Spontaneous brightening of dark excitons in GaAs/AlGaAs quantum dots near a cleaved facet

Dark excitons (DEs) confined in epitaxial quantum dots (QDs) are interesting because of their long lifetime compared to bright excitons (BEs). For the same reason they are usually difficult to access in optical experiments. Here we report on the observation of vertically polarized light emission from DEs confined in high-quality epitaxial GaAs/AlGaAs QDs located in proximity of a cleaved facet of the QD specimen. Calculations based on the eight-band k·p method and configuration interaction allow us to attribute the brightening of the DE to the anisotropic strain present at the sample edge, which breaks the symmetry of the system and enhances valence-band mixing. The mechanism of DE brightening is discussed in detail by inspecting both the Bloch and envelope wave functions of the involved hole states. In addition, by investigating experimentally and theoretically QDs with different sizes, we find that the energy separation between DE and BEs tends to decrease with increasing QD height. Finally, the presence of a cleaved facet is found also to enhance the BE fine structure splitting. This work provides a simple method to optically probe dark excitonic states in QDs and shows that the properties of QDs can be significantly affected by the presence of nearby edges.

Figure 1

(a), (c), and (e) Color-coded linear-polarization-resolved spectra collected from a cleaved facet of QD samples with GaAs QDs obtained by filling AlGaAs nanoholes with 1, 1.5, and 2 nm GaAs, respectively. 0° corresponds to the [110] crystal direction, while ${90}^{\circ }$ corresponds to the [001] direction (growth direction). Logarithmic color scale is used for the spectrum intensity. (b), (d), and (f) Spectra extracted from (a), (c), and (e), respectively, at polarization angles of $0^{\circ }$ (red squares) and ${90}^{\circ }$ (black circles). $D_1$ labels the DE component, $B_1/B_2$ labels the lower/higher components of the BE doublet. The intensity of $D_1$ and $B_1$ is magnified by a factor of 3. The insets in (b) show the experimental configuration for the measurements and the sketched crystal directions (the excitation laser and collection path are parallel to the [1–10] crystal direction).

Figure 2

Experimental and calculated energy separation between DE $\left(D_1\right)$ and BE $\left(B_2\right)$ as a function of dark exciton energy. The scattered symbols are experimental data. The line plus symbols show the calculated results of QDs with height from 2.6 to 8.6 nm with a step of 1 nm.

Figure 3

Relative DE decay rate (divided by the BE decay rate) and $|LH\downarrow \rangle$ weight (in the spin-up hole ground state ${\psi }_H^{\uparrow }$, which is dominated by $|HH\uparrow \rangle )$ as functions of local strain field (a) and (c) and electric field (b) and (d) for several QDs with different sizes. The $|LH\uparrow \rangle$ component is not included because it does not contribute to the optical response (see text). The strain along [1–10] and the electric field along the [1–10] crystal direction are taken as the independent variables.

Figure 4

Significant envelope functions (represented by probability density distributions) of the ground spin-up electron and hole states in a GaAs QD with a height of 6.6 nm. (a) and (b) electron, $|S\uparrow \rangle$ component. (c) and (d) QD planar cross sections on the (001) plane through the midheight and on the (1-10) plane through the center, respectively (black: GaAs, yellow: $\mathrm{A}{\mathrm{l}}_{0.4}\mathrm{G}{\mathrm{a}}_{0.6}\mathrm{As})$. (e)–(p) Components of the spin-up hole ground state ${\psi }_H^{\uparrow }$: $|HH\uparrow \rangle$ with no strain (e) and (f) and with an additional uniaxial strain $\left(\varepsilon =0.1\%\right)$ along the [1–10] direction (g) and (h); $|LH\uparrow \rangle$ with no strain (i) and (j) and with strain (k) and (l); $|LH\downarrow \rangle$ with no strain (m) and (n) and with strain (o) and (p). The two-dimensional graphs are constructed by integrating the density over the third (nondisplayed) coordinate. The color scale is normalized to the respective maxima.

Figure 5

(a) and (b) Calculated fine structure splitting (FSS) of the bright in-plane-polarized excitons as a function of strain (a) and electric field (b) for QDs with different sizes. (c) and (d) Representative color-coded polarization-resolved spectra (collected along the growth direction) of QDs, obtained by 2 nm GaAs filling, in the center and near the cleaved edge of a sample.