Self-assembled quantum dots with tunable thickness of the wetting layer: Role of vertical confinement on interlevel spacing

Epitaxial self-assembled quantum dots (QDs) are commonly obtained by the Stranski-Krastanow (SK) growth mode, in which QDs form on top of a thin two-dimensional (2D) wetting layer (WL). In SK QDs, the properties of the WL such as thickness and composition are hard to control independently of those of the overlying QDs. We investigate here strain-free GaAs/AlGaAs QDs located under a GaAs quantum well (QW), analogous to the WL in SK QDs. The thickness of such a QW can be arbitrarily controlled, allowing the optical properties of the QDs to be tuned without modifying the QD morphology and/or composition. By means of single-QD photoluminescence spectroscopy, we observe well-resolved excited-state shell structures with intershell spacing increasing monotonically with decreasing QW thickness. This behavior is well reproduced by eight-band $k\cdot p$ calculations combined with the configuration-interaction model taking the realistic QD morphology as input. Furthermore, for the thinnest GaAs layer investigated here, no QW emission is detected, indicating that it is possible to suppress the two-dimensional layer usually connecting QDs. Finally, we find that all recombination involving an electron-hole pair in the ground state, including the positive trion, occurs at the low-energy side of the neutral exciton emission. This behavior, previously observed for GaAs/AlGaAs QWs, is a consequence of the large lateral extent of the QDs, and hence of pronounced self-consistency and correlation effects.

Figure 1

(Color online) AFM image of ${\text{Al}}_{0.45}{\text{Ga}}_{0.55}\text{As}$ nanoholes (a) and of nanoholes filled with GaAs with nominal thickness $d$ of (b) 0.5 nm, (c) 1 nm, and (d) 4 nm followed by one min annealing prior to cooling to room temperature. Linescans of representative nanoholes in the (e) [110] and (f) $\left[1\overline{1}0\right]$ directions. The lines are offset in vertical direction by an amount equal to $d$. (g) Depth of the GaAs-filled nanoholes and the deduced height of GaAs QDs for different GaAs fillings. The QD height for each sample is extracted from the difference in depth for the ${\text{Al}}_{0.45}{\text{Ga}}_{0.55}\text{As}$ nanoholes and the GaAs-filled nanoholes plus $d$.

Figure 2

(Color online) (a) Low-temperature PL spectra of representative QDs for samples of various $d$. The energy axes are shifted horizontally to facilitate the comparison. (b) Binding energy for the positive trion as a function of $d$.

Figure 3

(Color online) (a) PL spectrum of a QD with $d=0.5\text{nm}$ acquired at a polarization angle of $45°$. (b) Polarization-angle-dependent PL intensity (grayscale coded) for the X, ${\text{X}}^{+}$, and XX lines. (c) Normalized PL spectra at polarization angle of $0°$ and $90°$ for the corresponding peaks.

Figure 4

(Color online) (a) Calculated binding energies of negative trion (squares), positive trion (circles), and biexciton (triangles) as a function of the WL thickness $h$, which is defined in the left bottom inset. The binding energies of the positive trion without taking into account the correlations (open circles) are also plotted. The top inset shows an example spectrum for $h=0$, where the binding energy for the positive trion is indicated (the energy in the horizontal axis is indicated in meV). (b) Calculated electron and hole densities (solid lines) and the effective potential (see also Fig. 8) felt by the electrons and holes (dashed lines) in the [110] direction.

Figure 5

(Color online) (a) PL spectra at different excitation powers for a QD with $d=0.5\text{nm}$. Grayscale-coded PL intensity measured at 6 K as a function of excitation power and emission energy for single QDs of samples with (b) $d=0.5\text{nm}$, (c) $d=1\text{nm}$, (d) $d=2\text{nm}$, and (e) $d=4\text{nm}$. The right panel shows corresponding PL spectra collected on a wider spectral range, where the emission from bulk GaAs, QDs, GaAs WL, and ${\text{Al}}_{0.35}{\text{Ga}}_{0.65}\text{As}$ are indicated. The red dotted lines in (f) and (g) show spectra collected at very high excitation power in the energy range of 1.65–2.02 eV. The inset in (i) shows a high-resolution spectrum between 1.9 and 2.1 eV, where the emission from bound excitons in the ${\text{Al}}_{0.35}{\text{Ga}}_{0.65}\text{As}$ barrier is emphasized.

Figure 6

(Color online) (a) Emission energy of GaAs QDs and WL for samples of various $d$. Solid lines are linear fits and serve as guide to the eyes. (b) Energy separation between ground state and first excited state for each sample as a function of confinement energy, which is defined by the energy difference between QDs and WL emission for each sample.

Figure 7

(Color online) (a) Calculated energy of the lowest transition, excluding (squares) or including (circles) Coulomb interaction, as a function of QD height. (b) Calculated energy spacing between ground state and first excited-state transition, excluding (squares) or including (circles) Coulomb interaction, as a function of QD height.

Figure 8

(Color online) (a) Calculated effective lateral potential (for electrons) along the [110] direction for different thicknesses of WL. (b) AFM linescan of the bottom QD barrier along the [110] direction with indicated filling levels of $h$ used for calculations.

Figure 9

(Color online) (a) Comparison of measured (symbols) and predicted $\left(\text{line}+\text{triangles}\right)$ transition energies and ground state to excited-state separation. Different symbols correspond to different thicknesses of WL $d$ as indicated. (b) Comparison of QD heights estimated from AFM images [see Fig. 1g] (squares) and heights of model structures fitted to the observed energies (circles). (c) Comparison of measured (symbols) and calculated (line) transition energies of GaAs/AlGaAs WL.