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Coupling effects between widely separated layers of self-assembled quantum dots

L. Berg1,*, J. Lange1,*, L. Schnorr1, F. Bartels1, C. Rothfuchs-Engels2,†, N. Bart2, S. Krüger2, A. Ludwig2, A. D. Wieck2 et al.

T. Heinzel1,‡

  • *These authors contributed equally to this work.
  • †Present address: DESY, Notkestr. 85, 22607 Hamburg, Germany.
  • ‡Contact author: thomas.heinzel@hhu.de
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Phys. Rev. B 114, 065307 – Published 27 July, 2026

DOI: https://doi.org/10.1103/6hxs-dvn7

Abstract

Coupling effects between self-assembled quantum dots in different layers separated by approximately 200nm are studied by transient capacitance spectroscopy. This coupling manifests itself via interdependent time constants of the transients. Two different coupling mechanisms that act over such large spacings are identified. The first one is electrostatic coupling, caused by electrons in the first layer that modify the electric field at the site of the second layer and with it the lifetime of the discrete states in the quantum dots therein. The second mechanism is cascade coupling, where electrons emitted by the first layer are recaptured by the second layer. A rate equation model combined with self-consistent band structure calculations provides a quantification of the proposed mechanisms.

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References (46)

  1. D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, Direct formation of quantum-sized dots from uniform coherent islands of InGaAs on GaAs surfaces, Appl. Phys. Lett. 63, 3203 (1993).
  2. P. M. Petroff, A. Lorke, and A. Imamoglu, Epitaxially self-assembled quantum dots, Phys. Today 54(5), 46 (2001).
  3. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamoglu, A quantum dot single-photon turnstile device, Science 290, 2282 (2000).
  4. M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, Optically programmable electron spin memory using semiconductor quantum dots, Nature (London) 432, 81 (2004).
  5. C. L. Salter, R. M. Stevenson, I. Farrer, C. Nicoll, D. A. Ritchie, and A. J. Shields, An entangled-light-emitting diode, Nature (London) 465, 594 (2010).
  6. A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vuckovic, Integrated quantum optical networks based on quantum dots and photonic crystals, New J. Phys. 13, 055025 (2011).
  7. E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Quantum cryptography with a photon turnstile, Nature (London) 420, 762 (2002).
  8. 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, Quantum teleportation using a light-emitting diode, Nat. Photon. 7, 311 (2013).
  9. D. J. Mowbray and M. S. Skolnick, New physics and devices based on self-assembled semiconductor quantum dots, J. Phys. D: Appl. Phys. 38, 2059 (2005).
  10. S. Buckley, K. Rivoire, and J. Vučković, Engineered quantum dot single-photon sources, Rep. Prog. Phys. 75, 126503 (2012).
  11. I. L. Krestnikov, N. A. Maleev, A. V. Sakharov, A. R. Kovsh, A. E. Zhukov, A. F. Tsatsulnikov, V. M. Ustinov, Z. I. Alferov, N. N. Ledentsov, D. Bimberg, and J. A. Lott, 1.3 µm resonant-cavity InGaAs/GaAs quantum dot light-emitting devices, Semicond. Sci. Technol. 16, 844 (2001).
  12. V. M. Ustinov, N. A. Maleev, A. E. Zhukov, A. R. Kovsh, A. Y. Egorov, A. V. Lunev, B. V. Volovik, I. L. Krestnikov, Y. G. Musikhin, N. A. Bert, P. S. Kopev, and Z. I. Alferov, InAs/InGaAs quantum dot structures on GaAs substrates emitting at 1.3 µm, Appl. Phys. Lett. 74, 2815 (1999).
