Shape transition of self-assembled InAs quantum dots on $\mathrm{Ga}\mathrm{As}\left(114\right)A$

InAs quantum dots (QD’s) grown by molecular beam epitaxy on $\mathrm{Ga}\mathrm{As}\left(114\right)A$ substrates were studied by atomically resolved in situ scanning tunneling microscopy. Two frozen-in QD distributions prepared at different temperatures are analyzed under the assumption that QD’s are depicted, which exhibit some variation in evolution mainly due to the statistics in nucleation. After nuclei formation, the QD’s were found to grow in a flat form with {137} oriented facets and an aspect ratio of only 0.10. Shapes of presumably different stability were observed. During the following growth, a shape transition from flat to more steep occurs, the latter being characterized by {110} and $\left(111\right)A$ facets and an aspect ratio of 0.20. The shape transition occurs at a critical size of the diameter which was found to be temperature dependent, i.e., $12.3\mathrm{nm}$ at $380°\mathrm{C}$ and $20\mathrm{nm}$ at $430°\mathrm{C}$, respectively. The steep shape stays for a large size range until it is changed again. At this point both edge and screw dislocations were incorporated, which could be depicted here on top of the facets. Arguments are given that the change in critical diameter is related to In and Ga alloying and the related change in induced strain. An according growth model is proposed. Overall we conclude that the island shape derives mainly from thermodynamics rather than from kinetics.

Figure 1

Overview STM image of InAs islands on $\mathrm{Ga}\mathrm{As}\left(114\right)A$ prepared at $380°\mathrm{C}$. The image size is $100\times 100{\mathrm{nm}}^2$. Some of the islands, whose shape is shown below in atomically resolved images, are marked.

Figure 2

Height of InAs islands as a function of their diameter. The straight lines are a guide to the eye. In the plot the positions are given for those islands, which are marked in Fig. 1 and are shown in atomically resolved images below.

Figure 3

Atomically resolved 3D STM images of InAs islands grown on $\mathrm{Ga}\mathrm{As}\left(114\right)A$. The diameter and height (in units of nm) of the individual QD are given in brackets at the bottom of each image. The image sizes are (a) $7.4\times 7.4{\mathrm{nm}}^2$, (b) $7.6\times 7.6{\mathrm{nm}}^2$, (c) $9.4\times 9.4{\mathrm{nm}}^2$, (d) $10.1\times 10.1{\mathrm{nm}}^2$, (e) $12.9\times 12.9{\mathrm{nm}}^2$, and (f) $12.5\text{×}12.5{\mathrm{nm}}^2$, respectively. The unit cells of {137} surfaces with unit vectors $u_1$ and $u_2$ are marked.

Figure 4

Schematic structure models of the QD’s at right-hand side. The corresponding original STM images are shown at the left-hand side. The diameter and height (in units of nm) of the individual QD are given in brackets at the bottom of each image. The image sizes are (a) $7.6\times 7.6{\mathrm{nm}}^2$, (b) $12.9\times 12.9{\mathrm{nm}}^2$, and (c) $12.5\times 12.5{\mathrm{nm}}^2$, respectively.

Figure 5

Cross-section profiles of growing InAs island on $\mathrm{Ga}\mathrm{As}\left(114\right)A$. The cross-section planes are parallel to $\left(\overline{1}10\right)$ and $\left(22\overline{1}\right)$, respectively.

Figure 6

Overview STM image of InAs islands on $\mathrm{Ga}\mathrm{As}\left(114\right)A$ prepared at $430°\mathrm{C}$. The image size is $800\times 800{\mathrm{nm}}^2$.

Figure 7

Aspect ratios of InAs QD heights as a function of their diameters. The QD’s are grown at (a) $430°\mathrm{C}$ and (b) $380°\mathrm{C}$, respectively.

Figure 8

3D STM images of two mature InAs QD’s on $\mathrm{Ga}\mathrm{As}\left(114\right)A$. The diameter and height (in units of nm) of the individual QD are given in brackets at the bottom of each image. The image sizes are (a) $12.5\times 12.5{\mathrm{nm}}^2$, and (b) $29.0\times 29.0{\mathrm{nm}}^2$. (c) Growth model; cut trough $\left(22\overline{1}\right)$.

Figure 9

(a) 3D STM image of InAs QD with a lattice defect. The size is $40\times 40{\mathrm{nm}}^2$. (b) Enlarged image of the defect.

Figure 10

(a) Overview 3D STM image of large InAs islands on $\mathrm{Ga}\mathrm{As}\left(114\right)A$. The size is $500\times 500{\mathrm{nm}}^2$. (b) The enlarged image of the island with an irregular shape marked by an arrow head in (a). The size is $64.3\times 64.3{\mathrm{nm}}^2$.