Advertisement

Multi-dimensional Modeling and Simulation of Semiconductor Nanophotonic Devices

  • Markus KantnerEmail author
  • Theresa Höhne
  • Thomas Koprucki
  • Sven Burger
  • Hans-Jürgen Wünsche
  • Frank Schmidt
  • Alexander Mielke
  • Uwe Bandelow
Chapter
  • 182 Downloads
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 194)

Abstract

Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semi-classical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperatures. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.

Notes

Acknowledgements

This work has been supported by the German Research Foundation (DFG) within the collaborative research center SFB 787 Semiconductor Nanophotonics under grant B4. The authors would like to thank Patricio Farrell, Jürgen Fuhrmann, Philipp Gutsche, Jan Pomplun, Nella Rotundo, Alexander Wilms, Benjamin Wohlfeil and Lin Zschiedrich for excellent collaboration and valuable discussions.

References

  1. 1.
    P. Bhattacharya, Z. Mi, Proc. IEEE 95(9), 1723 (2007).  https://doi.org/10.1109/JPROC.2007.900897CrossRefGoogle Scholar
  2. 2.
    P. Michler (ed.), in Single Semiconductor Quantum Dots. NanoScience and Technology (Springer, Berlin, Heidelberg, 2009). https://doi.org/10.1007/978-3-540-87446-1Google Scholar
  3. 3.
    D. Bimberg, U.W. Pohl, Mater. Today 14(9), 388 (2011). https://doi.org/10.1016/S1369-7021(11)70183-3CrossRefGoogle Scholar
  4. 4.
    P. Lodahl, S. Mahmoodian, S. Stobbe, Rev. Mod. Phys. 87(2), 347 (2015). https://doi.org/10.1103/revmodphys.87.347ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    P. Michler (ed.), in Quantum Dots for Quantum Information Technologies. Springer Series in Nano-Optics and Nanophotonics (Springer, Cham, 2017). https://doi.org/10.1007/978-3-319-56378-7zbMATHGoogle Scholar
  6. 6.
    M. Streiff, A. Witzig, M. Pfeiffer, P. Royo, W. Fichtner, IEEE J. Sel. Top. Quantum Electron. 9, 879 (2003). https://doi.org/10.1109/JSTQE.2003.818858ADSCrossRefGoogle Scholar
  7. 7.
    U. Bandelow, H. Gajewski, R. Hünlich, in Optoelectronic Devices, ed. by J. Piprek (Springer, New York, 2005), Chap. 3, pp. 63–85. https://doi.org/10.1007/0-387-27256-9_3
  8. 8.
    H. Wenzel, P. Crump, H. Ekhteraei, C. Schultz, J. Pomplun, S. Burger, L. Zschiedrich, F. Schmidt, G. Erbert, in 2011 11th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (IEEE, 2011), p. 143.  https://doi.org/10.1109/nusod.2011.6041183
  9. 9.
    J. Pomplun, H. Wenzel, S. Burger, L. Zschiedrich, M. Rozova, F. Schmidt, P. Crump, H. Ekhteraei, C.M. Schultz, G. Erbert, Proc. SPIE 8255, 825510 (2012).  https://doi.org/10.1117/12.909330
  10. 10.
    W.W. van Roosbroeck, Bell Syst. Tech. J. 29(4), 560 (1950).  https://doi.org/10.1002/j.1538-7305.1950.tb03653.xzbMATHCrossRefGoogle Scholar
  11. 11.
    S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer, Vienna, 1984). https://doi.org/10.1007/978-3-7091-8752-4CrossRefGoogle Scholar
  12. 12.
    M. Kantner, T. Koprucki, Opt. Quantum. Electron. 48(12), 543 (2016).  https://doi.org/10.1007/s11082-016-0817-2
  13. 13.
    M. Kantner, Modeling and simulation of electrically driven quantum dot based single-photon sources: From classical device physics to open quantum systems. Ph.D. thesis, Technical University Berlin, Berlin (2018). https://doi.org/10.14279/depositonce-7516
  14. 14.
    K. Hess, Advanced Theory of Semiconductor Devices, 2nd edn. (Wiley-IEEE Press, New York, 2000). https://doi.org/10.1109/9780470544105CrossRefGoogle Scholar
  15. 15.
    C. Jacoboni, Theory of Electron Transport in Semiconductors (Springer, Berlin, Heidelberg, 2010). https://doi.org/10.1007/978-3-642-10586-9CrossRefGoogle Scholar
  16. 16.
    S.M. Sze, Physics of Semiconductor Devices, 2nd edn. (Wiley, New York, 1981). https://doi.org/10.1002/0470068329CrossRefGoogle Scholar
  17. 17.
    V. Palankovski, R. Quay, Analysis and Simulation of Heterostructure Devices. Series in Computational Microelectronics (Springer, Vienna, 2004). https://doi.org/10.1007/978-3-7091-0560-3CrossRefGoogle Scholar
  18. 18.
    D. Schröder, Modelling of Interface Carrier Transport for Device Simulation. Series in Computational Microelectronics (Springer, Vienna, 1994). https://doi.org/10.1007/978-3-7091-6644-4zbMATHCrossRefGoogle Scholar
  19. 19.
    F. Schmidt, in Handbook of Optoelectronic Device Modeling and Simulation: Fundamentals, Materials, Nanostructures, LEDs, and Amplifiers, vol. 2, ed. by J. Piprek (CRC Press, Taylor & Francis Group, Boca Raton, 2017), Chap. Photonics, pp. 807–852.  https://doi.org/10.4324/9781315152318-27CrossRefGoogle Scholar
  20. 20.
    E.S.C. Ching, P.T. Leung, A.M. van den Brink, W.M. Suen, S.S. Tong, K. Young, Rev. Mod. Phys. 70(4), 1545 (1998).  https://doi.org/10.1103/revmodphys.70.1545ADSCrossRefGoogle Scholar
  21. 21.
    A. Fischer, T. Koprucki, K. Gärtner, M.L. Tietze, J. Brückner, B. Lüssem, K. Leo, A. Glitzky, R. Scholz, Adv. Funct. Mater. 24(22), 3367 (2014).  https://doi.org/10.1002/adfm.201303066CrossRefGoogle Scholar
  22. 22.
    G.K. Wachutka, IEEE Trans. Comput. Aided Design Integr. Circuits Syst. 9(11), 1141 (1990). https://doi.org/10.1109/43.62751CrossRefGoogle Scholar
  23. 23.
    U. Lindefelt, J. Appl. Phys. 75(2), 942 (1994).  https://doi.org/10.1063/1.356450ADSCrossRefGoogle Scholar
  24. 24.
    G. Albinus, H. Gajewski, R. Hünlich, Nonlinearity 15(2), 367 (2002).  https://doi.org/10.1088/0951-7715/15/2/307ADSMathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    M. Kantner, J. Comput. Phys. 402, 109091 (2020). https://doi.org/10.1016/j.jcp.2019.109091MathSciNetCrossRefGoogle Scholar
  26. 26.
  27. 27.
    M. Grmela, H.C. Öttinger, Phys. Rev. E 56, 6620 (1997).  https://doi.org/10.1103/PhysRevE.56.6620ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    A. Mielke, in Recent Trends in Dynamical Systems, ed. by A. Johann, H.P. Kruse, F. Rupp, S. Schmitz, no. 35 in Springer Proceedings in Mathematics & Statistics (Springer, Basel, 2013), Chap. 21, pp. 555–585. https://doi.org/10.1007/978-3-0348-0451-6_21CrossRefGoogle Scholar
  29. 29.
    A. Mielke, in Mathematical Results in Quantum Mechanics, ed. by P. Exner, W. König, H. Neidhardt (World Scientific, Singapore, 2015), pp. 331–348. https://doi.org/10.1142/9789814618144_0029
  30. 30.
    R. Michalzik (ed.), VCSELs–Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, Springer Series in Optical Sciences, vol. 166 (Springer, Berlin, Heidelberg, 2013). https://doi.org/10.1007/978-3-642-24986-0Google Scholar
  31. 31.
    T. Koprucki, A. Wilms, A. Knorr, U. Bandelow, Opt. Quantum. Electron. 42(11), 777 (2011).  https://doi.org/10.1007/s11082-011-9479-2CrossRefGoogle Scholar
  32. 32.
    A. Wilms, P. Mathé, F. Schulze, T. Koprucki, A. Knorr, U. Bandelow, Phys. Rev. B 88, 235421 (2013).  https://doi.org/10.1103/PhysRevB.88.235421
  33. 33.
    M. Kantner, M. Mittnenzweig, T. Koprucki, Phys. Rev. B 96(20), 205301 (2017).  https://doi.org/10.1103/PhysRevB.96.205301
  34. 34.
    M. Kantner, Proc. SPIE 10912, 109120U (2019).  https://doi.org/10.1117/12.2515209
  35. 35.
    M. Kantner, T. Koprucki, H.-J. Wünsche, U. Bandelow, in Proceedings of the 24th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), pp. 355–358 (2019). https://doi.org/10.1109/SISPAD.2019.8870459
  36. 36.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002). https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
  37. 37.
    W.W. Chow, F. Jahnke, Prog. Quantum Electron. 37(3), 109 (2013).  https://doi.org/10.1016/j.pquantelec.2013.04.001ADSCrossRefGoogle Scholar
  38. 38.
