

Figure 14. Schematic diagrams of a modified S-K growth mode at different growth stages. Reprinted with permission from [229], X. Z. Liao et al., Phys. Rev. B 60, 15605 (1999). © 1999, American Physical Society.

They found that the Ge content in islands is much higher than in the wetting layer and the Ge is nonuniformly distributed within an island with the highest Ge content located at the island center. These results imply alloying, elemental enrichment, interdiffusion, and composition redistribution occuring during the QD island growth process. Higher temperatures and lower growth rate will allow the QD composition to be distributed in such a way that the system can minimize the system energy more efficiently.

Combining all the information on the interfacial structure and composition mentioned above, a more complete image on the S-K island growth mode should be:

(i) the initial stage of layer-by-layer growth includes an alloying process between the deposited material and substrate material;

(ii) island nucleation is accompanied by the enrichment of a larger-misfit component of the deposited material and this will result in nonuniform composition distribution with the larger-misfit component concentrating at the center of the island;

(iii) the alloying process continues during the island growth and this lowers the island/substrate interface; and

(iv) if growth conditions permit, elements in islands will be redistributed to allow a larger-misfit component moving up to the top so that minimizing the island strain energy.

Stranski-Krastanow island growth mode normally involves a nucleation process. However, under some temperature and low-lattice, mismatch composition ranges, QDs in the Gex Si1_x/Si(001) system can apparently be formed in a so-called "nucleation-free" process involving a gradual evolution of surface roughness driven by misfit strain [231, 232]. Using in-situ, low-energy electron microscopy, Sutter and Lagally [231] and Tromp et al. [232] found that faceted GexSi1_x/Si(001) islands can form barrierlessly and continuously from strain-induced surface ripples with bunched steps as sidewalls. The sidewall angle of the ripples increases continuously until it reaches 11°, forming {501} facets. By assuming that the surface-energy anisotropy of strained GeSi allows all surface orientations near (001) with the first facet being {105}, Tersoff et al. [233] explained this phenomenon in terms of the barrierless formation of unfaceted prepyramid islands with low aspect ratio and indistinct edges.

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