GaAs quantum dots for laser applications in 1 µm wavelength range

GaAs quantum dots for laser applications in 1 µm wavelength range

Journal of Crystal Growth 517 (2019) 1–6 Contents lists available at ScienceDirect Journal of Crystal Growth journal homepage: www.elsevier.com/loca...

2MB Sizes 0 Downloads 1 Views

Journal of Crystal Growth 517 (2019) 1–6

Contents lists available at ScienceDirect

Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro

Optimization of size uniformity and dot density of InxGa1−xAs/GaAs quantum dots for laser applications in 1 µm wavelength range

T



Tanja Finke , Vitalii Sichkovskyi, Johann Peter Reithmaier Technische Physik, Institute of Nanostructure Technologies and Analytics (INA), Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), University of Kassel, Heinrich-Plett-Straße 40, 34132 Kassel, Germany

A R T I C LE I N FO

A B S T R A C T

Communicated by H. Asahi

This work reports on growth and characterization of self-assembled InxGa1−xAs quantum dots grown on GaAs (1 0 0) substrate designed to emit at 1030 nm. All structures were grown by molecular beam epitaxy and investigated by photoluminescence (PL) spectroscopy and atomic force microscopy. The growth parameters, such as the growth temperature, QD layer thickness and indium content were changed systematically. A strong reduction in PL linewidth from 54 meV down to 26 meV measured at 10 K for a single QD layer was achieved as the result of a more uniform QD size distribution. Additionally, a correlation between the linewidth and the temperature dependent wavelength shift of the PL peak was found.

Keywords: A1 Atomic force microscopy A1 Nanostructures A3 Molecular beam epitaxy A3 Quantum dots B2 Semiconducting III-V materials

1. Introduction Self-organized semiconductor quantum dots (QDs) have been an important research field for many years. They have shown a high potential for attractive device applications, such as lasers and amplifiers for high power light sources [1] or optical communication [2]. By using QDs for the active region, the material properties can be tailored over a wide range by additional geometry-based degrees of freedom [3]. As a result, QD lasers have shown advantages like high-temperature stability in wavelength [4–6] or very low threshold current density [4,7] compared to the conventional quantum well (QW) lasers. To date in the field of optically pumped semiconductor disk lasers (SDLs) best ultrafast passively mode-locked vertical external cavity surface emitting lasers (VECSELs) with saturable absorber mirrors (SESAMs) [8] in terms of output power and pulse duration have been obtained with InGaAs QWs [9]. However, in addition to the benefits already mentioned above, QDs based gain material offer advantages such as an inherently large inhomogeneous gain, which is wider compared to QW and is less sensitive to temperature changes [10,11]. Due to the increased gain bandwidth many different axial modes can lase at the same time which leads to an easier mode selection and should support shorter pulse durations. The first sub-300 femtosecond SESAM mode-locked VECSEL based on active QD layers was presented recently [12], where a nearly comparable level to the state-of-the-art QW VECSELs was achieved. However, the reliable device operation was obtained only at a very low temperature of −19 °C. One of the reason



Corresponding author. E-mail address: tanja.fi[email protected] (T. Finke).

https://doi.org/10.1016/j.jcrysgro.2019.04.002 Received 13 March 2019; Accepted 3 April 2019 Available online 04 April 2019 0022-0248/ © 2019 Elsevier B.V. All rights reserved.

could be the large QDs size variation with ∼180 meV full width at half maximum (FWHM) bandwidth at room temperature (RT) (corresponds to ∼50 meV at 10 K), resulting in much reduced maximum spectral gain value. Therefore in order to use all the advantages of QDs gain material the inhomogeneous linewidth broadening, i.e. QDs size distribution, has to be well controlled. In literature, there are many reports on self-assembled QDs with a narrow inhomogeneous linewidth (less than 30 meV at 10 K) available for emission wavelength near 1300 nm and longer [13,14]. Ensembles of QDs with emission wavelengths between 1000 nm and 1100 nm show typically larger linewidths of 40–90 meV [15]. Due to the fact that the change of energy levels by size is not linear [16], i.e. energy levels in smaller QDs are more sensitive to the QD size fluctuations, it is more difficult to reach lower inhomogeneous linewidth broadening for QDs emitting around 1000 nm. Only optimizations with a special technique like indium flush procedures were used to get the narrow linewidth of about 30 meV [17]. In studies with other approaches, the results were not reproducible [18]. Therefore, the control over homogeneous size distribution of QDs gets important to improve [19]. In this work, QDs ensembles with a narrow full-width at half-maximum (FWHM) emitting around 1 µm were achieved with the conventional QDs growth only by systematic and fine tuning of the growth parameters. Growth optimizations, by changing growth temperature, V/III ratio, QD layer nominal thickness and indium content, is needed to achieve a high QD density (above 1 × 1011 cm−2) while reducing the linewidth. The low-temperature photoluminescence (PL) FWHM and QDs height distribution function