    S. Reitzenstein, A. Forchel, J. Phys. D: Appl. Phys. 43(3), 033001 (2010).  https://doi.org/10.1088/0022-3727/43/3/033001ADSCrossRefGoogle Scholar
  39. 39.
    G.A. Baraff, R.K. Smith, Phys. Rev. A 61(4), 043808 (2000).  https://doi.org/10.1103/PhysRevA.61.043808
  40. 40.
    H. Wenzel, H.J. Wünsche, IEEE J. Quantum Electron. 30(9), 2073 (1994).  https://doi.org/10.1109/3.309867ADSCrossRefGoogle Scholar
  41. 41.
    A. Witzig, Modeling the optical processes in semiconductor lasers. Ph.D. thesis, ETH Zürich, Zürich (2002). https://doi.org/10.3929/ethz-a-004407405
  42. 42.
    S. Steiger, R.G. Veprek, B. Witzigmann, J. Comput. Electron. 7(4), 509 (2008).  https://doi.org/10.1007/s10825-008-0261-zCrossRefGoogle Scholar
  43. 43.
    M. Grupen, K. Hess, IEEE J. Quantum Electron. 34(1), 120 (1998).  https://doi.org/10.1109/3.655016ADSCrossRefGoogle Scholar
  44. 44.
    W.W. Chow, S.W. Koch, IEEE J. Quantum Electron. 41, 495 (2005).  https://doi.org/10.1109/JQE.2005.843948ADSCrossRefGoogle Scholar
  45. 45.
    K. Lüdge, E. Schöll, IEEE J. Quantum Electron. 45(11), 1396 (2009).  https://doi.org/10.1109/jqe.2009.2028159ADSCrossRefGoogle Scholar
  46. 46.
    E. Malić, K.J. Ahn, M.J.P. Bormann, P. Hövel, E. Schöll, A. Knorr, M. Kuntz, D. Bimberg, Appl. Phys. Lett. 89(10), 101107 (2006).  https://doi.org/10.1063/1.2346224ADSCrossRefGoogle Scholar
  47. 47.
    H. Haug, S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th edn. (World Scientific, Singapore, 2004). https://doi.org/10.1142/5394
  48. 48.
    T.R. Nielsen, P. Gartner, F. Jahnke, Phys. Rev. B 69, 235314 (2004).  https://doi.org/10.1103/PhysRevB.69.235314
  49. 49.
    A. Wilms, D. Breddermann, P. Mathé, Phys. Status Solidi C 9(5), 1278 (2012).  https://doi.org/10.1002/pssc.201100101ADSCrossRefGoogle Scholar
  50. 50.
    A. Wilms, Coulomb induced interplay of localized and reservoir carriers in semiconductor quantum dots. Ph.D. thesis, Technical University Berlin (2013). https://doi.org/10.14279/depositonce-3530
  51. 51.
    C. Santori, D. Fattal, Y. Yamamoto, Single-photon Devices and Applications (Wiley, Weinheim, 2010)Google Scholar
  52. 52.
    S. Buckley, K. Rivoire, J. Vučković, Rep. Prog. Phys. 75(12), 126503 (2012).  https://doi.org/10.1088/0034-4885/75/12/126503ADSCrossRefGoogle Scholar
  53. 53.
    P.I. Schneider, N. Srocka, S. Rodt, L. Zschiedrich, S. Reitzenstein, S. Burger, Opt. Express 26, 8479 (2018).  https://doi.org/10.1364/oe.26.008479ADSCrossRefGoogle Scholar
  54. 54.
  55. 55.
    D.J. Griffiths, Introduction to Electrodynamics (Cambridge University Press, Cambridge, 2017). https://doi.org/10.1017/9781108333511
  56. 56.
    M. Kantner, M. Mittnenzweig, T. Koprucki, Proc. SPIE 10526, 1052603 (2018).  https://doi.org/10.1117/12.2289185
  57. 57.
    N. Baer, P. Gartner, F. Jahnke, Eur. Phys. J. B 42(2), 231 (2004).  https://doi.org/10.1140/epjb/e2004-00375-6
  58. 58.
    E. Malić, M.J.P. Bormann, P. Hövel, M. Kuntz, D. Bimberg, A. Knorr, E. Schöll, IEEE, J. Sel. Top. Quantum Electron. 13(5), 1242 (2007).  https://doi.org/10.1109/ISLC.2006.1708081
  59. 59.
    I. Magnúsdóttir, A.V. Uskov, S. Bischoff, B. Tromborg, J. Mørk, J. Appl. Phys. 92(10), 5982 (2002).  https://doi.org/10.1063/1.1512694ADSCrossRefGoogle Scholar
  60. 60.
