Beyond the heteroepitaxial quantum dot: Self-assembling complex nanostructures controlled by strain and growth kinetics

Heteroepitaxial growth of GeSi alloys on Si (001) under deposition conditions that partially limit surface mobility leads to an unusual form of strain-induced surface morphological evolution. We discuss a kinetic growth regime wherein pits form in a thick metastable wetting layer and, with additional deposition, evolve to a quantum dot molecule—a symmetric assembly of four quantum dots bound by the central pit. We discuss the size selection and scaling of quantum dot molecules. We then examine the key mechanism—preferred pit formation—in detail, using ex situ atomic force microscopy, in situ scanning tunneling microscopy, and kinetic Monte Carlo simulations. A picture emerges wherein localized pits appear to arise from a damped instability. When pits are annealed, they extend into an array of highly anisotropic surface grooves via a one-dimensional growth instability. Subsequent deposition on this grooved film results in a fascinating structure where compact quantum dots and molecules, as well as highly ramified quantum wires, are all simultaneously self-assembled.

Figure 1

The process phase-space for strain-induced morphological evolution during $\mathrm{Ge}\mathrm{Si}∕\mathrm{Si}$ (001) MBE growth.

Figure 2

${\mathrm{Ge}}_{0.3}{\mathrm{Si}}_{0.7}$ films growth at $540–550°\mathrm{C}$. (a) $R_{\mathrm{dep}}=0.015\mathrm{nm}∕\mathrm{s}$, $h_f=5\mathrm{nm}$; (b) $R_{\mathrm{dep}}=0.015\mathrm{nm}∕\mathrm{s}$, $h_f=30\mathrm{nm}$; (c) $R_{\mathrm{dep}}=0.09\mathrm{nm}∕\mathrm{s}$, $h_f=5\mathrm{nm}$; (d) $R_{\mathrm{dep}}=0.09\mathrm{nm}∕\mathrm{s}$, $h_f=30\mathrm{nm}$. AFM images are $2\times 2\mu \mathrm{m}$.

Figure 3

Close-up images of QDMs at progressive stages of evolution. AFM images are $0.5\text{−}\mu \mathrm{m}$ wide. The labels in each image are for reference to Fig. 4.

Figure 4

(a) Line profiles through the QDMs in Fig. 3. On the left side, the profiles are drawn offset to represent the film thicknesses at which they occur, thus the bottom of the plot represents the heterointerface [note that two of the QDMs (a) and (c) in Fig. 3 occurred in the same $20\text{−}\mathrm{nm}$-thick film]. On the right side, the bottoms of the pits have been aligned, to better illustrate the shape evolution. (b) The surface angle relative to (001) from the linescan data. Diamonds from QDM (a), open circles from QDM (b), and closed circles from QDM (c).

Figure 5

The two states of a QCA cell comprised of four proximal quantum dots, two of which contain excess charge (gray circles).

Figure 6

Lateral size histograms for QDMs for various film thicknesses, including the effects of annealing.

Figure 7

(a) A linescan through a QDM defining the baseline height (solid line at $Z=0$) used for measurement of the volume of the islands (shaded above) and pit (shaded below). The dashed line shows the baseline required in order for the island volume to equal the $\text{pit}+\text{trench}$ volume. Note that the volume measurements were done on the full 3D AFM data, not the linescan. (b) the volume in the “hill” (or islands) vs the volume in the pit (and trenches if they exist). The slope is 2.7, and typical error bars are shown for select data points. The inset magnifies the measurements in the small volume regime.

Figure 8

The mean lateral size of QDMs vs strain (or Ge content). The dashed curve is a fit to ${\text{strain}}^{-1}$.

Figure 9

Pits forming at $h_f=\left(\mathrm{a}\right)7.2\mathrm{nm}$, (b) $8.4\mathrm{nm}$, and (c) $10.2\mathrm{nm}$. The lines show the linescan directions for Fig. 10, and have been offset so that the pits can be clearly seen. AFM images are $1.3\times 1.3\mu \mathrm{m}$.

Figure 10

(a) Line profiles through the pits in Fig. 9. On the left side, the profiles are drawn offset to represent the film thicknesses at which they occur, thus the bottom of the plot represents the heterointerface. On the right side, the bottoms of the pits have been aligned, to better illustrate the shape evolution. (b) The surface angle relative to (001) from the linescan data. Diamonds from pit (i), open circles from pit (ii), and closed circles from pit (iii).

Figure 11

$230\times 230\mathrm{nm}$ in situ STM image (part of a larger $1.1\mu \mathrm{m}$ scan) of a ${\mathrm{Ge}}_{0.3}{\mathrm{Si}}_{0.7}∕\mathrm{Si}$ (001) film grown by magnetron sputtering using the nominal QDM deposition parameters. A linescan across a deeper pit (location identified by the line on the image) is shown in the lower panel.

Figure 12

Surface height profiles resulting from 2D KMC calculations for ${\mathrm{Ge}}_{0.5}{\mathrm{Si}}_{0.5}∕\mathrm{Si}$ (01) growth. (a) $T_{\mathrm{dep}}=450°C$, with $R_{\mathrm{dep}}=1\mathrm{ml}∕\mathrm{s}$ (top), $2\mathrm{ml}∕\mathrm{s}$ (middle), and $4\mathrm{ml}∕\mathrm{s}$ (bottom). (b) $T_{\mathrm{dep}}=550°\mathrm{C}$, with $R_{\mathrm{dep}}=10\mathrm{ml}∕\mathrm{s}$ (top), $20\mathrm{ml}∕\mathrm{s}$ (middle), and $40\mathrm{ml}∕\mathrm{s}$ (bottom). In all panels, each contour represents a thickness increment of $20\mathrm{ml}$, and the $Z$ scale ticks are every $2\mathrm{nm}$.

Figure 13

Annealing a $5\text{−}\mathrm{nm}$-thick sample containing only pits [similar to Fig. 9a] at the deposition temperature for $1\mathrm{h}$ produces an array of faceted grooves and a variety of island shapes. The AFM image is $4\times 4\mu \mathrm{m}$.

Figure 14

The morphology resulting from the sequence: growth of ${\mathrm{Ge}}_{0.3}{\mathrm{Si}}_{0.7}$ at $550°\mathrm{C}$, $0.09\mathrm{nm}∕\mathrm{s}$, to $5\mathrm{nm}$ thickness, annealing in situ for $1\mathrm{h}$ at $550°\mathrm{C}$, continued alloy growth to $30\mathrm{nm}$ total thickness at $550°\mathrm{C}$, $0.09\mathrm{nm}∕\mathrm{s}$. The AFM image is $5\times 5\mu \mathrm{m}$.