I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. DESIGN AND FABRICATIO...III. RESULTS AND DISCUSSI...IV. CONCLUSIONV. METHODSSUPPLEMENTARY MATERIALREFERENCESQuantum dot (QD) single photon sources (SPSs) are good candidates for a light source in quantum information processing (QIP) applications. Epitaxial quantum dots have good single photon properties suitable for use in QIP, such as multiphoton suppression,11. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, Science 290(5500), 2282 (2000). https://doi.org/10.1126/science.290.5500.2282 indistinguishability,2–42. C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, Nature 419(6907), 594 (2002). https://doi.org/10.1038/nature010863. S. Ates, S. M. Ulrich, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 103(16), 167402 (2009). https://doi.org/10.1103/physrevlett.103.1674024. N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, Nat. Photonics 10(5), 340 (2016). https://doi.org/10.1038/nphoton.2016.23 Fourier transform-limited linewidth,3,53. S. Ates, S. M. Ulrich, S. Reitzenstein, A. Löffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 103(16), 167402 (2009). https://doi.org/10.1103/physrevlett.103.1674025. A. V. Kuhlmann, J. H. Prechtel, J. Houel, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, Nat. Commun. 6(1), 8204 (2015). https://doi.org/10.1038/ncomms9204 and entangled photon pair generation.66. O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 84(11), 2513 (2000). https://doi.org/10.1103/physrevlett.84.2513 With QD-based SPSs, good results have been reported in boson sampling,7,87. H. Wang, Y. He, Y.-H. Li, Z.-E. Su, B. Li, H.-L. Huang, X. Ding, M.-C. Chen, C. Liu, J. Qin, J.-P. Li, Y.-M. He, C. Schneider, M. Kamp, C.-Z. Peng, S. Höfling, C.-Y. Lu, and J.-W. Pan, Nat. Photonics 11(6), 361 (2017). https://doi.org/10.1038/nphoton.2017.638. H. Wang, J. Qin, X. Ding, M.-C. Chen, S. Chen, X. You, Y.-M. He, X. Jiang, L. You, Z. Wang, C. Schneider, J. J. Renema, S. Höfling, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 123(25), 250503 (2019). https://doi.org/10.1103/physrevlett.123.250503 quantum key distribution,9–129. P. M. Intallura, M. B. Ward, O. Z. Karimov, Z. L. Yuan, P. See, A. J. Shields, P. Atkinson, and D. A. Ritchie, Appl. Phys. Lett. 91(16), 161103 (2007). https://doi.org/10.1063/1.279975610. K. Takemoto, Y. Nambu, T. Miyazawa, Y. Sakuma, T. Yamamoto, S. Yorozu, and Y. Arakawa, Sci. Rep. 5, 14383 (2015). https://doi.org/10.1038/srep1438311. T. Kupko, M. von Helversen, L. Rickert, J.-H. Schulze, A. Strittmatter, M. Gschrey, S. Rodt, S. Reitzenstein, and H. Tobias, Npj Quantum Inf. 6(1), 29 (2020). https://doi.org/10.1038/s41534-020-0262-812. E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 420(6917), 762 (2002). https://doi.org/10.1038/420762a entangled photon pair generation,6,13–176. O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 84(11), 2513 (2000). https://doi.org/10.1103/physrevlett.84.251313. M. A. M. Versteegh, M. E. Reimer, K. D. Jöns, D. Dalacu, P. J. Poole, A. Gulinatti, A. Giudice, and V. Zwiller, Nat. Commun. 5, 5298 (2014). https://doi.org/10.1038/ncomms629814. M. Müller, S. Bounouar, K. D. Jöns, M. Glässl, and P. Michler, Nat. Photonics 8(3), 224 (2014). https://doi.org/10.1038/nphoton.2013.37715. Y. Chen, M. Zopf, R. Keil, F. Ding, and O. G. Schmidt, Nat. Commun. 9(1), 2994 (2018). https://doi.org/10.1038/s41467-018-05456-216. J. Liu, R. Su, Y. Wei, B. Yao, S. F. C. d. Silva, Y. Yu, J. Iles-Smith, K. Srinivasan, A. Rastelli, J. Li, and X. Wang, Nat. Nanotechnol. 14(6), 586 (2019). https://doi.org/10.1038/s41565-019-0435-917. H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 122(11), 113602 (2019). https://doi.org/10.1103/physrevlett.122.113602 and quantum teleportation.18–2118. J. Nilsson, R. M. Stevenson, K. H. A. Chan, J. Skiba-Szymanska, M. Lucamarini, M. B. Ward, A. J. Bennett, C. L. Salter, I. Farrer, D. A. Ritchie, and A. J. Shields, Nat. Photonics 7(4), 311 (2013). https://doi.org/10.1038/nphoton.2013.1019. M. Reindl, D. Huber, C. Schimpf, S. F. C. d. Silva, M. B. Rota, H. Huang, V. Zwiller, K. D. Jöns, A. Rastelli, and R. Trotta, Sci. Adv. 4(12), eaau1255 (2018). https://doi.org/10.1126/sciadv.aau125520. M. Anderson, T. Müller, J. Huwer, J. Skiba-Szymanska, A. B. Krysa, R. M. Stevenson, J. Heffernan, D. A. Ritchie, and