  13. E. U. Rafailov, M. A. Cataluna, and W. Sibbett, Mode-locked quantum-dot lasers, Nat. Photon. 1, 395 (2007).
  14. M. Geller, A. Marent, T. Nowozin, and D. Bimberg, Self-organized quantum dots for future semiconductor memories, J. Phys.: Condens. Matter 20, 454202 (2008).
  15. T. Nowozin, A. Marent, M. Geller, D. Bimberg, N. Akcay, and N. Öncan, Temperature and electric field dependence of the carrier emission processes in a quantum dot-based memory structure, Appl. Phys. Lett. 94, 042108 (2009).
  16. A. Marent, T. Nowozin, M. Geller, and D. Bimberg, The QD-Flash: A quantum dot-based memory device, Semicond. Sci. Technol. 26, 014026 (2011).
  17. P. Maier, F. Hartmann, M. Emmerling, C. Schneider, M. Kamp, S. Hoefling, and L. Worschech, Electro-photo-sensitive memristor for neuromorphic and arithmetic computing, Phys. Rev. Appl. 5, 054011 (2016).
  18. P. Boucaud, J. B. Williams, K. S. Gill, M. S. Sherwin, W. V. Schoenfeld, and P. M. Petroff, Terahertz-frequency electronic coupling in vertically coupled quantum dots, Appl. Phys. Lett. 77, 4356 (2000).
  19. M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski, Z. R. Wasilewski, O. Stern, and A. Forchel, Coupling and entangling of quantum states in quantum dot molecules, Science 291, 451 (2001).
  20. H.-W. Ren, S. V. Nair, J.-S. Lee, S. Sugo, and Y. Matsumoto, Photoluminescence of strain-induced coupled InGaAs/GaAs quantum-dot pairs, J. Electron. Mat. 29, 520 (2000).
  21. M. Korkusinski and P. Hawrylak, Electronic structure of vertically stacked self-assembled quantum disks, Phys. Rev. B 63, 195311 (2001).
  22. D. G. Austing, S. Tarucha, H. Tamura, K. Muraki, F. Ancilotto, M. Barranco, A. Emperador, R. Mayol, and M. Pi, Integer filling factor phases and isospin in vertical diatomic artificial molecules, Phys. Rev. B 70, 045324 (2004).
  23. P. Miska, J. Even, C. Panthoen, and O. Dehaese, Vertical electronic coupling between InAs/InP quantum-dot layers emitting in the near-infrared range, Appl. Phys. Lett. 86, 111905 (2005).
  24. F. Yuan, Z. Jiang, and F. Lu, Study of coupling effect in double-layer quantum dots by admittance spectroscopy, Appl. Phys. Lett. 89, 072112 (2006).
  25. S. M. Reimann and M. Manninen, Electronic structure of quantum dots, Rev. Mod. Phys. 74, 1283 (2002).
  26. D. Loss and D. P. DiVincenco, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
  27. O. Gywat, G. Burkard, and D. Loss, Biexcitons in coupled quantum dots as a source of entangled photons, Phys. Rev. B 65, 205329 (2002).
  28. R. J. Luyken, A. Lorke, M. Fricke, J. P. Kotthaus, G. Medeiros-Ribeiro, and P. Petroff, Coulomb-coupling in vertically aligned self-assembled InAs quantum dots, Nanotechnology 10, 14 (1999).
  29. G. Springholz, V. Holy, M. Pinczolits, and G. Bauer, Self-organized growth of three- dimensional quantum-dot crystals with fcc-like stacking and a tunable lattice constant, Science 282, 734 (1998).
  30. D. Grigoriev, M. Schmidbauer, P. Schäfer, S. Besedin, Y. I. Mazur, Z. M. Wang, G. J. Salamo, and R. Köhler, Three-dimensional self-ordering in an InGaAs/GaAs multilayered quantum dot structure investigated by x-ray diffuse scattering, J. Phys. D: Appl. Phys. 38, A154 (2005).
  31. Y. K. Su, S. J. Chang, L. W. Ji, C. S. Chang, L. W. Wu, W. C. Lai, T. H. Fang, and K. T. Lam, InGaN/GaN blue light-emitting diodes with self-assembled quantum dots, Semicond. Sci. Technol. 19, 389 (2004).