    R. Ferreira, G. Bastard, Capture and Relaxation in Self-Assembled Semiconductor Quantum Dots. 2053–2571 (Morgan & Claypool Publishers, San Rafael, CA, 2015). https://doi.org/10.1088/978-1-6817-4089-8
  61. 61.
    N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011). https://doi.org/10.1017/CBO9780511976186
  62. 62.
    M. Kantner, M. Mittnenzweig, A. Mielke, N. Rotundo, in Topics in Applied Analysis and Optimisation, ed. by M. Hintermüller and J. Rodrigues (Springer, Cham, 2019), pp. 269–293. https://doi.org/10.1007/978-3-030-33116-0_11Google Scholar
  63. 63.
  64. 64.
    M. Mittnenzweig, A. Mielke, J. Stat. Phys. 167(2), 205 (2017).  https://doi.org/10.1007/s10955-017-1756-4ADSMathSciNetzbMATHCrossRefGoogle Scholar
  65. 65.
  66. 66.
    D.L. Scharfetter, H.K. Gummel, IEEE Trans, Electron Dev. 16(1), 64 (1969).  https://doi.org/10.1109/t-ed.1969.16566ADSCrossRefGoogle Scholar
  67. 67.
    P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, T. Koprucki, in Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, vol. 2, ed. by J. Piprek (CRC Press, Taylor & Francis Group, Boca Raton, 2017), Chap. 50, pp. 733–771. https://doi.org/10.4324/9781315152318-25CrossRefGoogle Scholar
  68. 68.
    H. Si, K. Gärtner, J. Fuhrmann, Comput. Math. Math. Phys. 50(1), 38 (2010).  https://doi.org/10.1134/S0965542510010069ADSMathSciNetzbMATHCrossRefGoogle Scholar
  69. 69.
    H.K. Gummel, IEEE Trans. Electron Dev. 11(10), 455 (1964).  https://doi.org/10.1109/T-ED.1964.15364ADSCrossRefGoogle Scholar
  70. 70.
    H. Gajewski, K. Gärtner, J. Appl. Math. Mech. 72(1), 19 (1992).  https://doi.org/10.1002/zamm.19920720103ADSMathSciNetzbMATHCrossRefGoogle Scholar
  71. 71.
    F. Brezzi, L.D. Marini, P. Pietra, Comput. Methods Appl. Mech. Eng. 75(1–3), 493 (1989).  https://doi.org/10.1016/0045-7825(89)90044-3ADSMathSciNetzbMATHCrossRefGoogle Scholar
  72. 72.
    P.A. Markowich, in The Stationary Semiconductor Device Equations. Series in Computational Microelectronics (Springer, Vienna, 1986). https://doi.org/10.1007/978-3-7091-3678-2CrossRefGoogle Scholar
  73. 73.
    Silvaco International, Atlas User’s Manual (Santa Clara, CA, 2016)Google Scholar
  74. 74.
    Synopsys Inc, Sentaurus Device UserGuide (Mountain View, CA, 2010)Google Scholar
  75. 75.
    S.L.M. van Mensfoort, R. Coehoorn, Phys. Rev. B 78(8), 085207 (2008).  https://doi.org/10.1103/PhysRevB.78.085207
  76. 76.
    M. Kantner, U. Bandelow, T. Koprucki, J.H. Schulze, A. Strittmatter, H.J. Wünsche, IEEE Trans. Electron Dev. 63(5), 2036 (2016).  https://doi.org/10.1109/ted.2016.2538561ADSCrossRefGoogle Scholar
  77. 77.
    J.D. Cressler, H.A. Mantooth (eds.), Extreme Environment Electronics (CRC Press, Taylor & Francis Group, Boca Raton, 2012). https://doi.org/10.1201/b13001Google Scholar
  78. 78.
    J.S. Blakemore, Solid-State Electron. 25(11), 1067 (1982).  https://doi.org/10.1016/0038-1101(82)90143-5ADSCrossRefGoogle Scholar
  79. 79.
    T. Koprucki, K. Gärtner, Opt. Quantum. Electron. 45(7), 791 (2013).  https://doi.org/10.1007/s11082-013-9673-5CrossRefGoogle Scholar
  80. 80.
    M. Bessemoulin-Chatard, Numer. Math. 121(4), 637 (2012).  https://doi.org/10.1007/s00211-012-0448-xMathSciNetzbMATHCrossRefGoogle Scholar
  81. 81.
    T. Koprucki, N. Rotundo, P. Farrell, D.H. Doan, J. Fuhrmann, Opt. Quantum. Electron. 47(6), 1327 (2015).  https://doi.org/10.1007/s11082-014-0050-9CrossRefGoogle Scholar
  82. 82.
