# Optical Quality of InAs/InP Quantum Dots on Distributed Bragg Reflector Emitting at 3rd Telecom Window Grown by Molecular Beam Epitaxy

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{0.53}Al

_{0.1}Ga

_{0.37}As layers of 123 nm and 110 nm nominal thickness, respectively (Figure 1b). The standard epitaxial growth procedure has been modified by adding a ripening step during the QDs growth [90,91]. This results in large in plane QDs with density on the level of 10

^{9}/cm

^{2}. The base diameter of the nanoobjects is in the range of (55 ± 15) nm and height-up to 15 nm [92]. More details on the growth are given in Ref. [85]. The spatial QD density is inferred based on atomic force microscopy (AFM) of the QDs grown by the same recipe but without the capping layer [85]. The investigated InAs/InP QDs have previously been tested in view of the single-photon generation and exhibited triggered high-purity single-photon emission in the telecom C-band even under non-resonant excitation [93]. In this work, two structures from the same grown wafer were used: (a) as-grown planar sample and (b) structured sample with cylindrical mesas, which in the text will be referred as patterned sample. The mesa structures were defined on the surface by electron-beam lithography, using SiO

_{2}mask and dry-etched with inductively coupled plasma reactive ion etching. The mesas were processed non-deterministically, and the mesa design is not optimized. The purpose of using mesas is to enable repeatable experiments on the same dot and provides the possibility to investigate different aspects of a selected QD in various experimental setups. However, one has to keep in mind that patterning the sample can influence the optical properties of QDs. The relevant effects are change of the photonic confinement and generation of carrier traps on the atomically rough mesa sidewalls. The weak cavity effects can be present in such case due to high refractive index contrast at air/semiconductor interface of the mesa structure. Carrier traps on mesa sidewalls might influence the charge state of the QD, introduce spectral diffusion and nonradiative recombination due to e.g., Auger-type processes. These issues will also be addressed.

**k∙p**method [101,102]. These include realistic strain distribution calculated within the continuous elasticity approach and piezoelectric effect up to the second-order in strain tensor components. They were performed to support the interpretation of the temperature-dependent μPL results. QD parameters, namely the diameter of 42 nm and height of 15 nm (lens-shape), are used in the calculations. The QD is placed on top of a 1.2 nm thick wetting layer and embedded in an InP matrix. For such a large purely InAs QD, the emission energy appears far too low. Therefore, a high level of As-P intermixing (25%) was included to bring the calculated ground state energy in agreement with the experimental findings. Measured emission from the QD ensemble at 4.5 K is centered at 0.805 eV. For simplicity and due to the lack of statistically relevant data in this regard, a homogeneous P distribution was assumed. The exact material parameters and more details on the modeling can be found in Ref. [88]. The implementation of the used

**k∙p**method is described in [103].

## 3. Results

#### 3.1. Internal Quantum Efficiency

_{SSPD}is the count rate measured on the single-photon detector at saturation power, f

_{laser}is the repetition rate of the excitation laser, and η

_{setup}is the efficiency/transmission of the experimental setup. This efficiency is determined in an independent experiment. For that purpose, the transmission of each optical element in the setup was measured for a laser with a wavelength corresponding to the QD emission. The quantum efficiency of the detectors measured during their installation (this includes the transmission of the fiber attached to the detectors and coupling of the optical signal from the fiber to the detectors) was considered. The setup efficiency is then the product of transmission of all the elements in the setup, which in our case yields 1.15%.