Journal of Crystal Growth 517 (2019) 1–6

T. Finke, et al.

Fig. 1). It is obvious that AFM measurements correlate well with PL spectroscopy measurements at 10 K. Samples with broader dot size distribution show also larger FWHM due to the inhomogeneous broadening effect. The emission linewidth is determined by the Gaussian fitting of the recorded PL spectra. The correlation between the PL FWHM and growth temperatures is shown in Fig. 2a including additional data for a few more QDs growth temperatures. As one can see the PL linewidth is decreasing from nearly 60 meV at 480 °C to 34 meV at 430 °C as a result of a much-reduced size fluctuation of QDs. At the same time, the PL peak position shifts towards shorter wavelength (see Fig. 1) with decreasing growth temperature. This is directly correlated to the dot height, which is the dominating dimension for the quantum size effect [16]. A decrease in QDs height leads to stronger confinement resulting in an increase of the transition energy and resulting in a blueshift of the peak wavelength. In Fig. 2b, the temperature dependence of the QD density as well as the PL peak intensity are plotted. Both curves show similar temperature-dependent behaviour with maximum values between 450 and 460 °C. The dot density has its maximum value of 1.6 × 1011 cm−2 for the sample grown at 450 °C. Since QDs with a small PL linewidth and preferably high dot density are required for the use in VECSEL, for the next optimization step QDs sample grown at 450 °C was selected. In the following, it turned out that the indium content has a large influence on the QDs size uniformity. In a first step (see Figs. 3 and 4) the indium content of InxGa1−x As QDs was varied by changing the submonolayer thickness of the InAs and InGaAs sub-layers forming QDs. Samples with resulting indium content from 40% to 65% were grown and PL, as well as AFM measurements, were used to analyze the results of the growth investigation. The QDs nominal deposited thickness (1.4 nm) and growth temperature (450 °C) were kept constant during this optimization step. QDs with an indium content of 65% show stronger inhomogeneity in QDs size (see Fig. 3a) and a broadened PL signal of 40.6 meV (Fig. 4). By reducing the indium content to 60% (Fig. 3b) or 50% (Fig. 3d) the size distribution is becoming more homogeneous and the PL linewidth (Fig. 4) decreases as well as the QDs density. The thickness of the wetting layer (WL) formed during QDs growth in Stranski-Krastanov mode increases with reduced indium content [20,21]. With a further reduction of the indium content to 40% (Fig. 3e), a point is reached where the QDs density becomes extremely small and the linewidth with only 11.7 meV is not QD-like anymore. In the low In content regime, the formation of QDs is suppressed and planar growth is favorized because the strain and layer thickness are below the critical values for QD formation for the used growth conditions [21]. Additionally, the reduction of the In content influences significantly the wavelength. 5% less indium content produces a wavelength blueshift of about 20 nm. Even with a small number of QDs formed, the QW-like behaviour of the wetting layer becomes dominant causing a strong reduction in PL FWHM (Fig. 4). As it is seen from Fig. 3c, the sample with 55% of indium content still showed a high dot density and narrow PL FWHM. However, the emission wavelength has to be shifted in order to get the desired peak position at RT. Therefore, in the next step, the QDs with low indium content like 45% and 50% were grown again at 450 °C, but this time the nominal QDs layer thickness was changed as well (Figs. 5 and 6). The nominal thickness was optimized in a way that the PL peak shifts to the correct wavelength range (950–980 nm at 10 K) for the designed laser application. The QDs with 60% and 65% are already in the right wavelength area (Fig. 4). An increase of the nominally deposited material thickness would lead to QDs formation even for the samples with reduced indium content. For all the cases, a QD density higher than 1011 cm−2 was observed. The minimum linewidth was less than 25 meV. Fig. 7 presents a comparison of the best QDs samples (with dot density above 1 × 1011 cm−2) selected from each optimization series. A strong decrease of PL linewidth from 54 meV down to 26 meV is