    P. Farrell, M. Patriarca, J. Fuhrmann, T. Koprucki, Opt. Quant. Electron. 50, 101 (2018).  https://doi.org/10.1007/s11082-018-1349-8
  83. 83.
    P. Farrell, T. Koprucki, J. Fuhrmann, J. Comput. Phys. 346, 497 (2017).  https://doi.org/10.1016/j.jcp.2017.06.023ADSMathSciNetzbMATHCrossRefGoogle Scholar
  84. 84.
    M. Patriarca, P. Farrell, J. Fuhrmann, T. Koprucki, Comput. Phys. Commun. 235, 40 (2019).  https://doi.org/10.1016/j.cpc.2018.10.004ADSCrossRefGoogle Scholar
  85. 85.
  86. 86.
    Z. Yu, D. Chen, L. So, R.W. Dutton, PISCES-2ET 2D Device Simulator (Integrated Circuits Laboratory, Stanford University, Stanford, Tech. rep., 1994)Google Scholar
  87. 87.
    H. Gajewski, Mitt. Ges. Angew. Math. Mech. 16(1), 35 (1993)Google Scholar
  88. 88.
    H. Gajewski, K. Gärtner, J. Appl. Math. Mech. 76(5), 247 (1996).  https://doi.org/10.1002/zamm.19960760502ADSMathSciNetzbMATHCrossRefGoogle Scholar
  89. 89.
    D.M. Richey, J.D. Cressler, R.C. Jaeger, J. Phys. IV France 04(C6), C6 (1994).  https://doi.org/10.1051/jp4:1994620Google Scholar
  90. 90.
    S. Selberherr, IEEE Trans. Electron Dev. 36(8), 1464 (1989).  https://doi.org/10.1109/16.30960ADSCrossRefGoogle Scholar
  91. 91.
    M. Bergot, M. Duruflé, J. Comput. Phys. 232(1), 189 (2013).  https://doi.org/10.1016/j.jcp.2012.08.005ADSMathSciNetzbMATHCrossRefGoogle Scholar
  92. 92.
    J. Pomplun, S. Burger, L. Zschiedrich, F. Schmidt, Phys. Status Solidi B 244, 3419 (2007).  https://doi.org/10.1002/pssb.200743192ADSCrossRefGoogle Scholar
  93. 93.
    S. Burger, L. Zschiedrich, J. Pomplun, S. Herrmann, F. Schmidt, Proc. SPIE 9424, 94240Z (2015).  https://doi.org/10.1117/12.2085795
  94. 94.
    I. Babuška, M.R. Dorr, Numer. Math. 37(2), 257 (1981).  https://doi.org/10.1007/BF01398256MathSciNetzbMATHCrossRefGoogle Scholar
  95. 95.
    N. Srocka, A. Musiał, P.I. Schneider, P. Mrowiński, P. Holewa, S. Burger, D. Quandt, A. Strittmatter, S. Rodt, S. Reitzenstein, G. Sek, AIP Adv. 8, 085205 (2018).  https://doi.org/10.1063/1.5038137ADSCrossRefGoogle Scholar
  96. 96.
    M. Rozova, J. Pomplun, L. Zschiedrich, F. Schmidt, S. Burger, Proc. SPIE 8255, 82550K (2012).  https://doi.org/10.1117/12.906372
  97. 97.
    V. Shchukin, N. Ledentsov Jr., J. Kropp, G. Steinle, N. Ledentsov, S. Burger, F. Schmidt, IEEE J. Quantum Electron. 50, 990 (2014).  https://doi.org/10.1109/jqe.2014.2364544ADSCrossRefGoogle Scholar
  98. 98.
    V.A. Shchukin, N.N. Ledentsov, J.R. Kropp, G. Steinle, N.N. Ledentsov Jr., K.D. Choquette, S. Burger, F. Schmidt, Proc. SPIE 9381, 93810V (2015).  https://doi.org/10.1117/12.2077012
  99. 99.
    T. Höhne, L. Zschiedrich, N. Haghighi, J.A. Lott, S. Burger, Proc. SPIE 106821, 106821U (2018).  https://doi.org/10.1117/12.2307200
  100. 100.
    J. Pomplun, S. Burger, F. Schmidt, A. Schliwa, D. Bimberg, A. Pietrzak, H. Wenzel, G. Erbert, Phys. Status Solidi B 247, 846 (2010).  https://doi.org/10.1002/pssb.200945451ADSCrossRefGoogle Scholar
  101. 101.
