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Electrically Driven Quantum Dot Based Single-Photon Sources pp 125–149Cite as

Hybrid Simulation of an Electrically Driven Single-Photon Source

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Abstract

This chapter provides a proof-of-principle application of the hybrid modeling approach presented in the previous chapter. An electrically driven single-photon source based on a single QD embedded in a semiconductor pin-diode is investigated by numerical simulations. The numerical method introduced before is extended towards the hybrid model. Simulation results are presented for stationary and pulsed electrical excitation. A critical discussion of the numerical results and an outlook on possible extensions of the approach are given.

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Notes

  1. 1.

    More precisely, the capture rate models need to be expressed as functions of the spatially averaged potentials of the macroscopic environment, see Sects. 5.3.5 and 5.3.6.

References

  1. Albinus G, Gajewski H, Hünlich R (2002) Thermodynamic design of energy models of semiconductor devices. Nonlinearity 15(2):367–383. https://doi.org/10.1088/0951-7715/15/2/307

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Baer N, Gartner P, Jahnke F (2004) Coulomb effects in semiconductor quantum dots. Eur Phys J B 42(2):231–237. https://doi.org/10.1140/epjb/e2004-00375-6

    Article  ADS  Google Scholar 

  3. Bandelow U, Gajewski H, Hünlich R (2005) Fabry–Perot lasers: thermodynamics-based modeling. In: Piprek J (ed) Optoelectronic devices, chap 3. Springer, New York, pp 63–85. https://doi.org/10.1007/0-387-27256-9_3

  4. Bandelow U, Hünlich R, Koprucki T (2003) Simulation of static and dynamic properties of edge-emitting multiple-quantum-well lasers. IEEE J Sel Top Quant 9(3):798–806. https://doi.org/10.1109/JSTQE.2003.818343

    Article  Google Scholar 

  5. Baro M, Neidhardt H, Rehberg J (2005) Current coupling of drift-diffusion models and Schrödinger-Poisson systems: dissipative hybrid models. SIAM J Math Anal 37(3):941–981. https://doi.org/10.1137/040611690

    Article  MathSciNet  MATH  Google Scholar 

  6. Bayer M, Ortner G, Stern O, Kuther A, Gorbunov AA, Forchel A, Hawrylak P, Fafard S, Hinzer K, Reinecke TL, Walck SN, Reithmaier JP, Klopf F, Schäfer F (2002) Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots. Phys Rev B 65(19):195315. https://doi.org/10.1103/physrevb.65.195315

    Article  ADS  Google Scholar 

  7. Bennett AJ, Patel RB, Shields AJ, Cooper K, Atkinson P, Nicoll CA, Ritchie DA (2008) Indistinguishable photons from a diode. Appl Phys Lett 92(19):193503. https://doi.org/10.1063/1.2918841

    Article  ADS  Google Scholar 

  8. Bonani F, Ghione G (2001) Noise in semiconductor devices—modeling and simulation. No. 7 in advanced microelectronics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04530-5

    Book  Google Scholar 

  9. Breuer HP, Petruccione F (2002) The theory of open quantum systems. Oxford University Press, Oxford. https://doi.org/10.1093/acprof:oso/9780199213900.001.0001

  10. Bulnes Cuetara G, Esposito M, Schaller G (2016) Quantum thermodynamics with degenerate eigenstate coherences. Entropy 18(12):447. https://doi.org/10.3390/e18120447

    Article  ADS  Google Scholar 

  11. Carmele A, Milde F, Dachner MR, Harouni MB, Roknizadeh R, Richter M, Knorr A (2010) Formation dynamics of an entangled photon pair: a temperature-dependent analysis. Phys Rev B 81(19):195319. https://doi.org/10.1103/physrevb.81.195319

    Article  ADS  Google Scholar 

  12. Chow WW, Jahnke F (2013) On the physics of semiconductor quantum dots for applications in lasers and quantum optics. Prog Quantum Electron 37(3):109–184. https://doi.org/10.1016/j.pquantelec.2013.04.001

    Article  ADS  Google Scholar 

  13. Dachner MR, Malić E, Richter M, Carmele A, Kabuss J, Wilms A, Kim JE, Hartmann G, Wolters J, Bandelow U, Knorr A (2010) Theory of carrier and photon dynamics in quantum dot light emitters. Phys Status Solidi B 247(4):809–828. https://doi.org/10.1002/pssb.200945433

    Article  ADS  Google Scholar 

  14. Ferreira R, Bastard G (2015) Capture and relaxation in self-assembled semiconductor quantum dots. Morgan & Claypool Publishers, San Rafael, CA, pp 2053–2571. https://doi.org/10.1088/978-1-6817-4089-8

  15. Fischbach S, Schlehahn A, Thoma A, Srocka N, Gissibl T, Ristok S, Thiele S, Kaganskiy A, Strittmatter A, Heindel T, Rodt S, Herkommer A, Giessen H, Reitzenstein S (2017) Single quantum dot with microlens and 3d-printed micro-objective as integrated bright single-photon source. ACS Photonics 4(6):1327–1332. https://doi.org/10.1021/acsphotonics.7b00253

