Excitonic fine structure and binding energies of excitonic complexes in single InAs quantum dashes

The fundamental electronic and optical properties of elongated InAs nanostructures embedded in quaternary InGaAlAs barrier are investigated by means of high-resolution optical spectroscopy and many-body atomistic tight-binding theory. These wire-like shaped, self-assembled nanostructures are known as quantum dashes and are typically formed during the molecular beam epitaxial growth on InP substrates. In this paper, we study properties of excitonic complexes confined in quantum dashes emitting in a broad spectral range from below 1.2 to 1.55 μm. We find peculiar trends for the biexciton and negative trion binding energies, with pronounced trion binding in smaller size quantum dashes. These experimental findings are then compared and qualitatively explained by atomistic theory. The theoretical analysis shows a fundamental role of correlation effects for the absolute values of excitonic binding energies. Eventually, we determine the bright exciton fine structure splitting (FSS), where both the experiment and theory predict a broad distribution of the splitting varying from below 50 to almost 180 μeV. We identify several key factors determining the FSS values in such nanostructures, including quantum dash size variation and composition fluctuations.

Figure 1

(a) The STEM micrograph of cross-sectional sizes of single QDashes (after Ref. [12]) showing a triangular geometry and (b) the SEM image of the uncapped QDash layer.

Figure 2

Photoluminescence emission from quantum dash ensemble for different nominal InAs layer thicknesses overlapping with the second (1300 nm) and third (1550 nm) telecommunication low loss windows.

Figure 3

(a) Microphotoluminescence spectra for various excitation powers from 0.5 to 5 μW. The inset shows the intensity dependence with a slope variation depending on the spectral feature. (b) Polarization resolved spectra showing fine structure splitting indicating exciton and biexciton emission and no splitting for charged exciton.

Figure 4

Excitonic complexes for different emission wavelengths showing alike spectroscopic pattern for biexciton and trion transitions.

Figure 5

Binding energy of biexciton (circle) and charged exciton (star) state determined for ca. 50 single QDashes in dependence of exciton emission energy.

Figure 6

Exciton fine structure splitting averaged from biexciton and exciton transition in emission energy dependence.

Figure 7

Exciton ground state energy calculated using different atomistic approaches as a function of quantum dash size $(H$ – Height, $W=4\times H,L=4\times W)$.

Figure 8

Electron-electron $\left(J_{\mathrm{ee}}\right)$, electron-hole $\left(J_{\mathrm{eh}}\right)$, and hole-hole $\left(J_{\mathrm{hh}}\right)$ Coulomb integrals for electron and hole occupying their ground states calculated for several QDashes of different energy and using different atomistic approaches.

Figure 9

Binding energies of biexciton (circles) and charged exciton (stars) calculated using a configuration interaction model and different atomistic approaches (see the text) as a function of exciton emission energy.

Figure 10

Negatively charged exciton $\mathrm{\Delta }E\left(X^{-}\right)$ and the biexciton $\mathrm{\Delta }E\left(XX\right)$ binding energies in Hartree-Fock (HF) and configuration interaction (CI) pictures, calculated using VCA (see the text).

Figure 11

Exciton fine structure splitting calculated using different atomistic approaches (see the text) as a function of exciton emission energy.

Figure 12

Exciton fine structure splitting calculated to illustrate the role of lattice randomness. These results were obtained by putting together six random realizations (samples) for each quantum dash size (five different sizes) considered in the paper, giving a total of 30 systems. Each sample corresponds to different local atomic arrangements, whereas the average composition remains constant in all samples [46]. Calculations were performed using the ATM+Intermixing model, where $\mathrm{I}{\mathrm{n}}_{0.9}\mathrm{G}{\mathrm{a}}_{0.05}\mathrm{A}{\mathrm{l}}_{0.05}\mathrm{As}$ QDash was embedded in the $\mathrm{I}{\mathrm{n}}_{0.528}\mathrm{G}{\mathrm{a}}_{0.234}\mathrm{A}{\mathrm{l}}_{0.238}\mathrm{As}$ barrier.