The spontaneous formation of self-assembled nanostructures has become a driving force in nanoscience research during the last two decades. Semiconductor quantum dots are well-known examples of such a nanoscale system where the opto-eletronic behavior depends on the atomic-level configuration. In order to understand heteroepitaxial strained layer growth, Ge islands on Si(001) have been extensively investigated as a model system. Coherent Ge nanostructures are spontaneously formed on top of a three monolayer thick wetting-layer. Recent anomalous X-ray experiments have shown that a considerable amount of Si from the substrate is incorporated into Ge dome-shaped islands during growth [1]. However, the interdiffusion mechanism remains obscure at the atomic level. In this work basis forbidden reflections were measured in nominally pure Ge islands on Si(001). The existence of an atomically ordered alloy phase inside these islands confirm the crucial rule of surface kinetics to the final island structure and composition. 

A -2 radial scan in the vicinity of the in-plane Si(400) surface reflection is shown in Figure 93a. The broad intensity distribution along the qr axis indicates that the lattice parameter, which was initially constrained to the Si value, relaxes continuously towards the Ge lattice parameter with increasing height inside the islands. A rather unexpected result is obtained when the scattered intensity is measured in the vicinity of the (200) reflection (Figure 93b), which is forbidden for pure Si and Ge crystals and also for a random alloy of the two elements. This strongly indicates that the domes consist of a SiGe alloy with a long-range atomic order.

Performing a size-sensitive angular () scan for a fixed 2, one probes the corresponding Fourier transform of a region with constant lattice parameter. One angular profile close to the (400) reflection (Figure 93c) exhibits a broad peak and subsidiary maxima, resulting from the finite size and narrow size distribution of constant-lattice parameter region. In contrast to the (400) reflection, an angular scan performed at the (200) reflection yields a very different profile as shown in Figure 93c. A pronounced minimum is observed at qa = 0, which cannot be generated by structures that are interfering constructively. Such a profile is modeled by introducing anti-phase boundaries, which are generated by stacking faults in the in-plane atomic sequence, leading to phase inversions in the X-ray wave.

Fig. 93: Radial scans in the vicinity of (a) Si (400) reflection and (b) Si (200) reflection. The upper scale directly indicates the in-plane lattice parameter. (c) Angular scans performed at (400) and (200) reflections.

The complete qr/qa measured intensity map close to the Si (200) reflection is shown in Figure 94a. A weak narrow peak is seen exactly at the Si (200) position, indicating that the wetting-layer is partially ordered, but without establishing anti-phase boundaries. Hence, alloying and ordering begin as soon as Ge is deposited. Si atoms are incorporated into the wetting-layer in the initial phase of growth and into the islands after the beginning of their nucleation. The map shown in Figure 94b was obtained simulating the ordered domain size and distribution inside one island. Selected angular cuts from the experimental and calculated maps are shown in Figure 94c. A comparison between island and domain size is shown in Figure 94d, where the size of the anti-phase domains was obtained from fits of the (200) map and the island size from fits at the (400) reflection (not shown here). For both, island and domain, there is a linear variation of size with lattice parameter and height, suggesting the existence of a stress-mediated mechanism that determines the island and domain size. A three-dimensional concentration map of the domes was obtained from anomalous scattering measurements of the (400) reflection [1]. Figure 94e depicts schematically the distribution of domains inside the islands. Ordered regions are present mainly in parts of the island where the Ge concentration reaches approximately 0.5.

Fig. 94: Measured (a) and simulated (b) qr-qa intensity maps in the vicinity of the Si (200) reflection. Four numbered qa scans (dashed lines in maps (a) and (b)) are shown in (c). (d) Size of islands and domains as a function of lattice parameter and height. (e) Ge concentration and atomic ordering map showing the location of ordered domains inside islands.

It is worth noting that atomic ordering influences the electronic/optical properties of these islands. The presence of ordered domains results in a shift of the phonon frequency, band edge alignment and the semiconductor gap. Finally, the study of forbidden reflections can lead to a better understanding of the interdiffusion process in Si/Ge and similar Stranski-Krastanov systems.



[1] A. Malachias et. al., Phys. Rev. Lett., 91, 176101 (2003).

Principal Publication and Authors

A. Malachias (a,b), T.U. Schülli (b,d), G. Medeiros-Ribeiro (c), L.G. Cançado (a), R. Magalhães-Paniago (a,c), M. Stoffel (e), O.G. Schmidt (e), T.H. Metzger (b), Phys. Rev. B, 72, 165315 (2005).
(a) UFMG, Belo Horizonte (Brazil)
(b) ESRF (France)
(c) LNLS, Campinas (Brazil)
(d) CEA/Grenoble (France)
(e) Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany)