Evolution of a multimodal distribution of self-organized $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dots

Formation and evolution of a multimodal $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dot (QD) ensemble during a growth interruption prior to cap layer deposition is studied. These particular kinds of QDs form self-organized after deposition of an InAs layer close to the critical thickness for elastic relaxation and after a short growth interruption. The QDs consist of pure InAs with heights varying in steps of complete InAs monolayers, have well-defined, flat, top and bottom interfaces, and show indications for steep side facets in transmission electron micrographs. QDs with a common height represent a subensemble within the QD ensemble, showing an emission peak with small inhomogeneous broadening. The evolution occurs by an increased appearance of subensembles with higher QDs and disappearance of subensembles related to smaller QDs, which accordingly dissolve. Dissolution proceeds essentially by a decrease of height, and only to a small amount by lateral shrinking. Thickness and composition of the wetting layer do not change during this process; growth and dissolution originate solely from material exchange between different QD subensembles. The evolution slows down for prolonged growth interruption, but the QD ensemble does not attain equilibrium within a time scale of minutes being eventually limited by the onset of plastic relaxation. Formation and dynamics of the observed evolution of the multimodal QD size distribution is theoretically well described by a kinetic approach, which implies strain-controlled adatom kinetics in the mass exchange between the QDs mediated by the adatom sea.

Figure 1

Normalized PL spectra of an $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QD sample grown applying $5\mathrm{s}$ growth interruption after InAs deposition and a quantum well (QW) sample grown without growth interruption $\left(0\mathrm{s}\right)$, scale factors are given with respect to the $10\mathrm{K}$ spectrum of QDs. GaAs denotes matrix near band-edge emission, the thick gray curve is the sum of the dotted Gaussian fits. Numbers denote QD subensemble heights in units of InAs monolayers assigned to the individual peaks.

Figure 2

(a) Energies of individual QD subensemble emissions of a sample grown with $5\mathrm{s}$ growth interruption versus QD heights assigned to these energies (black symbols). Gray full circles refer to a sample with Sb added during InAs deposition and growth interruption, open circles show predicted exciton transitions of truncated pyramidal $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QDs with shell-like increased height and base length taken from Ref. 14. (b) Subensemble emission peak energies of samples with increasingly prolonged growth interruption of $2\mathrm{s}$, $5\mathrm{s}$, $10\mathrm{s}$, and $30\mathrm{s}$, respectively, obtained from multi-Gaussian fits to the PL spectra; the numbers at the curves denote assigned subensemble QD heights.

Figure 3

High resolution TEM images of $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QDs from a single sample (three upper images). The morphology is given by truncated pyramids with different heights of complete InAs monolayers as indicated. The lowest figure represents an image-processed lattice plane micrograph; extracted templates of the GaAs and InAs lattice structure are given in the inset above.

Figure 4

Photoluminescence (a) and PL excitation spectra (b) of multimodal $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QD samples grown with varied durations of the growth interruption $t_{\mathrm{GRI}}$. GaAs denotes matrix near band-edge emission, $hh$ and $lh$ in (b) denote transitions related to light and heavy holes of the wetting layer (WL), respectively; the luminescence was detected on the respective main QD emission maxima of the samples.

Figure 5

Plan view bright-field transmission electron micrographs of $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QD samples grown with growth interruptions as indicated. The black-white contrast for slightly off-axis two-beam conditions (left, middle) is oriented along the [220] diffraction vector.

Figure 6

Calculated relative oscillator strength of the exciton ground state emission in truncated pyramidal $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QDs as a function of height and simultaneously increased base length from $10\mathrm{nm}$ (3 ML height) to $15.8\mathrm{nm}$ (13 ML) as drafted in the inset.

Figure 7

Gibbs free energy of a QD due to the formation of consecutively smaller monolayer embryos on the top facet at an earlier stage of evolution (gray curve) and a later stage (black) with an adatom sea chemical potential ${\mu }_2<{\mu }_1$.

Figure 8

Two stages of simulated evolution of a multimodal QD ensemble. The bar diagram gives the island distribution function $f\left(t\right)$ in height, normalized relative to its maximum value at a given moment in time.