    D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, T. Schroeder, G. Capellini, T. Koprucki, I.E.E.E. Photon, J. 7(3), 1 (2015).  https://doi.org/10.1109/jphot.2015.2427093CrossRefGoogle Scholar
  102. 102.
    D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, M. Virgilio, S. Guha, T. Schroeder, G. Capellini, T. Koprucki, Opt. Quant. Electron. 48(2), 156 (2016).  https://doi.org/10.1007/s11082-016-0394-4
  103. 103.
    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, S. Reitzenstein, Nat. Commun. 6, 7662 (2015).  https://doi.org/10.1038/ncomms8662
  104. 104.
    P. Schnauber, A. Thoma, C.V. Heine, A. Schlehahn, L. Gantz, M. Gschrey, R. Schmidt, C. Hopfmann, B. Wohlfeil, J.H. Schulze, A. Strittmatter, T. Heindel, S. Rodt, U. Woggon, D. Gershoni, S. Reitzenstein, Technologies 4(1), 1 (2016).  https://doi.org/10.3390/technologies4010001CrossRefGoogle Scholar
  105. 105.
    P. Schnauber, J. Schall, S. Bounouar, T. Höhne, S.I. Park, G.H. Ryu, T. Heindel, S. Burger, J.D. Song, S. Rodt, S. Reitzenstein, Nano Lett. 18, 2336 (2018).  https://doi.org/10.1021/acs.nanolett.7b05218ADSCrossRefGoogle Scholar
  106. 106.
    T. Höhne, P. Schnauber, S. Rodt, S. Reitzenstein, S. Burger, Phys. Status Solidi B 256, 1800437 (2019). https://doi.org/10.1002/pssb.201800437ADSCrossRefGoogle Scholar
  107. 107.
    K. Żołnacz, A. Musiał, N. Srocka, J. Große, M.J. Schlösinger, P.-I. Schneider, O. Kravets, M. Mikulicz, J. Olszewski, K. Poturaj, G. Wójcik, P. Mergo, K. Dybka, M. Dyrkacz, M. Dłubek, S. Rodt, S. Burger, L. Zschiedrich, G. Sȩk, S. Reitzenstein, W. Urbańczyk, Method for direct coupling of a semiconductor quantum dot to an optical fiber for single-photon source applications. Opt. Express 27(19), 26772–26785 (2019). https://doi.org/10.1364/OE.27.026772ADSCrossRefGoogle Scholar
  108. 108.
    P. Mrowiński, P. Schnauber, P. Gutsche, A. Kaganskiy, J. Schall, S. Burger, S. Rodt, S. Reitzenstein, Directional emission of a deterministically fabricated quantum Dot–Bragg reflection multimode waveguide system. ACS Photonics 6(9), 2231–2237 (2019). https://doi.org/10.1021/acsphotonics.9b00369CrossRefGoogle Scholar
  109. 109.
    A. Fischer, P. Pahner, B. Lüssem, K. Leo, R. Scholz, T. Koprucki, J. Fuhrmann, K. Gärtner, A. Glitzky, Org. Electron. 13(11), 2461 (2012).  https://doi.org/10.1016/j.orgel.2012.06.046CrossRefGoogle Scholar
  110. 110.
    M. Richter, F. Schlosser, M. Schoth, S. Burger, F. Schmidt, A. Knorr, S. Mukamel, Phys. Rev. B 86, 085308 (2012).  https://doi.org/10.1103/physrevb.86.085308
  111. 111.
    V.E. Babicheva, S.S. Vergeles, P.E. Vorobev, S. Burger, J. Opt. Soc. Am. B 29, 1263 (2012).  https://doi.org/10.1364/josab.29.001263CrossRefGoogle Scholar
  112. 112.
    G. Kewes, A.W. Schell, R. Henze, R.S. Schonfeld, S. Burger, K. Busch, O. Benson, Appl. Phys. Lett. 102, 051104 (2013).  https://doi.org/10.1063/1.4790824ADSCrossRefGoogle Scholar
  113. 113.
    A. Abass, P. Gutsche, B. Maes, C. Rockstuhl, E.R. Martins, Opt. Express 24(17), 19638 (2016).  https://doi.org/10.1364/oe.24.019638ADSCrossRefGoogle Scholar
  114. 114.
    C. Becker, S. Burger, C. Barth, P. Manley, K. Jäger, D. Eisenhauer, G. Köppel, P. Chabera, J. Chen, K. Zheng, T. Pullerits, ACS Photonics 5, 4668 (2018).  https://doi.org/10.1021/acsphotonics.8b01199CrossRefGoogle Scholar
  115. 115.
    M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, M. Hetterich, Opt. Express 17, 1144 (2009).  https://doi.org/10.1364/oe.17.001144ADSCrossRefGoogle Scholar
  116. 116.