#### 3.2. Carrier Dynamics

_{1}in the range of (0.45–1.33) ns and the slower component τ

_{2}in the range of (1.06–1.95) ns and positive correlation between the two lifetimes; (iii) measurable rise time up to 0.15 ns followed by either mono- or two-component exponential decay—15% of cases (Figure 4c). As can be seen, the mono-exponential decay is by far the most typical behavior for the investigated structure. From the energy dispersion it seems it has no clear emission energy dependence. However, quite a broad distribution of the PL decay times is observed for a given emission energy. This might result from different excitonic complexes being analyzed, because identification of the origin of the emission lines was not performed. Flat lifetime dispersion was previously observed for nanostructures featuring an intermediate confinement regime. This is expected for large QDs [109]. It can also be a fingerprint that the emission energy is not determined by a single parameter. For example, both material composition and size differ from dot to dot. In that case, the emission energy changes, but the oscillator strength, and so the lifetime, is not strongly influenced. The limited structural data is insufficient to support the latter hypothesis. Observation of the PL rise time hints at the presence of an intermediate state in the relaxation path of the carriers created in the substrate material (non-resonant excitation). This can be the case, e.g., for a defect state in the vicinity of the QD effectively capturing the carriers on their way to QDs. Alternative might be a biexciton–exciton cascade. Recombination of the biexciton results in occupation of the exciton. Therefore, the PL rise time, corresponding to the lifetime of a biexciton, occurs in the PL time trace. This happens for excitation powers high enough to ensure occupation of the biexciton state [110]. In this case, the emission line which is analyzed is not occupied directly from the optical excitation, but some intermediate state within or in the vicinity of a QD mediates its occupation. The main relaxation mechanism in the case of non-resonant excitation–phonon relaxation, leads to the occupation of a given state in a femtosecond to single picosecond time scale [111]. This is too fast to be resolved in this experiment. The rise time is seen even for a low excitation power. In this excitation conditions, the probability of forming multicarrier complexes should be negligible. This suggests that it is rather not related to cascaded emission within the QD. The two-component exponential decay is not typical for investigated structures, as it is rarely observed. Similar decay curves, with a dispersion-less fast component, were previously observed in strongly asymmetric quantum dashes in InAs/InGaAlAs/InP. The two components were interpreted as corresponding to two bright excitons differing strongly in the transition oscillator strength [112]. In our case, the structures are symmetric, and therefore the same mechanism cannot be responsible for the substantial difference in lifetime between the two transitions. However, a significant degree of linear polarization of up to 50% was observed for single emission lines for these QDs (not shown here). This would be enough to explain the observed timescale differences. The gathered experimental data does not allow for unambiguous interpretation of the second PL decay time component, but this is something to keep in mind if fast QD depopulation is of interest.

#### 3.3. Thermal Stability of Emission

_{0.2}In

_{0.8}As

_{0.4}P

_{0.6}/InP quantum dashes [127]. This indicates that phonon modes of interest are related to the InP matrix. The LO phonon energy of bulk InP of 30 meV lies within this range [128]. The large distribution of obtained values is related to the fact that in the experiment, broadening does not originate only from the phonon effects but also from the spectral diffusion. The spectral diffusion is also temperature-dependent. Additionally, the figure of merit is the FWHM of the total emission (sum of the ZPL and acoustic phonon sidebands) [114]. Also, it is not without consequence that the emission can be observed on average up to 100 K, at which the LO phonon interactions become important.

_{i}of the respective processes are determined. These activation energies are around 25 meV and 3 meV for the higher and the lower efficiency process, respectively (Figure 8a). These are way too small for the carrier escape to the wetting layer or InP matrix directly. Therefore, they are interpreted as the carrier escape via the higher energy states within the QD. This is highly probable as the QDs are large, and the ladder of states is dense, so many states are confined within the QD. To get a deeper insight into the interpretation of determined activation energies, a single-particle energy spectrum of an exemplary QD was calculated. QD with a ground state transition corresponding to the energy of maximal PL intensity of the QDs’ ensemble was selected as the representative one. The results of the calculations are presented in Figure 8b. The s-p splitting equals to 20 meV and is shared in the relation 1:4 between the valence and conduction band, respectively. This allows us to interpret the lower/higher activation energy as a promotion of holes/electrons to the higher states within the QD. The determined activation energies do not show a clear dependence on the QDs’ emission energy (Figure 9b). This could be related to the fact that investigated examples are within a rather narrow energy range of 30 meV. It might be too small to reveal emission energy trends in the s-p splitting. Also, the dense energy spectrum can lead to a lack of dependence. Activation to different closely separated states is possible. Similar activation energies for PL quenching processes were previously reported for other InP-based structures emitting at 1.55 μm, i.e., low density InAs/InP quantum-dot-like structures grown by MOVPE [88] and MBE-grown InAs/InGaAlAs/InP QDs [90] as well as strongly elongated quantum dashes [122,130]. In the former, it was interpreted as a carrier escape to the excited state within QD alike our case. The investigated structures are also relatively large, with the height exceeding 9 nm. For quantum dashes, 20 meV was already enough for the electrons to escape directly to the wetting layer.