were used as a measure of QD size uniformity. The RT peak emission wavelength was designed to be at 1030 nm, which corresponds to a wavelength of about 950–990 nm measured at 10 K depending on the temperature sensitivity of the particular QDs ensemble. High-temperature stability of QDs spectral gain maximum is desired for the stable laser operation. 2. Experimental details The InGaAs QD samples studied here were grown on semi-insulating GaAs (1 0 0) substrates by a Varian Gen II MBE system. All samples were grown in the same manner, starting with an oxide desorption step at 600 °C under As4 overpressure for about 5 min. The subsequent growth continued with a 150 nm GaAs buffer layer deposited at 590 °C in order to smoothen the growth front before QDs deposition. The embedded and the top QD layers used for PL and morphology investigations, respectively, were separated by a 70 nm thick GaAs barrier layer. The QDs were formed by alternate deposition of several pairs of InAs and In0.2Ga0.8As layers with sub-monolayer thicknesses. The number of layer pairs was changed depending on the needed QD layer thickness. The resulting indium content in QDs was varied in the range of 40–65%. The lower QD layer of the structure is embedded in two 5 nm thick GaAs layers, grown at the same temperature as used for the QD growth. After the growth of the top QDs layer, which is left exposed on the surface for later AFM measurements, the sample was cooled down immediately. Growth conditions were the same for both QD layers, but the QDs growth temperature has been changed from sample to sample. The substrate temperature was recorded using the infrared pyrometer. For all samples, the V/III beam equivalent pressure ratio was kept constant at 20 for the QDs and at 30 for GaAs layers. Growth rates of 931 nm/h for GaAs and 250 nm/h for InAs were used, respectively. For PL signal enhancement at RT, QDs were embedded into 100 nm thick Al0.3Ga0.7As barrier layers on both sides grown at 600 °C. In this case, also two QD layers instead of one with 50 nm GaAs barrier were used. To avoid oxidation of the Al-containing layer, 20 nm thick GaAs cap layer was grown on top at 590 °C. For morphology analysis of the uncapped InGaAs QDs, an atomic force microscope (DME DS-95) was used. The PL emission properties were investigated with a diode pumped solid state (DPSS) laser emitting at a wavelength of 532 nm. The investigations at 10 K were done with a low excitation power density of about 0.8 W/cm2 whereas for RT measurements a higher excitation power density of about 21 W/cm2 was necessary. 3. Results and discussion In Fig. 1, the influence of the growth temperature on QDs morphology is shown between 430 °C and 480 °C. InGaAs QDs samples with a nominal thickness of 1.2 nm and an indium content of 60% were grown. Apart from the QDs growth temperature, sample structure and growth conditions were identical for all the shown samples. The left image column in Fig. 1 shows 1 × 1 µm2 AFM scans while the corresponding height distribution histograms with a number of QDs per cm2 are shown in the middle. On closer examination, the AFM images reveal round-shaped QDs in all cases but with a systematic slight reduction in the lateral dimensions by decreasing the growth temperature. However, the most significant impact of the growth temperature is on the height distribution. The height of the dots decreases significantly with decreasing of growth temperature from 8 nm at 480 °C to 4 nm at 430 °C, e.g. because of the decreased surface migration length of In ad-atoms at lower temperature [18]. It is also clearly seen from the histogram in Fig. 1 that the distribution of QDs grown at higher temperature is broader. This leads to the conclusion that also the QDs size distribution is more homogeneous at lower growth temperatures. The FWHM values of the PL measurement confirm this assumption (right column in 2

Journal of Crystal Growth 517 (2019) 1–6

T. Finke, et al.

(a)

480°

(b)

Density 1.0x1011 cm-2

Peak: 960 nm FWHM: 59.2 meV

Density 1.4x1011 cm-2

Peak: 947 nm FWHM: 46.6 meV

Density 1.6x1011 cm-2

Peak: 936 nm FWHM: 37.2 meV

200μm

470°

(c)

450°

(d)

Density 1.2x1011 cm-2

Peak: 934 nm FWHM: 33.7 meV

430° Fig. 1. From the top to the bottom growth temperature of the 1.2 nm nominally thick QDs with 60% of indium content has been changed: (a) 480 °C, (b) 470 °C, (c) 450 °C, (d) 430 °C. On the left side 1 × 1 µm AFM measurements, in the middle the corresponding height distribution histograms with a QDs density and on the right side the PL spectroscopy measurements at 10 K are shown. The values of the peak wavelength and the linewidth are inserted.

