Excited-state indirect excitons in GaAs quantum dot molecules

We demonstrate the fabrication of strain-free and widely adjustable GaAs quantum-dot molecules (QDMs) by filling of droplet etched nanoholes in AlGaAs. Gate-voltage dependent optical spectra of highly asymmetric QDMs exhibit anticrossings that clearly indicate strong coupling with delocalized molecule states. Furthermore, indirect excitons are observed that are related to recombinations of excited-state electrons and ground-state holes both located in different dots. Simple numerical simulations reproduce the electric-field dependent energy shifts of direct and indirect transitions and predict their radiative lifetimes. The visibility of excited-state indirect excitons even for strong off-resonant energy detuning indicates the presence of a phonon bottleneck which suppresses the relaxation of excited electrons into lower levels.

Figure 1

(a) Schematic of the QDM fabrication process with droplet material deposition, self-assembled droplet etching, and hole filling with $\mathrm{QD}{}_{\mathrm{B}}$, tunnel barrier, and $\mathrm{QD}{}_{\mathrm{T}}$. (b) Micro-PL measurement at $T=8$ K of a single QDM with $d_B=0.45$ nm, $d_T=0.88$ nm, and AlAs tunnel barrier of $d_{TB}=3$ nm. The exciton peaks are marked by X and the respective linewidths are given. (c) $\mathrm{QD}{}_{\mathrm{T}}$ and $\mathrm{QD}{}_{\mathrm{B}}$ PL ground-state energies from samples with varied $d_T$ and tunnel barrier material (AlGaAs or AlAs), $d_B=0.45$ nm, and $d_{TB}=3$–5 nm. The error bars represent measurements of 5 to 10 QDMs from each sample. Green arrows mark the sample that is discussed in this paper. (d) Schematic band diagram of the studied QDMs with average ground-state and quantization energies in meV. Note that the band gap does not scale with the size quantization as indicated by the $\approx$ signs.

Figure 2

(a) AFM line scans with equal $x$- and $y$-axis scales along [110] direction from a sample series illustrating the different interfaces during QDM fabrication, i.e., the initial nanohole in the AlGaAs substrate (green), the hole filled with $\mathrm{QD}{}_{\mathrm{B}}$ (red), the AlAs tunnel barrier (blue), $\mathrm{QD}{}_{\mathrm{T}}$ (red), and the AlGaAs cap layer (green). The baselines of the individual AFM scans are offset by the respective deposited layer thickness. (b) Approximated QDM shape used for the simulations. The QD axis is at $x=0$ and the dot is rotational symmetric to this axis. (c) Simulated square of the wave function of the 19th QDM hole level representing the $\mathrm{QD}{}_{\mathrm{T}}$ hole ground state at $F=0$. (d) The 10th QDM electron level at $F=0$, (e) the 11th QDM electron level representing the $\mathrm{QD}{}_{\mathrm{T}}$ electron ground state at $F=0$, (f) the 10th QDM electron level at $F=F_0=5$ kV/cm (resonance), and (g) the 11th QDM electron level at $F=F_0$.

Figure 3

(a) Gray-scale plot of the PL emission intensity at $T=8$ K from the top dot of a GaAs QDM as function of electric field $F$ varied by a gate voltage. (b) Simulated energy of a direct exciton X $({\mathrm{E}}_{e11},{\mathrm{E}}_{h19})$ and indirect exciton iX $({\mathrm{E}}_{e10},{\mathrm{E}}_{h19})$ at varied $F$. The electric field is given relative to the field $F_0$ at resonance.

Figure 4

(a) Lifetimes of X and (b) iX at varied $F$. The lifetimes are calculated from the overlap integral ${\langle {\mathrm{\Psi }}_e|{\mathrm{\Psi }}_h\rangle }^2$ of the simulated electron and hole wave functions according to Fermi's golden rule [24].