**Table 1.**Summary of the parameters determined from temperature-dependent microphotoluminescence measurements.

Parameter | Experiment | Literature | |
---|---|---|---|

$\alpha $ | $\left(0.24-0.38\right)\mathrm{meV}/\mathrm{K}$ | InAs: 0.276 meV/K InP: 0.363 meV/K | [117] |

$\beta $ | $\left(161-340\right)\mathrm{K}$ | InAs: 93 K; InP: 162 K | [117] |

$S$ | $\left(0.92-1.30\right)$ | ||

$\langle \hslash \omega \rangle $ | $\left(9.2-12.6\right)\mathrm{meV}$ | 2.07–23.99 meV | [120] |

${\gamma}_{Ac}$ | $\left(0.03-1.65\right)\mathsf{\mu}\mathrm{eV}/\mathrm{K}$ | ||

${\gamma}_{LO}$ | $\left(1.2-105.2\right)\mathrm{meV}$ | ||

$\Delta E$ | $\left(14-86\right)\mathrm{meV}$ | 29.77 meV | [128] |

${E}_{1}$ | $\left(1.6-5.7\right)\mathrm{meV}$ | ||

${E}_{2}$ | $\left(15.1-41.0\right)\mathrm{meV}$ |

## 4. Conclusions

**k·p**calculations of the single-particle energy spectrum allows us to identify the main cause of the PL quenching. That is the activation of electrons and holes to higher-energy states within the QD due to closely spaced energy levels, which is expected for large nanostructures. Improving the temperature stability of emission would require engineering of structures towards smaller heights. This would result in increasing the energy separation within the electron and hole ladder of states. The study on carrier dynamics revealed characteristic lifetimes, allowing in principle for GHz operation of QD-based devices. The obtained data from the patterned sample show a broader distribution of lifetimes and more complex dynamics with a second (longer) component present for most of the emission lines. To gain better understanding, further improvement of the fabrication process is required. To maintain the high optical quality of investigated QDs in photonic structures, optimization of the mesa design as well as deterministic positioning technology are required. These will allow for maximizing the emission extraction efficiency by matching to the optical properties of single QDs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic diagram summarizing the steps used in this work (

**b**) Scheme of layer design of the investigated structure with InAs/InP QDs on distributed Bragg reflector. Nominal (designed) thicknesses of the respective layers are presented on the right-hand side.

**Figure 2.**(

**a**) Exemplary photoluminescence spectra used for extraction efficiency measurements (non-resonant pulsed excitation with power corresponding to saturation conditions) (

**b**) Experimental (black squares) and calculated (blue dots) extraction efficiency for NA = 0.4 (left axis) with Gaussian fits (solid lines); right axis–PL intensity under non-resonant pulsed excitation with saturation power measured on SSPD at 5 K (whole spectrum on Figure 3; (

**c**) calculated extraction efficiency vs. numerical aperture of the first lens collecting the optical signal for source wavelength of 1535 nm for which maximal extraction efficiency was obtained; NA = 0.4 corresponding to experimental conditions marked with solid black lines; (

**d**) calculated distribution of electromagnetic field for 1535 nm wavelength, for which maximal extraction efficiency was obtained; the intensity of electric field component is color-coded and presented in a logarithmic scale; the calculations are performed for numerical aperture of 0.4.

**Figure 3.**Low-temperature (T = 4.5 K) photoluminescence (PL) spectrum from planar Scheme 0. (μW) using single-photon superconducting nanowire detectors.