experimental details section. In principle, the behaviour of the linewidth at 300 K is comparable to the measurement at 10 K. The sample with the broadest PL FWHM at 10 K (grown at 480 °C with 60% of indium content) shows also the highest FWHM values at 300 K. This QDs sample has with 60 nm the highest total wavelength change between the PL peak position at 10 K and at 300 K. The narrower the PL linewidth of QDs is, the smaller is the temperature dependent wavelength shift. This behaviour is observed for the first time. For the third sample

observed. Furthermore, it was also possible to increase the PL intensity by optimization of the growth conditions and the composition of QDs. After that, the temperature dependant behaviour of PL properties for all in Fig. 8 presented QDs samples were analyzed. The results of the temperature dependent PL peak position difference and respective linewidth measured at 10 and 300 K are summarized in Table 1. To get an enhancement in PL signal measured at RT for this investigation, the QDs are embedded in an AlGaAs barrier as described earlier in the 3

Journal of Crystal Growth 517 (2019) 1–6

T. Finke, et al.

Fig. 2. (a) Dependence of PL FWHM and (b) QD density as well as PL peak intensity on the growth temperature of 1.2 nm nominally thick InGaAs QDs with 60% of In.

in Table 1 (grown at 450 °C with 50% of Indium) the wavelength changed only by 40 nm. The detailed PL measurements of this sample are shown in Fig. 8. As explained in the beginning there is a direct correlation between the dot height and the peak wavelength. In Ref. [22] it has been reported that for more broader, multi dispersed QD ensembles different dot families with varied dot sizes occur. The PL peak energies of every dot family show different temperature dependencies. Additionally, at lower temperatures, the PL spectra of smaller dot families is more dominant and at higher temperature the PL spectra of the bigger dots. The broader the QD ensemble is, the higher is the temperature-dependent shift of the PL peak because the number of dot families with different wavelength shift increases and the larger QDs get dominant. In principle, high-temperature stability is helpful for the laser application because thus thermal effects have a lower influence on the laser operation. In the case of VECSEL, it is especially difficult to uniformly remove the heat resulting from the laser process. There are temperature gradients within the sample. The better the temperature stability, the less it affects the wavelength and broadens the linewidth.

Fig. 4. Low-temperature PL spectra of InxGa1−x As QDs with indium content varied in the range of (40–65%). QDs were grown at 450 °C with a nominal deposited thickness of 1.4 nm. PL spectra were measured at 10 K. Indium content and FWHM values for every sample are specified.

size distribution. The obtained results, here for the 1 µm emission wavelength range, are comparable to the best values published yet for the 1.3 µm range [13,14]. It could be observed that the growth temperature, as well as the indium content of QDs, have a huge influence on quality, emission wavelength and size uniformity of QDs. From the temperature dependent PL studies it was found that QDs samples with a

4. Conclusion In conclusion, we have demonstrated a possibility to reduce the PL linewidth of InxGax−1As QDs emitting around 1 µm from 54 meV down to 26 meV with increased intensity as result of better control over QDs

Fig. 3. 1 × 1 µm2 AFM scans showing an influence of the indium content varied in the range of 40–65% on the density of InxGa1−x As QDs grown at 450 °C with a nominal deposited thickness of 1.4 nm. Indium content and QDs density are specified on the image for every sample. 4

Journal of Crystal Growth 517 (2019) 1–6

T. Finke, et al.

Fig. 5. 1 × 1 µm2 AFM scans showing the density of InxGa1−x As QDs with an indium content of 45% and 50%. QDs were grown at 450 °C with varied nominal deposited thickness. Indium content, nominal deposited thickness and QDs density are specified on the image. We relate the slight elongation of the dots mainly to an artefact caused by inaccuracies of the AFM system.

Fig. 8. Temperature-dependent wavelength shift of the optimized InxGa1−x As QDs grown at 450 °C with 50% indium content and a nominal deposited thickness of 1.8 nm. The red curve shows a PL measurement at 10 K while the blue curve shows a measurement at 300 K. Table 1 Temperature-dependent PL peak position wavelength shift between 10 K and 300 K and corresponding linewidths for three QDs samples shown in Fig. 7. Where d – nominal deposited thickness, TS – growth temperature, XIn – indium content. Sample #

Growth details

1

d = 1.2 nm TS = 480 °C XIn = 60% d = 1.4 nm TS = 450 °C XIn = 60% d = 1.8 nm TS = 450 °C XIn = 50%

2

Fig. 6. Low-temperature PL spectra of InxGa1−x As QDs with an indium content of 45% and 50%. QDs were grown at 450 °C with varied nominal deposited thickness, optimized to the right wavelength area. PL spectra were measured at 10 K. Indium content, nominal deposited thickness and FWHM values are specified.

