InAs/AlGaAs quantum dots for single-photon emission in a red spectral range

We report on comparative optical studies of InAs/Al0.44Ga0.56As quantum dots (QDs) grown by molecular beam epitaxy either with or without a thin GaAs interlayer inserted between the AlGaAs barrier and InAs QDs. Emission properties of individual QDs are investigated by micro-photoluminescence spectroscopy using 500-nm-size etched cylindric mesa structures. The single-photon statistics of the QDs of both types, emitting in the red spectral range between 636 and 750 nm, is confirmed by the measurements of the second-order correlation function. A negligibly small exciton fine structure splitting is detected in the majority of the QDs grown with the GaAs interlayer that implies the possibility of generating pairs of entangled photons with high entanglement fidelity.

Generation of the polarization-entangled photons, realized with the use of a biexciton-exciton radiative cascade 31 , requires thorough control over exciton fine structure splitting (FSS), originating in the QDs with a zinc-blende structure from an asymmetric dot shape, strain, or piezoelectric effects 32 . Due to the respective reduction of the confinement symmetry (down to C 2v or lower), the anisotropic part of the electron-hole exchange interaction splits the exciton bright state into two eigenstates, which are linearly polarized along the crystallographic axes [110] and [110] [33][34][35] . If the FSS is larger than the exciton homogeneous linewidth, it prevents the polarization entanglement of the emission 36,37 . Thus, the key condition of the generation of entangled photon pairs in a QD is the FSS reduction. The published data on the FSS values in the self-organized QDs, fabricated using the (In,Ga,Al)As material system, are sparse and contradictory. Finley et al. 20 reported on observation of the FSS as large as ~1 meV in InAs/Al 0.6 Ga 0.4 As QDs emitting over the range between 1.55 and 1.64 eV (800 and 756 nm correspondingly). On the other hand, Gaisler et al. 22 have recently observed a large number of Al 0.1 In 0.9 As/ Al 0.24 Ga 0.76 As QDs (~30% of the total amount), emitting near 770 nm, with a record small FSS values below 10 μeV. These data imply a complicated dependence of the exciton FSS in the InAs/AlGaAs QDs on precise details of the involved growth procedure.
In this paper, we present comparative optical studies of InAs/Al 0.44 Ga 0.56 As QDs grown by MBE either with or without an ultra thin GaAs interlayer inserted between the bottom AlGaAs barrier and InAs QDs. Emission properties of individual QDs are investigated by micro-photoluminescence (μ-PL) spectroscopy, which confirms the single-photon nature of the QDs emission in the red spectral range between 636 and 750 nm and demonstrates a pronounced effect of the GaAs interlayer formation, consisting in an essential decrease of the exciton FSS.
The rest of the paper is organized as follows. In the next section, we sequentially present and discuss the findings pertaining to general structural and optical characteristics of the InAs/AlGaAs QD structures, exciton FSS in the differently grown QDs, and statistical properties of the single-QD emission. Then, our conclusions are summarized. Finally, details of the measurement techniques are described in the section Methods.