A. J. Shields, Npj Quantum Inf. 6(1), 14 (2020). https://doi.org/10.1038/s41534-020-0249-521. F. Basso Basset, F. Salusti, L. Schweickert, M. B. Rota, D. Tedeschi, S. F. Covre da Silva, E. Roccia, V. Zwiller, K. D. Jöns, A. Rastelli, and R. Trotta, Npj Quantum Inf. 7(1), 7 (2021). https://doi.org/10.1038/s41534-020-00356-0In terms of structure, high-efficiency SPSs using quantum dots have utilized micropillar4,224. N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Antón, J. Demory, C. Gómez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaítre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart, Nat. Photonics 10(5), 340 (2016). https://doi.org/10.1038/nphoton.2016.2322. X. Ding, Y. He, Z. C. Duan, N. Gregersen, M. C. Chen, S. Unsleber, S. Maier, C. Schneider, M. Kamp, S. Höfling, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 116(2), 020401 (2016). https://doi.org/10.1103/physrevlett.116.020401 and bull’s eye16,1716. J. Liu, R. Su, Y. Wei, B. Yao, S. F. C. d. Silva, Y. Yu, J. Iles-Smith, K. Srinivasan, A. Rastelli, J. Li, and X. Wang, Nat. Nanotechnol. 14(6), 586 (2019). https://doi.org/10.1038/s41565-019-0435-917. H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 122(11), 113602 (2019). https://doi.org/10.1103/physrevlett.122.113602 structures. These structures have high quality factors and spectrally narrow characteristics. However, such sources require very sophisticated fabrication methods, and in particular, the narrow band of the micropillar structure makes it difficult for QD-based polarization entangled photon pair applications requiring the efficient emission of both the exciton (X) and biexciton (XX) photons. On the other hand, spectrally broad and efficient SPSs on metal reflectors have been reported in nanowire2323. J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gérard, Nat. Photonics 4(3), 174 (2010). https://doi.org/10.1038/nphoton.2009.287x and optical antenna1515. Y. Chen, M. Zopf, R. Keil, F. Ding, and O. G. Schmidt, Nat. Commun. 9(1), 2994 (2018). https://doi.org/10.1038/s41467-018-05456-2 structures. Recently, several groups fabricated microlens on a reflector;24–2824. M. Sartison, L. Engel, S. Kolatschek, F. Olbrich, C. Nawrath, S. Hepp, M. Jetter, P. Michler, and S. L. Portalupi, Appl. Phys. Lett. 113(3), 032103 (2018). https://doi.org/10.1063/1.503827125. M. Schmidt, M. V. Helversen, S. Fischbach, A. Kaganskiy, R. Schmidt, A. Schliwa, H. Tobias, S. Rodt, and S. Reitzenstein, Opt. Mater. Express 10(1), 76 (2019). https://doi.org/10.1364/ome.10.00007626. M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J.-H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, Nat. Commun. 6, 7662 (2015). https://doi.org/10.1038/ncomms866227. S. Fischbach, A. Schlehahn, A. Thoma, N. Srocka, T. Gissibl, S. Ristok, S. Thiele, A. Kaganskiy, A. Strittmatter, T. Heindel, S. Rodt, A. Herkommer, H. Giessen, and S. Reitzenstein, ACS Photonics 4(6), 1327 (2017). https://doi.org/10.1021/acsphotonics.7b0025328. S. Li, X. Shang, Y. Chen, X. Su, H. Hao, H. Liu, Y. Zhang, H. Ni, and Z. Niu, Nanomaterials 11(5), 1136 (2021). https://doi.org/10.3390/nano11051136 the first, on a distributed Bragg reflector, resulted in 23% brightness at an NA of 0.4.2626. M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B. Wohlfeil, L. Krüger, J.-H. Schulze, T. Heindel, S. Burger, F. Schmidt, A. Strittmatter, S. Rodt, and S. Reitzenstein, Nat. Commun. 6, 7662 (2015). https://doi.org/10.1038/ncomms8662 The brightness was later enhanced up to 40% by using an additional 3D-printed lens on the structure.2727. S. Fischbach, A. Schlehahn, A. Thoma, N. Srocka, T. Gissibl, S. Ristok, S. Thiele, A. Kaganskiy, A. Strittmatter, T. Heindel, S. Rodt, A. Herkommer, H. Giessen, and S. Reitzenstein, ACS Photonics 4(6), 1327 (2017). https://doi.org/10.1021/acsphotonics.7b00253 To further improve the brightness, a QD-GaAs lens on a metal reflector has been proposed.2525. M. Schmidt, M. V. Helversen, S. Fischbach, A. Kaganskiy, R. Schmidt, A. Schliwa, H. Tobias, S. Rodt, and S. Reitzenstein, Opt. Mater. Express 10(1), 76 (2019). https://doi.org/10.1364/ome.10.000076 To date, though, the maximum reported brightness remains around 20%, despite the theoretically expected brightness of 42%.

