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Low-Dimensional Semiconductor Structures

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Semiconductor Optics 1

Part of the book series: Graduate Texts in Physics ((GTP))

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Abstract

Low-dimensional semiconductor structures are nowadays the centerpiece of many electronic and optoelectronic devices. This is a result of their interesting properties like carrier confinement and localization, tunability of electronic energies by geometric dimension, or a spectrally narrow and high density of states. But low-dimensional structures are also perfect model systems for quantum mechanics and lead to new physics phenomena like the quantum Hall effect. We will discuss here the electronic states and wavefunctions in (square-well) potentials of different dimensionalities. We will address the consequences of finite size and depth of the potentials and how the bandstructure characteristics affect the electronic states. Starting with single quantum wells (QWs) we proceed via coupled QWs to superlattices where miniband formation leads to transport perpendicular to the quantization layers. We focus in particular on a novel class of materials—mono-layer semiconductors—like graphen and transition-metal dichalcogenides. These materials show extraordinary electronic properties due to location of their bandgaps at the corners of a hexagonal Brillouin zone leading to the phenomena of valleytronics. We then describe electronic states in quantum wires, rods and dots and how to realize such systems.

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References

  1. F. Wooten, Optical Properties of Solids (Academic, New York, 1972)

    Google Scholar 

  2. Y.-C. Chang, L.L. Chang, L. Esaki, Appl. Phys. Lett. 47, 1324 (1985)

    Article  ADS  Google Scholar 

  3. G. Bastard, J.A. Brum, IEEE J. QE- 22, 1625 (1986)

    Article  Google Scholar 

  4. G.H. Döhler, IEEE J. QE- 22, 1682 (1986)

    Article  Google Scholar 

  5. R.M. Cohen, Z.M. Fang, J. Appl. Phys. 65, 612 (1989)

    Article  ADS  Google Scholar 

  6. E. Kapon, D.M. Hwang, R. Bhat, Phys. Rev. Lett. 63, 430 (1989)

    Article  ADS  Google Scholar 

  7. P.C. Sercel, K.J. Vahala, Phys. Rev. B 42, 3690 (1990)

    Article  ADS  Google Scholar 

  8. R.K. Hayden et al., Phys. Rev. Lett. 66, 1749 (1991)

    Article  ADS  Google Scholar 

  9. P.C. Sercel, K.J. Vahala, Phys. Rev. B 44, 5681 (1991)

    Article  ADS  Google Scholar 

  10. S. Malzer et al., Phys. Status Solidi (b) 173, 459 (1992)

    Article  ADS  Google Scholar 

  11. M. Missous, in Properties of Aluminium Gallium Arsenide, EMIS Datareviews Series No. 7, ed. by S. Adachi (1993), p. 73

    Google Scholar 

  12. C.B. Murray, D.J. Norris, M.G. Bawendi, J. Am. Chem. Soc. 115, 8706 (1993)

    Article  Google Scholar 

  13. U. Woggon, S.V. Gaponenko, Phys. Status Solidi (b) 189, 285 (1995)

    Article  ADS  Google Scholar 

  14. A.P. Alivisatos, Science 271, 933 (1996)

    Article  ADS  Google Scholar 

  15. D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, D. Park, Phys. Rev. Lett. 76, 3005 (1996)

    Article  ADS  Google Scholar 

  16. W. Langbein, H. Gislason, J. Hvam, Phys. Rev. B 54, 14595 (1996)

    Article  ADS  Google Scholar 

  17. J. Hasen et al., Nature 390, 54 (1997)

    Article  ADS  Google Scholar 

  18. L.P. Kouwenhoven et al., in Proceedings of the NATO Advanced Study Institute on Mesoscopic Electron Transport. Kluwer Series, E345 (1997), p. 105