    B. Maes, J. Petráček, S. Burger, P. Kwiecien, J. Luksch, I. Richter, Opt. Express 21, 6794 (2013).  https://doi.org/10.1364/oe.21.006794ADSCrossRefGoogle Scholar
  117. 117.
    J.R. de Lasson, L.H. Frandsen, P. Gutsche, S. Burger, O.S. Kim, O. Breinbjerg, A. Ivanskaya, F. Wang, O. Sigmund, T. Häyrynen, A.V. Lavrinenko, J. Mork, N. Gregersen, Opt. Express 26, 11366 (2018).  https://doi.org/10.1364/oe.26.011366ADSCrossRefGoogle Scholar
  118. 118.
    G. Kewes, F. Binkowski, S. Burger, L. Zschiedrich, O. Benson, ACS Photonics 5, 4089 (2018).  https://doi.org/10.1021/acsphotonics.8b00766CrossRefGoogle Scholar
  119. 119.
    L. Zschiedrich, F. Binkowski, N. Nikolay, O. Benson, G. Kewes, S. Burger, Phys. Rev. A 98, 043806 (2018).  https://doi.org/10.1103/PhysRevA.98.043806
  120. 120.
    F. Binkowski, L. Zschiedrich, M. Hammerschmidt, S. Burger, Modal analysis for nanoplasmonics with nonlocal material properties. Phys. Rev. B. 100(15), 155406 (2019). https://doi.org/10.1103/PhysRevB.100.155406
  121. 121.
    P. Lalanne, W. Yan, A. Gras, C. Sauvan, J.-P. Hugonin, M. Besbes, G. Demésy, M.D. Truong, B. Gralak, F. Zolla, A. Nicolet, F. Binkowski, L. Zschiedrich, S. Burger, J. Zimmerling, R. Remis, P. Urbach, H.T. Liu, T. Weiss, Quasinormal mode solvers for resonators with dispersive materials. J. Opt. Soc. Am. A 36(4), 686–704 (2019). https://doi.org/10.1364/JOSAA.36.000686ADSCrossRefGoogle Scholar
  122. 122.
    R. Holzlöhner, S. Burger, P.J. Roberts, J. Pomplun, J. Europ. Opt. Soc: Rap. Comm. 1, 06011 (2006).  https://doi.org/10.2971/jeos.2006.06011
  123. 123.
    J. Bethge, G. Steinmeyer, S. Burger, F. Lederer, R. Iliew, J. Light. Technol. 27, 1698 (2009).  https://doi.org/10.1109/jlt.2009.2021583ADSCrossRefGoogle Scholar
  124. 124.
    P. Gutsche, R. Mäusle, S. Burger, Photonics 3, 60 (2016).  https://doi.org/10.3390/photonics3040060CrossRefGoogle Scholar
  125. 125.
    P. Gutsche, L.V. Poulikakos, M. Hammerschmidt, S. Burger, F. Schmidt, Proc. SPIE 9756, 97560X (2016).  https://doi.org/10.1117/12.2209551
  126. 126.
    D. Werdehausen, I. Staude, S. Burger, J. Petschulat, T. Scharf, T. Pertsch, M. Decker, Opt. Mater. Express 8, 3456 (2018).  https://doi.org/10.1364/OME.8.003456ADSCrossRefGoogle Scholar
  127. 127.
    D. Werdehausen, S. Burger, I. Staude, T. Pertsch, M. Decker, Dispersion-engineered nanocomposites enable achromatic diffractive optical elements. Optica. 6(8),1031–1038 (2019). https://doi.org/10.1364/OPTICA.6.001031ADSCrossRefGoogle Scholar
  128. 128.
    B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, Proc. SPIE 8988, 89880K (2014).  https://doi.org/10.1117/12.2044461
  129. 129.
    B. Wohlfeil, G. Rademacher, C. Stamatiadis, K. Voigt, L. Zimmermann, K. Petermann, I.E.E.E. Photon, Technol. Lett. 28, 1241 (2016).  https://doi.org/10.1109/lpt.2016.2514712ADSCrossRefGoogle Scholar
  130. 130.
    H.J. Kimble, Nature 453(7198), 1023 (2008).  https://doi.org/10.1038/nature07127ADSCrossRefGoogle Scholar
  131. 131.
    I. Aharonovich, D. Englund, M. Toth, Nat. Photonics 10(10), 631 (2016).  https://doi.org/10.1038/nphoton.2016.186ADSCrossRefGoogle Scholar
  132. 132.
    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, P. Senellart, Nat. Photonics 10, 340 (2016).  https://doi.org/10.1038/nphoton.2016.23ADSCrossRefGoogle Scholar
  133. 133.