3

Total PL peak position shift between 10 K and 300 K [nm]

FWHM at 300 K, [meV]

FWHM at 10 K [meV]

59

120

54

50

83

36

40

65

27

Acknowledgements The financial support by the DFG through the project QD-MIXSEL (RE 1110/17-1) is gratefully acknowledged. We would like to thank D. Albert and U. Gernhardt for technical support. References [1] O. Eyal, A. Willinger, S. Banyoudeh, F. Schnabel, V. Sichkovskyi, V. Mikhelashvili, J.P. Reithmaier, G. Eisenstein, Static and dynamic characteristics of an InAs/InP quantum-dot optical amplifier operating at high temperatures, Opt. Express 25 (2017) 27262–27269, https://doi.org/10.1364/OE.25.027262. [2] A. Abdollahinia, S. Banyoudeh, A. Rippien, F. Schnabel, O. Eyal, I. Cestier, I. Kalifia, E. Mentovich, G. Eisenstein, J. Reithmaier, Temperature stability of static and dynamic properties of 1.55 μm quantum dot lasers, Opt. Express 26 (2018) 6056–6066, https://doi.org/10.1364/OE.26.006056. [3] M. Henini, Quantum dot nanostructures, Mater. Today 5 (2002) 48–53, https://doi. org/10.1016/S1369-7021(02)00639-9. [4] S. Banyoudeh, A. Abdollahinia, V. Sichkovskyi, J. Reithmaier, 1.5 μm quantum dot laser material with high temperature stability of threshold current density and external differential efficiency, Proc SPIE. 9767, Novel In-Plane Semiconductor Lasers XV (2016). 97670I. https://doi.org/10.1117/12.2209085. [5] E.-M. Pavelescu, C. Gilfert, J.P. Reithmaier, A. Martín-Mínguez, GaInAs/(Al)GaAs quantum-dot lasers with high wavelength stability, Semicond. Sci. Technol. 23 (2008) 085022, https://doi.org/10.1088/0268-1242/23/8/085022. [6] E.M. Pavelescu, J.P. Reithmaier, W. Kaiser, P. Weinmann, M. Kamp, A. Forchel, Wavelength stabilized quantum dot lasers for high power applications, Phys. Status Solidi B 246 (2009) 872–875, https://doi.org/10.1002/pssb.200880635. [7] H. Shimizu, S. Saravanan, J. Yoshida, S. Ibe, N. Yokouchi, InAs quantum dot lasers with extremely low threshold current density (7 A/cm2/Layer), Jpn. J. Appl. Phys. 44 (2005) 1103–1104, https://doi.org/10.1143/JJAP.44.L1103. [8] A.-R. Bellancourt, D. Maas, B. Rudin, M. Golling, T. Südmeyer, U. Keller, Modelocked integrated external-cavity surface emitting laser, IET Optoelectron. 3 (2009) 61–72, https://doi.org/10.1049/iet-opt.2008.0038. [9] D. Waldburger, S.M. Link, M. Mangold, C.E. Alfieri, E. Gini, M. Golling, B.W. Tilma, U. Keller, High-power 100 fs semiconductor disk lasers, Optica 3 (2016) 844–852,

Fig. 7. PL spectra measured at 10 K showing an evolution in PL FWHM and intensity for QDs samples selected from three different optimization steps. All samples were grown again and measured together in the PL setup. The strong reduction of PL linewidth from 54 meV to 26 meV with a simultaneous increase in integrated intensity from 3.5 × 10−3 (480 °C with 60% In content) to 5.4 × 10−3 (450 °C with 50% In content) by optimization of growth conditions and composition of QDs were achieved.

narrow PL linewidth show also a reduced temperature dependent wavelength shift, which is beneficial for the device applications operating at elevated temperatures. We expect a significant improvement of the device performance of VECSELs by implementing these optimized QDs utilizing the much higher spectral gain based on the reduction of the size distribution and increasing the QD density.