    Article  Google Scholar 

  16. Florian M, Gies C, Gartner P, Jahnke F (2012) Improved antibunching by using high-excitation pulses from a single semiconductor quantum dot—a theoretical study. J Opt Soc Am B 29(2):A31. https://doi.org/10.1364/josab.29.000a31

    Article  ADS  Google Scholar 

  17. Gajewski H, Liero M, Nürnberg R, Stephan H (2016) WIAS-TeSCA—two-dimensional semi-conductor analysis package. WIAS Technical report No. 14

    Google Scholar 

  18. Gegg M, Richter M (2016) Efficient and exact numerical approach for many multi-level systems in open system CQED. New J Phys 18(4):043037. https://doi.org/10.1088/1367-2630/18/4/043037

    Article  Google Scholar 

  19. Gies C, Florian M, Steinhoff A, Jahnke F (2017) Theory of quantum light sources and cavity-QED emitters based on semiconductor quantum dots. In: Michler P (ed) Quantum dots for quantum information technologies. Springer Series in Nano-Optics and Nanophotonics, chap 1. Springer, Cham, pp 3–40. https://doi.org/10.1007/978-3-319-56378-7_1

    Chapter  Google Scholar 

  20. Gies C, Gericke F, Gartner P, Holzinger S, Hopfmann C, Heindel T, Wolters J, Schneider C, Florian M, Jahnke F, Höfling S, Kamp M, Reitzenstein S (2017) Strong light-matter coupling in the presence of lasing. Phys Rev A 96:023806. https://doi.org/10.1103/PhysRevA.96.023806

    Article  ADS  Google Scholar 

  21. Gies C, Wiersig J, Lorke M, Jahnke F (2007) Semiconductor model for quantum-dot-based microcavity lasers. Phys Rev A 75(1):013803. https://doi.org/10.1103/PhysRevA.75.013803

    Article  ADS  Google Scholar 

  22. Gilbert JR, Moler C, Schreiber R (1992) Sparse matrices in MATLAB: design and implementation. SIAM J Matrix Anal Appl 13(1):333–356. https://doi.org/10.1137/0613024

    Article  MathSciNet  MATH  Google Scholar 

  23. Grupen M, Hess K (1998) Simulation of carrier transport and nonlinearities in quantum-well laser diodes. IEEE J Quantum Electron 34(1):120–140. https://doi.org/10.1109/3.655016

    Article  ADS  Google Scholar 

  24. Gschrey M, Thoma A, Schnauber P, Seifried M, Schmidt R, Wohlfeil B, Krüger L, Schulze JH, Heindel T, Burger S, Schmidt F, Strittmatter A, Rodt S, Reitzenstein S (2015) Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography. Nat Commun 6:7662. https://doi.org/10.1038/ncomms8662

    Article  ADS  Google Scholar 

  25. Haug H, Koch SW (2004) Quantum theory of the optical and electronic properties of semiconductors, 4th edn. World Scientific, Singapore. https://doi.org/10.1142/5394

  26. Kantner M (2020) Generalized Scharfetter–Gummel schemes for electro-thermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient. J Comput Phys 402:109091. https://doi.org/10.1016/j.jcp.2019.109091

    Article  MathSciNet  Google Scholar 

  27. Kantner M (2019) Hybrid modeling of quantum light emitting diodes: self-consistent coupling of drift-diffusion, Schrödinger-Poisson, and quantum master equations. In: Proceedings of the SPIE photonics west: physics and simulation of optoelectronic devices XXVII, vol 10912. SPIE, p 109120U. https://doi.org/10.1117/12.2515209

  28. Kantner M, Bandelow U, Koprucki T, Wünsche HJ (2016) Modeling and simulation of injection dynamics for quantum dot based single-photon sources. In: Proceedings of the international conference on numerical simulation of optoelectronic devices, pp 219–220. https://doi.org/10.1109/nusod.2016.7547005

  29. Kantner M, Mittnenzweig M, Koprucki T (2017) Hybrid quantum-classical modeling of quantum dot devices. Phys Rev B 96(20):205301. https://doi.org/10.1103/PhysRevB.96.205301

    Article  ADS  Google Scholar 

  30. Koprucki T, Wilms A, Knorr A, Bandelow U (2011) Modeling of quantum dot lasers with microscopic treatment of Coulomb effects. Opt Quantum Electron 42(11):777–783. https://doi.org/10.1007/s11082-011-9479-2

    Article  Google Scholar 

  31. Levinstein M, Rumyantsev S, Shur M (eds) (1996) Handbook series on semiconductor parameters—ternary and quaternary III–V compounds, vol 2. World Scientific, Singapore. https://doi.org/10.1142/2046-vol2

    Book  Google Scholar 

  32. Lodahl P, Mahmoodian S, Stobbe S (2015) Interfacing single photons and single quantum dots with photonic nanostructures. Rev Mod Phys 87(2):347–400. https://doi.org/10.1103/revmodphys.87.347

    Article  ADS  MathSciNet  Google Scholar 

  33. Lorke M, Jahnke F, Chow WW (2007) Excitation dependences of gain and carrier-induced refractive index change in quantum-dot lasers. Appl Phys Lett 90(5):051112. https://doi.org/10.1063/1.2437670

