Excitonic complexes in MOCVD-grown InGaAs/GaAs quantum dots emitting at telecom wavelengths

Hereby, we present a comprehensive experimental and theoretical study of the electronic structure and optical properties of excitonic complexes in strain-engineered InGaAs/GaAs quantum dots (QDs) grown by metalorganic chemical vapor deposition and emitting at the 1.3-µm telecommunication window. Single QD properties have been determined experimentally for a number of nanostructures by means of excitation-power-dependent and polarization-resolved microphotoluminescence and further compared with the results of confined states calculations employing the eight-band k·p theory combined with the configuration interaction method. The origin of excitonic complexes has been exemplarily confirmed based on magneto-optical and correlation spectroscopy study. Understanding the influence of structural parameters and compositions (of QDs themselves as well as in the neighboring strain-reducing layer) allows identification of which of them are crucial to control the emission wavelength to achieve the telecommunication spectral range or to affect binding energies of the fundamental excitonic complexes. The obtained results provide deeper knowledge of control and limitations of the investigated structures in terms of good spectral isolation of individual optical transitions and spatial confinement, which are crucial in view of QD applications in single-photon sources of high purity at telecom wavelengths.

Figure 1

(a) Sample layout of the investigated QD structure with GaAs substrate and buffer layer — 23 pairs of $\mathrm{GaAs}/\mathrm{A}{\mathrm{l}}_{0.9}\mathrm{G}{\mathrm{a}}_{0.1}\mathrm{As}$ layers to form the DBR, a single $\mathrm{I}{\mathrm{n}}_{0.75}\mathrm{G}{\mathrm{a}}_{0.25}\mathrm{As}$ QD layer on the wetting layer, and embedded in an $\mathrm{I}{\mathrm{n}}_{0.2}\mathrm{G}{\mathrm{a}}_{0.8}\mathrm{As}$ strain-reducing layer (SRL) capped with a thick GaAs layer suitable for the fabrication of a nanophotonic mesa structures with a 2-λ cavity. (b) High-resolution low-temperature microphotoluminescence spectrum of single QDs located in the 1.5-µm-diameter mesa structure obtained under nonresonant excitation. To facilitate single QD experiments, a regular pattern of cylindrical mesas with varying diameters was fabricated using standard electron-beam lithography followed by reactive-ion etching. Inset: Scanning electron microscope image of the investigated mesa structure.

Figure 2

(a) High-resolution low-temperature microphotoluminescence (µPL) spectra from a single QD for two orthogonal linear polarization directions: along the [1-10] direction (black solid line) and [110] direction (red solid line) with various excitonic complexes marked as X (neutral exciton), XX (biexciton), ${\mathrm{X}}^{+}$ and ${\mathrm{X}}^{-}$ (positively and negatively charged excitons). Other spectral features might be related to further excitonic complexes, those including carrier(s) in an excited state. Also, their origin from a second QD located in the same mesa cannot be excluded due to the relatively high QD spatial density. (b) Analysis of the µPL emission intensity as a function of excitation power for the emission lines marked in (a).

Figure 3

(a) Polarization-resolved µPL showing the same fine-structure splitting (FSS) for X (two bright excitons ${\mathrm{X}}_b$) and XX with opposite polarizations as well as the lack of the FSS for ${\mathrm{X}}^{+}$ and ${\mathrm{X}}^{-}$. (b, c) µPL spectra measured in magnetic fields of 0 and 5 T in Voigt configuration for two orthogonal linear polarizations together with extracted energy dependence of respective emission lines on the strength of the magnetic field showing the same quadruplet splitting of ${\mathrm{X}}^{+}$ and ${\mathrm{X}}^{-}$ as well as the dark exciton states ${\mathrm{X}}_d$. The following system parameter values could be determined: $g_{e,\perp }=0.99$; $g_{h,\perp }=0.28$ (absolute values); diamagnetic coefficient $a_{X,\perp }=2\mu \mathrm{eV}/{\mathrm{T}}^2$; exciton fine structure $\mathrm{\Delta }{E}_{X_b}=60\mu \mathrm{eV}, \mathrm{\Delta }{E}_{X_d}=20\mu \mathrm{eV}, \mathrm{\Delta }{E}_{X_b-X_d}=430$ µeV. (d, e) µPL spectra measured in magnetic field of 0 and 5 T in Faraday configuration together with extracted energy dependence of the respective emission lines on the strength of the magnetic field, based on which the exciton $g$ factor (absolute value) equaling 1.75 and diamagnetic coefficient of $a_X=13\mu \mathrm{eV}/T^2$ are obtained.