5

Journal of Crystal Growth 517 (2019) 1–6

T. Finke, et al.

1511.01001. [17] K. Watanabe, T. Akiyama, Y. Yokoyama, K. Takemasa, Growth of high-density 1.06μm InGaAs/GaAs quantum dots for high gain lasers by molecular beam epitaxy, J. Crystal Growth 378 (2013) 627–630, https://doi.org/10.1016/j.jcrysgro.2012.12. 107. [18] A. Gushterov, L. Lingys, J.P. Reithmaier, Control of dot geometry and photoluminescence linewidth of InGaAs/GaAs quantum dots by growth conditions, J. Crystal Growth 311 (2009) 1783–1786, https://doi.org/10.1016/j.jcrysgro.2008. 10.067. [19] S. Banyoudeh, J.P. Reithmaier, High-density 1.54 μm InAs/InGaAlAs/InP(100) based quantum dots with reduced size inhomogeneity, J. Crystal Growth 425 (2015) 299–302, https://doi.org/10.1016/j.jcrysgro.2015.03.027. [20] L. Seravalli, G. Trevisi, P. Frigeri, F. Rossi, E. Buffagni, C. Ferrari, Wetting layer states in low density InAs/InGaAs quantum dots from sub-critical InAs coverages, J. Appl. Phys. 46 (2013), https://doi.org/10.1088/0022-3727/46/31/315101. [21] G. Sek, P. Poloczek, K. Ryczko, J. Misiewicz, A. Löffler, J.P. Reithmaier, A. Forchel, Photoreflectance determination of the wetting layer thickness in the InxGa1−xAs∕GaAs quantum dot system for a broad indium content range of 0.3–1, J. Appl. Phys. 100 (2006) 103529, https://doi.org/10.1063/1.2364604. [22] L. Brusaferri, S. Sanguinetti, E. Grilli, M. Guzzi, A. Bignazzi, F. Bogani, L. Carraresi, M. Colocci, A. Bosacchi, P. Frigeri, S. Franchi, Thermally activated carrier transfer and luminescence line shape in self-organized InAs quantum dots, Appl. Phys. Lett. 69 (1996) 3354–3356, https://doi.org/10.1063/1.117304.

https://doi.org/10.1364/OPTICA.3.000844. [10] M. Hoffmann, Y. Barbarin, D.J. Maas, M. Golling, I.L. Krestnikov, S.S. Mikhrin, A.R. Kovsh, T. Südmeyer, U. Keller, Modelocked quantum dot vertical external cavity surface emitting laser, Appl. Phys. B 93 (2008) 733–736, https://doi.org/10. 1007/s00340-008-3267-0. [11] M. Hoffmann, O.D. Sieber, V.J. Wittwer, I.L. Krestnikov, D.A. Livshits, Y. Barbarin, T. Südmeyer, U. Keller, Femtosecond high-power quantum dot vertical external cavity surface emitting laser, Opt. Express 19 (2011) 8108–8116, https://doi.org/ 10.1364/OE.19.008108. [12] C.E. Alfieri, D. Waldburger, M. Golling, U. Keller, High-power sub-300-femtosecond quantum dot semiconductor disk lasers, IEEE Photon. Technol. Lett. 30 (2018) 525–528, https://doi.org/10.1109/LPT.2018.2801024. [13] R.P. Mirin, K.L. Silverman, D.H. Christensen, A. Roshko, Narrow photoluminescence linewidths from ensembles of self-assembled InGaAs quantum dots, J. Vac. Sci. Technol. 18 (2000) 1510–1513, https://doi.org/10.1116/1.591415. [14] W. Ouerghuia, A. Mellitia, M. Maarefa, J. Blochb, Dependence on temperature of homogeneous broadening of InGaAs/InAs/GaAs quantum dot fundamental transitions, Physica E 28 (2005) 519–524, https://doi.org/10.1016/j.physe.2005.05.051. [15] N. Ozak, S. Kanehira, Y. Hayashi, S. Ohkouchi, N. Ikeda, Growth of quantum threedimensional structure of InGaAs emitting at ∼1 mm applicable for a broadband near-infrared light source, J. Crystal Growth 477 (2017) 230–234, https://doi.org/ 10.1016/j.jcrysgro.2016.11.104. [16] E. Rajaei, M.A. Borji, Energy levels of InGaAs/GaAs quantum dot lasers with different sizes, Int. J. Nanosci. Nanotechnol. 12 (2016) 45–53 https://arxiv.org/abs/

6