**Figure 4.**Normalized low-temperature (T = 4.5 K) and low-excitation time traces of exemplary single emission lines from the planar structure with InAs/InP QDs showing distinct behavior: (

**a**) mono-exponential decay with much different PL decay times; (

**b**) two-component exponential decay; (

**c**) decay with initial rise time (0.08 ns) together with linear fits to experimental data.

**Figure 5.**Normalized low-temperature (T = 4.5 K) and low-excitation time traces of exemplary single emission lines from patterned structure with InAs/InP QDs showing distinct behavior: (

**a**) mono-exponential decay with much different PL decay times; (

**b**,

**c**) two-component exponential decay; (

**d**) decay with initial rise time together with exponential fits to experimental data.

**Figure 6.**Carrier lifetime distribution for (

**a**) planar and (

**b**) patterned sample with initial PL decay time τ

_{1}marked in black and longer PL decay time τ

_{2}marked in red. (

**c**) PL decay lifetime τ

_{1}dispersion for planar (black) and patterned (red) sample.

**Figure 7.**(

**a**) Temperature series (5–100) K of microphotoluminescence spectra under non-resonant cw excitation with 2 μW. (

**b**) Emission energy of exemplary emission line with respect to the temperature determined from Gaussian fit to experimental data (black squares) fitted with Varshni formula [115] (solid red line) and formula derived from microscopic description of the exciton-phonon interaction (Equation (2), solid blue line) with respective fitting parameters. (

**c**) Examples of typical behavior for full width at half maximum (FWHM) of the emission line with respect to the temperature determined from Gaussian fit to experimental data (symbols) fitted with the formula [116] Equation (3) for emission lines with initial FWHM (at the temperature of 5 K) of 30 (black), 50 (red), 60 (pink), and 120 μeV (blue). The spectral resolution of the experimental setup (20 μeV) is marked with a black horizontal line.

**Figure 8.**(

**a**) Arrhenius analysis (solid red line is a fit with Equation (1)) of temperature dependence of the integral emission intensity determined from Gaussian fit to experimental data (black squares) for exemplary emission line. (

**b**) Calculated single-particle energy spectrum (ground state-1 and first excited state-2) for electrons (e) and heavy holes (hh) with the band edges for conduction band (cb) and hole subbands (lh-light holes, so-spin-orbit split-off subband) for the typical QD (42 nm base diameter, 15 nm height, 25% P content), with energy difference between ground state single-particle levels (e1–h1) equal to 0.810 eV (1531 nm).

**Figure 9.**(

**a**) Emission energy dependence of the Varshni parameter α for emission lines investigated on the patterned sample determined from a fit to experimental data (black squares with error bars corresponding to the fitting accuracy); theoretical values for bulk InAs and InP are marked with the red and blue horizontal line, respectively; (

**b**) activation energies as a function of QD emission energy (symbols, error bars correspond to the fitting accuracy, left axis) with low-temperature (13 K) PL spectra of the QD ensemble (solid blue line, right axis).

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Smołka, T.; Posmyk, K.; Wasiluk, M.; Wyborski, P.; Gawełczyk, M.; Mrowiński, P.; Mikulicz, M.; Zielińska, A.; Reithmaier, J.P.; Musiał, A.;
et al. Optical Quality of InAs/InP Quantum Dots on Distributed Bragg Reflector Emitting at 3rd Telecom Window Grown by Molecular Beam Epitaxy. *Materials* **2021**, *14*, 6270.
https://doi.org/10.3390/ma14216270

**AMA Style**

Smołka T, Posmyk K, Wasiluk M, Wyborski P, Gawełczyk M, Mrowiński P, Mikulicz M, Zielińska A, Reithmaier JP, Musiał A,
et al. Optical Quality of InAs/InP Quantum Dots on Distributed Bragg Reflector Emitting at 3rd Telecom Window Grown by Molecular Beam Epitaxy. *Materials*. 2021; 14(21):6270.
https://doi.org/10.3390/ma14216270

**Chicago/Turabian Style**

Smołka, Tristan, Katarzyna Posmyk, Maja Wasiluk, Paweł Wyborski, Michał Gawełczyk, Paweł Mrowiński, Monika Mikulicz, Agata Zielińska, Johann Peter Reithmaier, Anna Musiał,
and et al. 2021. "Optical Quality of InAs/InP Quantum Dots on Distributed Bragg Reflector Emitting at 3rd Telecom Window Grown by Molecular Beam Epitaxy" *Materials* 14, no. 21: 6270.
https://doi.org/10.3390/ma14216270