Quantum-confined Stark shifts of charged exciton complexes in quantum dots

We probe the permanent excitonic dipole of neutral and positively charged excitons in individual ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{As}$ self-assembled quantum dots using Stark effect perturbation spectroscopy. A systematic reduction of the permanent excitonic dipole is found as excess holes are controllably added to individual dots containing a single exciton $\left(X^0\right)$. Calculations of the few-body states show that this effect arises from a strong, Coulomb-mediated, spatial redistribution of the few-body wave function upon charging. By investigating correlations between the permanent dipole, polarizability, and the emission energy of $X^0$ for many dots, we also show that the strength of the $\mathrm{In}:\mathrm{Ga}$ composition gradient is related to the absolute In content.

Figure 1

Single dot PL spectra obtained from (a) dot $A$ and (b) dot $B$ as a function of $V_g$ from $+1.9\mathrm{V}$ (lower trace) to $-0.3\mathrm{V}$ (upper trace). Neutral $\left(X^0\right)$ and charged ($X^{+}$, $X^{++}$) single excitons are observed. (c) Peak positions of the $X^0$, $X^{+}$, and $X^{++}$ transitions as a function of $V_g∕F_z$. Parabolic fits to the data are also shown from which $p_z$ and $\beta$ are extracted.

Figure 2

Summary of (a) $p_z$ and (b) $\beta$ values measured from many single dots for $X_0$ plotted as a function of $E_0$. (c) Percentage change of exciton dipole upon adding one [$X^0\to X^{+}$ (open symbols)] or two [$X^0\to X^{++}$ (filled symbols)] holes.

Figure 3

(Color online) Calculated values of (a) $\Delta p_z^{+}$ and (b) $\Delta p_z^{++}$ as a function of dot width for linear (squares), inverted pyramidal (circles), and trumpet (triangles) $\mathrm{In}$ profiles. The shaded regions show the mean experimental values.

Figure 4

(Color online) Electron and heavy hole $\sim 50\%$ constant probability isosurfaces for $X^0$ and $X^{+}$ for QDs having a width of $w=14$ and $20\mathrm{nm}$. As described in the text, the lateral redistribution of the electron and hole components of the wave function can clearly be seen.