In this work, we present a deterministically fabricated QD double solid immersion lens (SILs) SPS. The SPS is expected to provide a brightness of 88% at 0.5 NA in the optimized structure by numerical simulations, while demonstrating an experimental brightness of 51.6% ± 2% and a g(2)(0) of 0.029 ± 0.005 at saturation. Our SPSs are fabricated with only two-photon absorption (TPA) and wet etching processes; in other words, neither e-beam lithography nor dry etching is required. The simple fabrication provides better precision than that of e-beam lithography by introducing novel exposure and wet etching methods.

II. DESIGN AND FABRICATION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. DESIGN AND FABRICATIO... <<III. RESULTS AND DISCUSSI...IV. CONCLUSIONV. METHODSSUPPLEMENTARY MATERIALREFERENCESA schematic of our structure is shown in Fig. 1(a). The double SIL is optimized to provide efficient extraction of the directed emission from a QD located at the first antinode from the bottom. A low index polymer SIL on top of the GaAs SIL improves the directionality of the emission for increased collection with low NA optics. From finite-difference time-domain (FDTD) simulation, we have found that the position of the first antinode is within 2 nm from 890 to 960 nm (see the supplementary material).

FDTD Solutions (Ansys Lumerical) was used to optimize the QD double SIL SPS structure. The GaAs SIL has a diameter of 660 nm and a height of 440 nm, and the elliptic polymer SIL on the GaAs SIL has a diameter of 3000 nm and a height of 2000 nm. Below the double SIL structure is 15 nm of SiN and a 100 nm thick gold film. The X-polarized dipole source is located 45 nm above the SiN layer. The polymer SIL is designed based on an AZ series photoresist (PR) with a refractive index of 1.6.

