Tuning the Exciton Binding Energies in Single Self-Assembled $\mathrm{InGaAs}/\mathrm{GaAs}$ Quantum Dots by Piezoelectric-Induced Biaxial Stress

We study the effect of an external biaxial stress on the light emission of single $\mathrm{InGaAs}/\mathrm{GaAs}(001)$ quantum dots placed onto piezoelectric actuators. With increasing compression, the emission blueshifts and the binding energies of the positive trion ($X^{+}$) and biexciton ($XX$) relative to the neutral exciton ($X$) show a monotonic increase. This phenomenon is mainly ascribed to changes in electron and hole localization and it provides a robust method to achieve color coincidence in the emission of $X$ and $XX$, which is a prerequisite for the possible generation of entangled photon pairs via the recently proposed “time reordering” scheme.

Figure 1

(a) Level schemes showing the $XX\mathrm{\text{−}}X$ cascade. The solid (dashed) line represents the decay channel that yields $H$ ($V$) polarized photons. Across generation color coincidence of $X$ and $XX$ ($E_X=E_{XX}$) can be achieved by applying tensile (compressive) stress to a QD with positive (negative) $E_B(XX)$. (b) Schematic drawing of the experiment and optical microscopy image of a 200 nm-thick GaAs membrane (inset). (c) Low temperature PL spectra of QDs with negative (QD1) and positive (QD2) $XX$ binding energy.

Figure 2

Color-coded PL intensity of QD1 (a) and QD2 (c) as a function of emission energy and voltage applied to the actuator. The binding energies of $XX$ and $X^{+}$ show a linear increase with $E_X$ for both QDs, as shown in (b) and (d). (e) Binding energies at $V=0$ and (f) slopes ${\gamma }_{XX}$ and ${\gamma }_{X^{+}}$ for 14 different QDs.

Figure 3

(a) Calculated emission energies of $X$, $XX$, and $X^{+}$ as a function of in-plane biaxial strain ${\epsilon }_{\parallel }$. (b) Relative binding energies of $X^{+}$ and $XX$ vs $E_X$. (c) Changes in Coulomb integrals with biaxial strain. (d) Calculated band offset diagram at ${\epsilon }_{\parallel }=0$; for the valence band, the size of the circles is proportional to the heavy-hole character of the bands. (e) Changes in CBO (VBO) with strain ${\epsilon }_{\parallel }$. (f) HOMO and LUMO wave functions at ${\epsilon }_{\parallel }=0.1\%$ and $-1\%$. The red color encloses 75% of the charge density, while light gray color represents the outline of the QD.

Figure 4

(a) Biexciton binding energy of QD3 as a function of $E_X$. Several spectra are shown, demonstrating the decreasing distance between $X$ and $XX$ with increasing $E_X$. (b) Polarization-resolved PL map for the $X$ and $XX$ lines at several voltages. At 0 V $E_B(XX)$ is much larger than $\delta$, while $E_B(XX)$ vanishes (limited by the system resolution) and $\delta$ dominates at 1100 V.