  32. J. Chen, Q. Zhao, B. Yu, and U. Lemmer, A review on quantum dot-based color conversion layers for mini/micro-LED displays: Packaging, light management, and pixelation, Adv. Opt. Mater. 12, 2300873 (2024).
  33. R. A. Abbas, Y. M. Sabry, H. Omran, Z. Huang, M. Zimmer, M. Jetter, P. Michler, and D. Khalil, Modelling and experimental characterization of double layer InP/AlGaInP quantum dot laser, Opt. Quant. Electron. 56, 205 (2024).
  34. Q. Li, X. Wang, Z. Zhang, H. Chen, Y. Huang, C. Hou, J. Wang, R. Zhang, J. Ning, J. Min, and C. Zheng, Development of modulation p-doped 1310 nm InAs/GaAs quantum dot laser materials and ultrashort cavity Fabry-Perot and distributed feedback laser diodes, ACS Photon. 5, 1084 (2018).
  35. T. Sugaya, O. Numakami, R. Oshima, S. Furue, H. Komaki, T. Amano, K. Matsubara, Y. Okano, and S. Niki, Ultra-high stacks of InGaAs/GaAs quantum dots for high efficiency solar cells, Energy Environ. Sci. 5, 6233 (2012).
  36. S. M. Hubbard, C. D.Cress, C. G. Bailey, R. P. Raffaelle, S. G. Bailey, and D. M. Wilt, Effect of strain compensation on quantum dot enhanced GaAs solar cells, Appl. Phys. Lett. 92, 123512 (2008).
  37. L. Schnorr, J. Labes, L. Kurten, T. Heinzel, C. Rothfuchs-Engels, S. Scholz, A. Ludwig, and A. D. Wieck, Electron capture and emission dynamics of self-assembled quantum dots far from equilibrium with the environment, Phys. Rev. B 104, 035303 (2021).
  38. See Supplemental Material at https://link.aps.org/supplemental/10.1103/6hxs-dvn7 for IV- and CV-characteristics of the samples, details on the sensitivity correction and the bi-exponential analysis of the capacitance transients, as well as Poisson-Schrödinger calculations of the inter-layer electric field coupling and its influence on the simulated transients.
  39. M. C. Löbl, S. Scholz, I. Söllner, J. Ritzmann, T. Denneulin, A. Kovács, B. E. Kardynal, A. D. Wieck, A. Ludwig, and R. J. Warburton, Excitons in InGaAs quantum dots without electron wetting layer states, Commun. Phys. 2, 93 (2019).
  40. L. Schnorr, T. Heinzel, S. Scholz, A. Ludwig, and A. D. Wieck, Laplace deep level transient spectroscopy on self-assembled quantum dots, J. Appl. Phys. 124, 104301 (2018).
  41. L. Berg, Occupation dynamics of self-assembled quantum dots and deep level traps, Ph.D. thesis, University of Düsseldorf, Germany, 2024.
  42. V. Korobov and V. Ochkov, Chemical Kinetics with Mathcad and Maple (Springer, Vienna, 2011).
  43. G. Snider, 1D Poisson-Schrödinger solver (2025), version beta 8j1. [Accessed on February 28, 2025].
  44. C. Schulhauser, R. Warburton, A. Högele, A. Govorov, K. Karrai, J. Garcia, B. Gerardot, and P. Petroff, Emission from neutral and charged excitons in a single quantum dot in a magnetic field, Physica E 21, 184 (2004).
  45. L. Berg, L. Schnorr, J. Wilkens, T. Heinzel, C. Rothfuchs-Engels, S. Scholz, A. Ludwig, and A. D. Wieck, Electron capture dynamics into self-assembled quantum dots far from equilibrium with their environment, Phys. Rev. B 109, 235433 (2024).
  46. L. Berg, J. Lange, L. Schnorr, F. Bartels, C. Rothfuchs-Engels, N. Bart, S. Krüger, A. Ludwig, A. D. Wieck, and T. Heinzel, Electrostatic coupling between self-assembled quantum dot layers [data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.17952494.

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Phys. Rev. B 114, 065307– Published 27 July, 2026
  • Received 24 July 2024
  • Revised 29 June 2026
  • Accepted 6 July 2026
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