We calculated the brightness of the device as displayed in Fig. 1(b). The device has a maximum brightness of 88% at 925 nm with 0.5 NA optics. Furthermore, we found that the structure can be operated as a broadband SPS with an efficiency higher than 80% over a wavelength range of 65 nm. The radiation pattern of the structure is highly directional, as shown in the far-field emission profile in Fig. 1(d), in contrast to the one without the polymer SIL shown in Fig. 1(e). We then compared the brightness of the device with and without the polymer SIL; as can be seen in Fig. 1(c), the brightness improved more than twice at 0.5 NA with the low index polymer SIL. The improvement in brightness is even more significant at low NAs. This result suggests that the radiation along the higher angles from the dipole in the GaAs lens structure is effectively directed toward lower angles thanks to the polymer SIL. The brightness drops to 72% with a 50 nm lateral deviation of the QD position from the center, requiring precise positioning of the QD in the structure (see the supplementary material).

We employ TPA to make an etch mask on a QD to deterministically fabricate QD SPSs at high precision. We set the wavelengths of the searching (diode laser) and exposing (femtosecond pulse laser) lasers to be the same (800 nm). Then we couple the two lasers to the same single mode fiber to make the two beams perfectly coincide in the mode and beam path. In this way, we can produce an SPS with the QD at the center most precisely, without any misalignment or aberration.

After coating a PR of 300 nm (AZ 5214) on the substrate, we find the position of the QDs with the continuous wave laser at low temperature and expose the PR at the same position with the pulsed laser. The spatial resolution is further improved by using confocal microscopy with a single mode fiber. After the PR development, the resultant negative-tone PR disk is used as a wet etch mask to fabricate the GaAs SIL structure.

The QD sample is isotropically etched until the gold film is exposed by dipping the sample into a slow etchant.2424. M. Sartison, L. Engel, S. Kolatschek, F. Olbrich, C. Nawrath, S. Hepp, M. Jetter, P. Michler, and S. L. Portalupi, Appl. Phys. Lett. 113(3), 032103 (2018). https://doi.org/10.1063/1.5038271 After removing the PR mask with acetone, the sample is immersed in the etchant for a short time to round the tip and remove the remaining GaAs layer. The fabricated SIL typically has a parabolic shape with a small GaAs tail. The structures are measured with a scanning electron microscope (SEM), as shown in Fig. 2(a). To see the profile of the lens, we measure the dimensions with an atomic force microscope (AFM) and fit the results to a parabolic curve. The bottom diameter is 1750 nm and the height is 720 nm from the fitting, as shown in Fig. 2(c). We complete the double SIL structure by fabricating a solid immersion lens using an AZ 5214 PR on top of the GaAs SIL. Figure 2(b) shows an SEM image of the final double SIL structures. The elliptic SILs have a diameter of 3.0 µm and a thickness of 1.8 µm.

We have fabricated larger GaAs SIL structures because our target GaAs SIL is rather small for deterministic fabrication using optical methods. The diameter of the etch mask can be as small as 800 nm, but it is at present difficult to achieve this mainly due to the aberration effect when the focused beam propagates through the optical window. However, we expect that a smaller etch mask diameter can be achieved with an aberration-corrected objective lens or an objective lens inside a cryostat.