Results and Discussion
Optical and structural characterization. The experiments were carried out using two series of samples fabricated by MBE, which contain self-assembled InAs QDs grown using the Stranski-Krastanow growth mode. In the samples of both kinds, the intended average thickness of the InAs deposition amounts to 1.7 monolayers (ML). The structures are grown on a GaAs (100) substrate capped with a 0.2-μm thick GaAs buffer, which is followed by InAs QDs formed between 200-nm-thick bottom and 50-nm-thick top Al 0.44 Ga 0.56 As barrier layers at a growth temperature 510-520 °C and growth rate ~0.01 ML/s ( Fig. 1(a)). In the samples of one series, QDs were grown with a predeposition of a 2-ML-thick GaAs interlayer, whereas in the samples of the other series, QDs were formed directly on the Al 0.44 Ga 0.56 As barrier layer. Further we discuss properties of two representative samples named as sample A (with the GaAs interlayer) and sample B (without the interlayer).
Surface density and geometrical parameters of QDs were estimated in samples A and B by means of transmission electron microscopy (TEM). Figure 1 shows the selective TEM images allowing estimation of the average QD surface density as ~10 10 cm −2 in sample A and ~5 · 10 9 cm −2 in sample B. Most of the QDs in sample A possess lateral sizes 10-20 nm and a height 3-4 nm. The QDs in this sample are square-based and show no indication for in-plane elongation ( Fig. 1(d)). In sample B, accurate evaluation of the QD shape is hampered by a much weaker contrast of the TEM images, arising from the smaller In content in the alloyed QDs and/or smaller QD size along the growth direction.
The PL spectrum of sample A with the inserted GaAs interlayer demonstrates two separated peaks ( Fig. 1(b)), which can be attributed to the emission of the QDs and a wetting layer (WL). The QD PL line is centered between 900 and 1000 nm that is similar to the emission of the InAs/GaAs QDs, while the higher energy tail of the line spreads up to the WL peak located near 690 nm. The emission line in sample B is markedly blue-shifted relative to that in sample A. This shift indicates smaller sizes of the formed QDs and, possibly, stronger incorporation of Al atoms into the QDs, induced by diffusion and/or segregation during growth. The QD emission line merges with the WL emission, spreading over the extremely wide energy range between ~1.4 and ~2 eV (890-620 nm).
The μ-PL spectra measured at 8 K reveal a number of relatively narrow lines (~100 μeV), which can be assigned to the emission of neutral excitons (X) and electron-hole complexes: biexcitons (XX) and charged excitons (negatively (X − ) and positively (X + ) charged trions) in individual QDs. The origin of the particular lines can be identified by performing excitation-and polarization-dependent measurements (see Fig. 2) [38][39][40] . Thus, the exciton and biexciton emissions are distinguished by their characteristic excitation-power dependence, which is either linear (exciton) or quadratic (biexciton) (insert in Fig. 2(a)). In the experiments described further, the excitation power was kept low enough to ensure dominant excitation of neutral excitons rather than biexcitons. As for trions, either negative or positive, their emergence implies loading of a QD with an additional charge carrier (electron or hole), which is provided by doping or is injected optically due to the difference in the electron-and hole-diffusion lengths. In the InGaAs/GaAs QDs, the X − emission line emerges 4.5-6.0 meV below X, whereas X + line in most cases is slightly (~1 meV) blueshifted with respect to X 41 . The major signature of the singlet trion state Fine structure splitting. It was found that within the measurement accuracy many emission lines (~80%) in both samples are unsplit and nonpolarized. An example of such lines observed in sample A is shown in Fig. 2(b). In principle, they can be attributed either to the emission of excitons with negligibly small FSS, or to the emission of trions. The remnant part of QDs in this sample display different FSS in the range of values from nearly zero to the extremely large FSS of the order of 450 μeV. Moreover, certain lines demonstrate small but distinct negative FSS, as shown in Fig. 2(c) demonstrating two doublet lines with different both signs and amplitudes of the FSS. Note that the FSS sign inversion was previously observed in the ensemble of InAs/GaAs QDs with small sizes 39 . All observed strongly split lines with certain linear polarization possess likely the strong asymmetry that reflects strong valence band mixing induced by the in-plain strain and shape anisotropy [42][43][44][45] . Such asymmetric QDs are definitely useless for the generation of the entangled photons. However, only few such lines were found in measured spectra, while the majority of the detected lines were only weakly split (if at all) that is a signature of the symmetric QDs.
The narrow emission lines in sample A emerge between 1.25 and 1.8 eV. All together, 118 randomly located lines were taken into account to estimate statistical distribution of FSS versus the emission photon energy. Among them, there are 95 lines with the FSS values less than the measurement accuracy (see Methods), which are considered as unsplit lines, and 23 split lines with measurable FSS values. The latter lines can be reliably attributed to the emission of neutral excitons. Filled squares in Fig. 2(d) represent the measured FSS of these excitonic lines as a function of the respective photon energy. The FSS is large and positive at small energies below 1.4 eV and rapidly decreases with the energy increase so that above ~1.5 eV the FSS values scatter around zero. By analogy with InAs/GaAs QDs 39 , this dependence indicates a rapid reduction of the FSS with a decrease in the QD size. The symmetric scattering of the data points around zero implies that at least a part of the "unsplit" lines, in fact, originate from the excitonic states with negligibly small FSS. Thus the smallest QDs emerging in sample A look very promising for both quantum cryptography and quantum computing applications, since they emit light near 750 nm, have small surface density, and possess negligibly small FSS.
In sample B, the statistical distribution of FSS values is essentially different (see filled triangles in Fig. 2(d)). There are 13 lines with measurable FSS among 84 lines, which were taken into account. These lines emerge between 1.7 and 2.0 eV and the respective average FSS values relatively weakly depend on the photon energy. The FSS sign is always positive and its amplitude scatters among different lines in the range of 10-180 μeV. The nonsymmetric distribution of the FSS values around zero (absence of negative values) implies that most of the "unsplit" lines observed in this sample correspond to the truly nonpolarized emission of trions. Note that, although the singlet trion states are not suitable for the generation of entangled photon pairs, their application for ultrafast generation of single photons is preferable, as compared with neutral excitons, due to the absence of dark-state configurations 46 .
Single-photon emission. Figure 3 presents examples of autocorrelation function g (2) (τ) measured at T = 8 K within the narrow emission lines representative for samples A and B. The function is normalized according to the formula: C N (t) = c(t)/ (N 1 N 2 ωT), where c(t) is raw coincidence number, N 1,2 are single counters rates, ω is width of time bin, and T is a total acquisition time 47 . The shape of the functions is characteristic of excitonic lines and can be well fitted with the equation For the measured correlation functions, the fitting gives the value of g (2) (0) < 0.2 that is a clear signature of the single-photon nature of the emission. The value at zero time does not reach zero as for a perfect single-photon emitter, most probably, because of presence of a background radiation, which contributes to the registered correlated counts. The achieved intensity of the single photon emission is about ~100 kHz being limited by the non-optimized extraction efficiency of photons in the simplified test mesa-structures. Further improvements in both purity and intensity of the emission imply the development of a cavity structure or a broadband waveguide nanoantenna with improved photons extraction efficiency 48 , as well as the realization of background-free resonance fluorescence 49 .