    W.L. Barnes, G. Björk, J.M. Gérard, P. Jonsson, J.A.E. Wasey, P.T. Worthing, V. Zwiller, Eur. Phys. J. D 18(2), 197 (2002).  https://doi.org/10.1140/epjd/e20020024ADSGoogle Scholar
  134. 134.
    P.I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, C. Rockstuhl, ACS Photonics 6(11), 2726–2733 (2019). https://doi.org/10.1021/acsphotonics.9b00706CrossRefGoogle Scholar
  135. 135.
    P. Bienstman, R. Baets, J. Vukusic, A. Larsson, M.J. Noble, M. Brunner, K. Gulden, P. Debernardi, L. Fratta, G.P. Bava, H. Wenzel, B. Klein, O. Conradi, R. Pregla, S.A. Riyopoulos, J.F.P. Seurin, S.L. Chuang, IEEE J. Quantum Elect. 37, 1618 (2001).  https://doi.org/10.1109/3.970909ADSCrossRefGoogle Scholar
  136. 136.
    K. Iga, IEEE, J. Sel. Top. Quantum Electron. 6, 1201 (2000).  https://doi.org/10.1109/2944.902168ADSCrossRefGoogle Scholar
  137. 137.
    M. Dems, I.S. Chung, P. Nyakas, S. Bischoff, K. Panajotov, Opt. Express 18, 16042 (2010).  https://doi.org/10.1364/oe.18.016042ADSCrossRefGoogle Scholar
  138. 138.
    D. Taillaert, P. Bienstman, R. Baets, Opt. Lett. 29, 2749 (2004).  https://doi.org/10.1364/ol.29.002749ADSCrossRefGoogle Scholar
  139. 139.
    B. Wohlfeil, C. Stamatiadis, M. Jäger, L. Zimmermann, S. Burger, K. Petermann, in 2014 The European Conference on Optical Communication (ECOC) (2014), pp. 1–3. https://doi.org/10.1109/ecoc.2014.6963980
  140. 140.
    W. Unrau, D. Quandt, J.H. Schulze, T. Heindel, T.D. Germann, O. Hitzemann, A. Strittmatter, S. Reitzenstein, U.W. Pohl, D. Bimberg, Appl. Phys. Lett. 101(21), 211119 (2012).  https://doi.org/10.1063/1.4767525ADSCrossRefGoogle Scholar
  141. 141.
    A. Strittmatter, A. Holzbecher, A. Schliwa, J.H. Schulze, D. Quandt, T.D. Germann, A. Dreismann, O. Hitzemann, E. Stock, I.A. Ostapenko, S. Rodt, W. Unrau, U.W. Pohl, A. Hoffmann, D. Bimberg, V.A. Haisler, Phys. Status Solidi A 209(12), 2411 (2012).  https://doi.org/10.1002/pssa.201228407ADSCrossRefGoogle Scholar
  142. 142.
    A. Strittmatter, A. Schliwa, J.H. Schulze, T.D. Germann, A. Dreismann, O. Hitzemann, E. Stock, I.A. Ostapenko, S. Rodt, W. Unrau, U.W. Pohl, A. Hoffmann, D. Bimberg, V.A. Haisler, Appl. Phys. Lett. 100(9), 093111 (2012).  https://doi.org/10.1063/1.3691251ADSCrossRefGoogle Scholar
  143. 143.
    F. Kießling, T. Niermann, M. Lehmann, J.H. Schulze, A. Strittmatter, A. Schliwa, U.W. Pohl, Phys. Rev. B 91(7), 075306 (2015).  https://doi.org/10.1103/physrevb.91.075306
  144. 144.
    M. Strauß, A. Kaganskiy, R. Voigt, P. Schnauber, J.H. Schulze, S. Rodt, A. Strittmatter, S. Reitzenstein, Appl. Phys. Lett. 110(11), 111101 (2017).  https://doi.org/10.1063/1.4978428ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Markus Kantner
    • 1
    Email author
  • Theresa Höhne
    • 2
  • Thomas Koprucki
    • 1
  • Sven Burger
    • 2
  • Hans-Jürgen Wünsche
    • 1
    • 3
  • Frank Schmidt
    • 2
  • Alexander Mielke
    • 1
    • 4
  • Uwe Bandelow
    • 1
  1. 1.Weierstraß-Institut für Angewandte Analysis und StochastikBerlinGermany
  2. 2.Zuse-Institut BerlinBerlinGermany
  3. 3.Ferdinand-Braun-Institut, Leibniz-Institut für HöchstfrequenztechnikBerlinGermany
  4. 4.Institut für Mathematik, Humboldt-Universität zu BerlinBerlinGermany

Personalised recommendations