III. RESULTS AND DISCUSSION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. DESIGN AND FABRICATIO...III. RESULTS AND DISCUSSI... <<IV. CONCLUSIONV. METHODSSUPPLEMENTARY MATERIALREFERENCESFigure 3(a) shows the measured micro-photoluminescence spectrum (PL) from a QD double SIL structure at 7 K (red). At a low excitation power, only the neutral exciton state (X0, 928.2 nm) was observed (see the supplementary material). As the power increased, the charged exciton (CX, 927.5 nm) and biexciton (931.6 nm) were also observed. We assigned the two states to the polarization-dependent PL spectra (see the supplementary material).To obtain the brightness, we integrated the intensity of each peak at the saturation point. The count rate of each state was divided by the transmission efficiency, repetition rate of the pulse laser, and detector efficiency (see Sec. ). The brightness of the CX and X0 states was measured as 30.2% ± 1.2% and 21.4% ± 0.8%, respectively. Since a single photon is emitted from either the CX or X0 state, i.e., not from both states at the same pulse, the brightness of the device should be the sum of both states, resulting in 51.6% ± 2%.27,2927. S. Fischbach, A. Schlehahn, A. Thoma, N. Srocka, T. Gissibl, S. Ristok, S. Thiele, A. Kaganskiy, A. Strittmatter, T. Heindel, S. Rodt, A. Herkommer, H. Giessen, and S. Reitzenstein, ACS Photonics 4(6), 1327 (2017). https://doi.org/10.1021/acsphotonics.7b0025329. M. E. Reimer, G. Bulgarini, N. Akopian, M. Hocevar, M. B. Bavinck, M. A. Verheijen, E. P. A. M. Bakkers, L. P. Kouwenhoven, and V. Zwiller, Nat. Commun. 3(1), 737 (2012). https://doi.org/10.1038/ncomms1746To analyze the effect of the polymer SIL, we compared the PL spectrum of the double SIL device to one without the polymer SIL [black line in Fig. 3(a)]. The exciton peak was shifted to a shorter wavelength of about 0.6 nm with the polymer SIL, likely due to the added strain near the QD.3030. M. Sartison, S. L. Portalupi, T. Gissibl, M. Jetter, H. Giessen, and P. Michler, Sci. Rep. 7(1), 39916 (2017). https://doi.org/10.1038/srep39916 For a device without the polymer SIL, the brightness of the dominant X0 and CX states was measured to be 18% ± 1% and 4% ± 1%, respectively, resulting in a brightness of 22% ± 1%. Compared to this value, the brightness of the device with the polymer SIL is enhanced by a factor of 2.3.We also note a linewidth reduction for the X0 state after fabricating the polymer SIL, as shown in Fig. 3(a). The full width at half maximum of the X0 line was decreased from 0.29 to 0.16 nm, which is resolution limited. We attribute this reduction to the stabilization of the charge environment in the vicinity of the emitter, as explained in more detail in the supplementary material.Next, we measured the single photon purity of the device. We selected only the PL at the desired wavelength by adjusting the tilt angle of a narrow band-pass filter under non-resonant excitation at 870 nm and coupled it to a single mode fiber. Figures 3(b) and 3(c) show g(2)(τ) histograms obtained from Hanbury Brown–Twiss (HBT) measurements for the device without and with the polymer SIL, respectively. The values of g(2)(0) were 0.015 ± 0.003 without the polymer SIL and 0.029 ± 0.005 with the polymer SIL at the saturation condition. The value was 0.013 ± 0.001 at 1/4 of the saturated signal for the double SIL. The exciton lifetime of the QD in the double SIL SPS was measured to be 530 ps by a picosecond streak camera (Hamamatsu C4742-95), which is displayed in the supplementary material. Here, we could not see blinking characteristics even up to 1 µs through the autocorrelation measurement, which are sometimes observed in high-brightness QD SPSs.17,31,3217. H. Wang, H. Hu, T.-H. Chung, J. Qin, X. Yang, J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, X. Ding, Y.-H. Deng, Q. Dai, Y.-H. Huo, S. Höfling, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett. 122(11), 113602 (2019). https://doi.org/10.1103/physrevlett.122.11360231. H. Wang, Y.-M. He, T.-H. Chung, H. Hu, Y. Yu, S. Chen, X. Ding, M.-C. Chen, J. Qin, X. Yang, R.-Z. Liu, Z.-C. Duan, J.-P. Li, S. Gerhardt, K. Winkler, J. Jurkat, L.-J. Wang, N. Gregersen, Y.-H. Huo, Q. Dai, S. Yu, S. Höfling, C.-Y. Lu, and J.-W. Pan, Nat. Photonics 13(11), 770 (2019). https://doi.org/10.1038/s41566-019-0494-332. Y. Wei, S. Liu, X. Li, Y. Yu, X. Su, S. Li, X. Shang, H. Liu, H. Hao, H. Ni, S. Yu, Z. Niu, J. Iles-Smith, J. Liu, and X. Wang, Nat. Nanotechnol. 17(5), 470 (2022). https://doi.org/10.1038/s41565-022-01092-6We confirmed the assignment of the X0 and CX states by measuring the autocorrelation of emission from the two states with two band-pass filters of 5 nm bandwidth transmitting two sharp peaks, as shown in Fig. 4(a). Although the two peaks had comparable intensity, Fig. 4(b) shows that the g(2)(0) value was as small as 0.050 ± 0.003. The slight bunching at zero delay is likely due to unwanted background emission within the 5 nm band.

