Shapes of InxGa1xAsGaAs001 QDs

Many shapes have been reported for QDs in the Inx Ga1-xAs/GaAs system. One of the most commonly reported is the pyramid with a square base, deduced from plan-view [001] zone-axis transmission electron microscopy (TEM) diffraction contrast images [121, 122]. However, direct interpretation of such images can lead to a wrong conclusion about shape because diffraction contrast in TEM does not directly relate to QD shapes but to the strain field around and within the QDs [123].

Zou et al. [124] presented the first unambiguous shape determination of unburied Inx Ga1-xAs/GaAs(001) QDs using a direct imaging TEM technique. Using a very thick (>300 nm) cross-section TEM sample, images of different side projections (see an example image in Fig. 3) proved that the QDs are lens shaped with a circular base.

Liao et al. [123] studied the shape of buried met-alorganic chemical vapor deposition (MOCVD) grown In0.6Ga0.4As/GaAs(001) QDs using TEM combined with image simulations. As shown in Figure 4, the buried QDs have side projections similar to the unburied QDs reported by Zou et al. [124], suggesting the QDs to be lens shaped. Although plan-view [001] zone-axis images show a square contrast, interpretation of the contrast is not straightforward because image simulations show that lens-shaped QDs can produce a square-shaped image [123] (see Fig. 5).

Other shapes of Inx Ga1-xAs/GaAs QDs have also been reported. For example, using contact mode atomic force microscopy (AFM) with a B-doped Si tip, Yoon et al. [125] reported that MOCVD grown InAs/InGaAs QDs are truncated pyramids with four {136} facets and with base edges parallel to (130). Lee et al. [126, 127] reported a similar result using reflection high-energy electron diffraction (RHEED). Combining AFM and RHEED techniques, Kaizu and Yamaguchi [128] also reported {136} faceted InAs/GaAs(001) QDs grown by solid-source MBE. However, Nabetani et al. [129] interpreted the same RHEED pattern as showing {113} facets. An in-situ investigation of InAs/GaAs(001) QDs by STM [130] revealed a pyramidal QD shape dominated by {137} facets. Using a highresolution grazing incidence small angle X-ray scattering technique, Zhang et al. [131] determined an InAs QD

20 nm

Figure 3. A cross-section TEM image of a side projection of an unburied Ina6Gaa4As/GaAs(001) QD.

Figure 4. A cross-section high-resolution TEM image of two buried In06Ga04As/GaAs(001) QDs observed along (110). The QD boundaries are marked with white stars.

shape of octagonal-based truncated pyramid with {111} and {110} sidewalls and a (001) top facet. Anders et al. [132] also reported large InxGa1-X As/GaAs(001) QDs bounded by {111} sidewalls and a (001) top facet.

Moll et al. [133] calculated the equilibrium shapes of InAs/GaAs(001) QDs using an approach that includes density functional calculations of microscopic parameters, surface energies, and surface stresses with elasticity theory for the long-range strain fields and strain relaxations. In their calculations, they considered only low-index surface facets (001), {110} and {111}. Also, they neglected the island-island interaction and the alloying effect between QDs and the matrix. The equilibrium shapes they presented are islands bounded by an (001) top facet and {110} and {111} side facets. They found that the island shape changes continuously with the island volume. The {111} facets are more prominent than {110} facets for larger islands. However, most of the experimentally observed shapes in the InAs/GaAs(001) system differ from those predicted by Moll et al. They therefore concluded that the growth conditions of these InAs/GaAs QDs do not represent thermo-dynamic equilibrium but are driven by kinetics, and that it should be possible to achieve thermodynamic equilibrium by choosing appropriate experimental conditions.

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