    Article  ADS  Google Scholar 

  34. Michler P (2009) Quantum dot single-photon sources. In: Michler P (ed) Single semiconductor quantum dots, nanoscience and technology, chap 6. Springer, Berlin, Heidelberg, pp 185–225. https://doi.org/10.1007/978-3-540-87446-1_6

    Chapter  Google Scholar 

  35. Michler P, Kiraz A, Becher C, Schoenfeld WV, Petroff PM, Zhang L, Hu E, İmamoğlu A (2000) A quantum dot single-photon turnstile device. Science 290(5500):2282–2285. https://doi.org/10.1126/science.290.5500.2282

    Article  ADS  Google Scholar 

  36. Munteanu D, Autran JL (2012) A 2-D/3-D Schrödinger–Poisson drift-diffusion numerical simulation of radially-symmetric nanowire MOSFETs. In: Peng X (ed) Nanowires, chap 15. IntechOpen, London, pp 341–370. https://doi.org/10.5772/52587

    Google Scholar 

  37. Palankovski V, Quay R (2004) Analysis and simulation of heterostructure devices. Series in computational microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0560-3

    Book  Google Scholar 

  38. Purcell EM, Torrey HC, Pound RV (1946) Resonance absorption by nuclear magnetic moments in a solid. Phys Rev 69(1–2):37–38. https://doi.org/10.1103/physrev.69.37

    Article  ADS  Google Scholar 

  39. Ritter S, Gartner P, Gies C, Jahnke F (2010) Emission properties and photon statistics of a single quantum dot laser. Opt Express 18(10):9909–9921. https://doi.org/10.1364/oe.18.009909

    Article  ADS  Google Scholar 

  40. Schaller G (2014) Open quantum systems far from equilibrium. Lecture notes in physics, vol 881. Springer, Cham

    Book  Google Scholar 

  41. Schlehahn A, Krüger L, Gschrey M, Schulze JH, Rodt S, Strittmatter A, Heindel T, Reitzenstein S (2015) Operating single quantum emitters with a compact Stirling cryocooler. Rev Sci Instrum 86:013113. https://doi.org/10.1063/1.4906548

    Article  ADS  Google Scholar 

  42. Schnauber P, Schall J, Bounouar S, Höhne T, Park SI, Ryu GH, Heindel T, Burger S, Song JD, Rodt S, Reitzenstein S (2018) Deterministic integration of quantum dots into on-chip multimode interference beamsplitters using in situ electron beam lithography. Nano Lett 18(4):2336–2342. https://doi.org/10.1021/acs.nanolett.7b05218

    Article  ADS  Google Scholar 

  43. Scully MO, Zubairy MS (1997) Quantum optics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511813993

  44. Steiger S, Veprek RG, Witzigmann B (2008) Unified simulation of transport and luminescence in optoelectronic nanostructures. J Comput Electron 7(4):509–520. https://doi.org/10.1007/s10825-008-0261-z

    Article  Google Scholar 

  45. Strauf S, Jahnke F (2011) Single quantum dot nanolaser. Laser Photonics Rev 5(5):607–633. https://doi.org/10.1002/lpor.201000039

    Article  Google Scholar 

  46. Tischler JG, Bracker AS, Gammon D, Park D (2002) Fine structure of trions and excitons in single GaAs quantum dots. Phys Rev B 66(8):081310. https://doi.org/10.1103/PhysRevB.66.081310

    Article  ADS  Google Scholar 

  47. Vogel W, Welsch DG (2006) Quantum optics, 3rd edn. Wiley, Weinheim. https://doi.org/10.1002/3527608524

  48. Weisskopf V, Wigner E (1930) Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie. Z Phys 63(1–2):54–73. https://doi.org/10.1007/bf01336768

    Article  ADS  MATH  Google Scholar 

  49. Wilms A, Mathé P, Schulze F, Koprucki T, Knorr A, Bandelow U (2013) Influence of the carrier reservoir dimensionality on electron-electron scattering in quantum dot materials. Phys Rev B 88:235421. https://doi.org/10.1103/PhysRevB.88.235421

    Article  ADS  Google Scholar 

  50. Wojs A, Hawrylak P, Fafard S, Jacak L (1996) Electronic structure and magneto-optics of self-assembled quantum dots. Phys Rev B 54(8):5604–5608. https://doi.org/10.1103/physrevb.54.5604

    Article  ADS  Google Scholar 

  51. Yuan Z, Kardynal BE, Stevenson RM, Shields AJ, Lobo CJ, Cooper K, Beattie NS, Ritchie DA, Pepper M (2002) Electrically driven single-photon source. Science 295(5552):102–105. https://doi.org/10.1126/science.1066790

    Article  ADS  Google Scholar 

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  1. Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Leibniz Institute in Forschungsverbund Berlin e. V., Berlin, Germany

    Dr. Markus Kantner

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Kantner, M. (2020). Hybrid Simulation of an Electrically Driven Single-Photon Source. In: Electrically Driven Quantum Dot Based Single-Photon Sources. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-39543-8_6

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