Since the present structure is much larger than the optimum size, we calculated the expected brightness of the fabricated device using FDTD simulation. The brightness calculated at a wavelength of 925 nm was about 60% at 0.5 NA. The measured brightness is slightly lower than the simulation result, likely due to the position of the QD not being exactly at the center due to the limitation in the step size of our stage (50 nm). Despite this, considering the proximity of the experimental value to the calculated one, we expect to achieve a brightness close to 88% if we fabricate the structure close to the optimum dimensions.

IV. CONCLUSION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. DESIGN AND FABRICATIO...III. RESULTS AND DISCUSSI...IV. CONCLUSION <<V. METHODSSUPPLEMENTARY MATERIALREFERENCES

In conclusion, we demonstrated a high-brightness QD SPS that was deterministically fabricated without using e-beam lithography or dry etching. The double SIL structure consists of a QD-embedded GaAs SIL covered with a polymer SIL. From numerical simulations, the optimized structure is expected to provide a brightness of over 88% at 0.5 NA with a bandwidth of 65 nm over 80% brightness. We fabricated the device deterministically through the TPA process and wet etching, achieving better precision than the e-beam lithography and dry etching combination. The fabricated non-optimized double SIL structure provided a brightness of 51.6% ± 2% at 0.5 NA and a g(2)(0) value of 0.029 ± 0.005. With optimized dimensions, we expect an experimental brightness of close to the predicted 88%. The high-performance QD SPS with simple yet precise fabrication processes, together with simple QD growth, may become the main workhorse in QIP applications.

V. METHODS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. DESIGN AND FABRICATIO...III. RESULTS AND DISCUSSI...IV. CONCLUSIONV. METHODS <<SUPPLEMENTARY MATERIALREFERENCES

A. QD growth

The quantum dot structure we used was grown by molecular beam epitaxy. After growing a 200 nm GaAs buffer layer on a semi-insulating (001) GaAs substrate, 300 nm thick Al0.76Ga0.24As, 1500 nm thick GaAs, InAs quantum dots, and 50 nm thick GaAs were grown successively. The growth temperature of the InAs QDs was 500 °C. The growth temperatures of GaAs and AlGaAs were 580 and 600 °C, respectively. The QD density was about 1 × 108/cm2.