Figure 4

Energy-level scheme for basic excitonic complexes (X – neutral exciton, XX – biexciton, ${\mathrm{X}}^{+/-}$-positive/negative trion) and its evolution in external magnetic field in Voigt (a) and Faraday (b) configuration due to Zeeman effect (diamagnetic shift neglected for the sake of simplicity). The arrows indicate possible optical transitions, and the style of the line corresponds to the polarization of emitted radiation with dotted (solid) lines indicating circular (linear) polarization. H and V correspond to two orthogonal linear polarizations and ${\sigma }^{+/-}$ to right and left circular polarization.

Figure 5

(a) Cross-correlation of photon-emission events for emission lines preliminarily identified as XX and X, as well as for (c) X and ${\mathrm{X}}^{+}$ from a single QD (cf. Figs. 2 and 3); (b) photon autocorrelation for the X emission line measured at 5 K under nonresonant cw excitation: black line – measurement data, red line – (b) symmetric fit, and (c) asymmetric fit using the function $1-\left[1-g^{\left(2\right)}\left(0\right)\right]e^{-\left(\left|\tau \right|/t_c\right)},$ including convolution with the temporal resolution of the experimental setup (80 ps).

Figure 6

Summary of the statistical measurements on more than 10 QDs. (a) Fine-structure splitting (FSS) of the X (neutral exciton) as a function of X emission energy and FSS histogram (inset). (b) XX (biexciton), ${\mathrm{X}}^{+}$ (positive trion), and ${\mathrm{X}}^{-}$ (negative trion) binding energies as a function of X emission energy with solid lines providing a guide to the eye.

Figure 7

(a) Applied model structure of a QD. The In composition of $\mathrm{I}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{As}$ is color coded. (b) Composition evaluation by lattice fringe analysis (CELFA) image from TEM measurement of the representative InGaAs/GaAs QD taken upon rotation of the sample by 2°–4° out of plane [010] with the color scale referring to In content averaged over the sample thickness (see text for interpretation of the signal). Strongly inhomogeneous In distribution within the nanostructure volume is clearly visible.

Figure 8

(a) Influence of the number of electron/hole basis states included in the configuration interaction calculations on the binding energies of the basic excitonic complexes: positively (${\mathrm{X}}^{+}$) and negatively charged (${\mathrm{X}}^{-}$) trion and (XX) biexciton. (b) Coulomb interaction matrix elements for electron-electron $V_{ee}$ (black squares), electron-hole $V_{eh}$ (blue triangles) and hole-hole $V_{hh}$ (red dots) dependence on the average In content in the QD.

Figure 9

(a) Single-particle levels (dotted lines) calculated within the eight-band ${\mathrm{k}}^{.}\mathrm{p}$ model with the band edge along the growth direction marked for the conduction band (yellow solid line) and for the valence subbands: blue, green, and purple for heavy holes, light holes, and spin-orbit split-off band, respectively. (b) Probability density of the carrier distribution for the first hole (right column) and electron (left column) levels for cross sections along the growth direction (upper panel) and in plane (lower panel) through the center of the QD.

Figure 10

(a) Photoluminescence spectra of the QD ensemble for increasing excitation power exhibiting the state filling effect with higher energy states clearly resolved (upper panel) compared to the calculated excitonic spectrum (lower panel). (b) Calculated single QD spectrum (black solid line) and experimental values of the binding energies of the excitonic complexes (red arrows). The energy of the neutral exciton from experiment and calculations coincides and it is subtracted from the results.

Figure 11

Results from calculations within the eight-band ${\mathrm{k}}^{.}\mathrm{p}$ model combined with the configuration interaction method for binding energies of excitonic complexes as a function of (a) QD size – the height-to-base size ratio is kept constant, so the size scaling factor (SSF) represents the multiplication factor for dimensions in both directions; (b) average In content in the QD; and (c) In content in the InGaAs strain-reducing layer (SRL). The data are presented in dependence on the exciton emission energy. Nominal fixed parameters: (a) QD $r_b$: $15\mathrm{nm}\times \mathrm{SSF}$, QD h: 6 nm × SSF, average In content in QD: 73%, In content in SRL: 20%; (b) QD $r_b:15\mathrm{nm}$, h: 6 nm, In content in SRL: 20%; (c) QD $r_b:15\mathrm{nm}, h$ = 6 nm, average In content in QD: 73%. The marked region in (b) and (c) corresponds to the energy range and SRL composition, respectively, of experimental data available in the investigated sample. In the case of (a) the energy ranges are similar for both theoretical calculations and experimental data.