Conclusion
To summarize, we have presented comparative studies of self-assembled InAs/Al 0.44 Ga 0.56 As QDs grown either with or without a GaAs interlayer. Both approaches allowed us to obtain QDs generating single-photon emission in the red visible spectral range. The QDs grown on top of the thin GaAs interlayer emit light in an extended range of 700-1000 nm. Especially useful for the development of the red single-photon sources are the QDs of smallest sizes, demonstrating small spectral density of the single-QD excitonic lines in the spectral range 700-750 nm and demonstrating negligibly small exciton FSS that is advantageous for the generation of entangled photon pairs. The structures grown without the interlayer are especially suitable for the single-photon generation at the shortest wavelengths down to 636 nm. These characteristics of single InAs/AlGaAs QDs make them promising for development of either cavity or photonic waveguide structures, intended for the generation of intense and pure quantum light in the red spectral range.

Methods
Measurements. TEM measurements were carried out using a Jeol JEM-2100F microscope. The emission of a limited number of individual QDs was detected by a confocal μ-PL set-up in cylindrical mesa-structures of 500 nm in diameter, which were fabricated by electron beam lithography and Ar + -ion etching for reducing the number of registered QDs.
μ-PL data were obtained at low temperature of 8 K. The samples were mounted in a He-flow cryostat with an Attocube XYZ piezo-driver inside, which allowed us to optimize and precisely maintain the positioning of a chosen mesa with respect to a laser spot during a long time (few hours). The luminescence was dispersed by a 0.5 m monochromator with a 1200/mm grating, providing direct spectral resolution ~70 μeV. Nonresonant optical excitation by a cw laser line (405 nm) was used for the μ-PL measurements. The laser power density was below 4 W/cm 2 . The measurements were carried out in a backward geometry for orthogonal linear polarizations corresponding to [110] and [110] crystal directions of the QD sample. Polarization control was achieved by means of a halfwave plate and a Glan-Taylor prism installed in the detection channel. In order to register the splitting between two linearly-polarized excitonic lines with the accuracy beyond the spectrometer resolution, the measured lines were fitted by Lorentzian curves and the maxima of the fitted contours were taken as the peak maxima. The limiting precision of thus measured FSS was estimated as ~20 μeV.
Photon correlation measurements were performed in a Hanbury Brown-Twiss detection scheme exploiting two single-photon avalanche silicon diodes possessing the photon timing resolution of about 40 ps.
Data availability statement. The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.