B. Fabrication

The SiN of 15 nm was deposited on top of a GaAs epilayer containing QDs, followed by e-beam deposition of a 100 nm gold film. After spin-coating SU-8 on the substrate, the sample was flipped, and the gold side was attached to the substrate. The bulk GaAs was etched with citric acid until the AlGaAs layer was visible, after which the AlGaAs layer was removed with a HCl solution. The remaining GaAs layer was etched with citric acid down to 800 nm. The thickness of the GaAs layer was precisely controlled by measuring the reflectivity during the etching to check the thickness accurately. The fabrication process for the GaAs SIL is described in the main text. After coating 2 µm of AZ 5214, a negative disk pattern was fabricated with the image reversal process on top of the GaAs SIL. After a hard bake at 120 °C, the sample was baked at 190 °C for 3 min to produce an elliptic polymer SIL through the reflow process.3333. D. H. Ahn, Y. D. Jang, J. S. Baek, C. Schneider, S. Höfling, and D. Lee, Appl. Phys. Lett. 118(17), 174001 (2021). https://doi.org/10.1063/5.0046065

C. Optical measurements

For optical measurements, a 0.5 NA objective lens was used for excitation and collection. As the exposing laser, a femtosecond-pulsed Ti-sapphire laser with a repetition rate of 76 MHz was used. A 300 mm spectrometer and a liquid nitrogen cooled Si charge-coupled device were used to measure the QD PL spectra. For the HBT measurement, we coupled the PL from a QD to a single mode fiber after going through a narrow band-pass filter of 0.45 nm width (Alluxa Corp). After a fiber-based beam splitter, we measured the autocorrelation of the source with two single photon counting modules based on Si avalanche photodiodes (Perkin Elmer and Excelitas) by time-correlated single photon counting measurement.

D. Brightness estimation

For the brightness estimation, we measured the transmission and efficiency of our setup. The total efficiency of our setup was measured as 0.37% (averaged over polarization) with an attenuated laser beam of the same wavelength. Individual transmissions were as follows: cryostat window 92%, objective lens 55%, beam splitter 55%, two mirrors 93%, long pass filter 97%, lens 99%, grating 38%, and the detector quantum efficiency with the electron to count conversion 3.6%, yielding an efficiency of 0.34%. There was a 10% discrepancy between the total transmission directly measured and that individually counted, likely due to the polarization effect. We utilized the total efficiency (0.37%) for the brightness estimation since it is less susceptible to this effect.

E. Numerical simulations

For modeling, we used a parabola structure for the GaAs SIL and a hemisphere structure for the double SIL. To find the antinode position in the z-axis to locate a dipole source, we performed simulations with a plane wave source while changing the diameter and height of the GaAs SIL. The dimensions of the polymer SIL were fixed at a diameter of 3000 nm and a height of 2000 nm. We read the position of the maximum E-field intensity and then positioned a point dipole at the antinode and swept the dimensions of the GaAs SIL again. After optimizing the GaAs SIL dimensions, the diameter and height of the second SIL were swept to select the structure with the best brightness and good tolerance in dimension. The total simulation region was 10 × 10 × 3.7 µm3, and the minimum mesh size was 2 nm near the QD in 100 × 100 × 100 nm3. For the simulation, the refractive indices of GaAs at room temperature (n = 3.5158 at 925 nm) determined by Papatryfonos et al.3434. K. Papatryfonos, T. Angelova, A. Brimont, B. Reid, S. Guldin, P. R. Smith, M. Tang, K. Li, A. J. Seeds, H. Liu, and D. R. Selviah, AIP Adv. 11(2), 025327 (2021). https://doi.org/10.1063/5.0039631 and gold determined by Johnson and Christy3535. P. B. Johnson and R. W. Christy, Phys. Rev. B 6(12), 4370 (1972). https://doi.org/10.1103/physrevb.6.4370 were used.

ACKNOWLEDGMENTS

We are grateful for the financial support from the Institute for Information and Communication Technology Planning and Evaluation (Grant No. 2021-0-01540) and the National Research Foundation of Korea (Grant Nos. 2020R1I1A3061815, 2021R1I1A1A01040695, and 2020R1A6A1A03047771). D.L. acknowledges the financial support from the Chungnam National University. S.I.P. and J.D.S. acknowledge the financial support from the Korea Institute of Science and Technology institutional program under Grant No. 2E31532.