    Google Scholar 

  19. H. Akiyama, J. Phys. Condens. Matter 10, 3095 (1998)

    Article  ADS  Google Scholar 

  20. G. Biasiol, E. Kapon, J. Crystal Growth 201/202, 62 (1999)

    Google Scholar 

  21. D. Bimberg, N. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures (Wiley, Chicester, 1999)

    Google Scholar 

  22. G. Biasiol, K. Leifer, E. Kapon, Phys. Rev. B 61, 7223 (2000)

    Article  ADS  Google Scholar 

  23. D. LĂĽerĂźen, R. Bleher, H. Kalt, Phys. Rev. B 61, 15812 (2000)

    Article  ADS  Google Scholar 

  24. Y. Cui, Q. Wei, H. Park, C.M. Lieber, Science 293, 1289 (2001)

    Article  ADS  Google Scholar 

  25. Q. Huang et al., J. Crystal Growth 227/228, 117 (2001)

    Google Scholar 

  26. M.H. Huang et al., Science 292, 1897 (2001)

    Article  ADS  Google Scholar 

  27. C. Klingshirn in Landolt-Börnstein III/34: Semiconductor Quantum Structures, Subvol. C Optical Properties, Part 1, (Springer, Berlin, 2001)

    Google Scholar 

  28. Z.W. Pan, Z.R. Dai, Z.L. Wang, Science 291, 1947 (2001)

    Article  ADS  Google Scholar 

  29. P.K. Basu, Theory of Optical Processes in Semiconductors: Bulk and Microstructures (Oxford University Press, Oxford, 2002)

    Google Scholar 

  30. E. Kapon, in Spectroscopy of Systems with Spatially Confined Structures (2001). NATO Science Series II, vol. 90 (Kluwer, Dordrecht, 2002), p. 243

    Google Scholar 

  31. D. Katz et al., Phys. Rev. Lett. 89, 086801 (2002)

    Article  ADS  Google Scholar 

  32. J.Y. Lao et al., Nano Lett. 3, 235 (2003)

    Article  ADS  Google Scholar 

  33. L. Li, A.P. Alivisatos, Phys. Rev. Lett. 90, 097402 (2003)

    Article  ADS  Google Scholar 

  34. T. Mokari, U. Banin, Chem. Mater. 15, 3955 (2003)

    Article  Google Scholar 

  35. K. Matsuda et al., Phys. Rev. Lett. 91, 177401 (2003)

    Article  ADS  Google Scholar 

  36. B.P. Zhang et al., Appl. Phys. Lett. 83, 1635 (2003)

    Article  ADS  Google Scholar 

  37. H. Kalt in Landolt-Börnstein III/34: Semiconductor Quantum Structures, Subvol. C Optical Properties, Part 2 (Springer, Berlin, 2004)

    Google Scholar 

  38. V.A. Scubin, N.N. Ledentsov, D. Bimberg, Epitaxy of Nanostructures (Springer, Heidelberg, 2004)

    Google Scholar 

  39. T.Y. Tan, N. Li, U. Gösele, Appl. Phys. A 78, 519 (2004)

    Article  ADS  Google Scholar 

  40. B.P. Zhang et al., Appl. Phys. Lett. 84, 4098 (2004) ; J. Appl. Phys. 96, 340 (2004)

    Google Scholar 

  41. J.C. Charlier, P.C. Eklund, J. Zhu, A.C. Ferrari, Electron and phonon properties of graphene: their relationship with carbon nanotubes, in Carbon Nanotubes, Topics in Applied Physics, vol. 111 ed. by A. Jorio, G. Dresselhaus, M.S. Dresselhaus (Springer, Berlin, 2007)

    Google Scholar 

  42. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    Article  ADS  Google Scholar 

  43. C. Klingshirn, Phys. Status Solidi B 244, 3027 (2007)

    Article  ADS  Google Scholar 

  44. R.R. Nair et al., Science 320, 1308 (2008)

    Article  ADS  Google Scholar 

  45. A.H. Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  46. H. Ibach, H. Löth, Solid State Physics (Springer, Berlin, 2009)

    Book  Google Scholar 

  47. V. Schmidt, J.V. Wittemann, S. Senz, U. Gösele, Adv. Mater. 21, 2681 (2009)

    Article  Google Scholar 

  48. M. Willander et al., Nanotechnology 20, 332001 (2009)

    Article  Google Scholar 

  49. R. Yan, D. Gargas, P. Yang, Nat. Photonics 3, 569 (2009)

    Article  ADS  Google Scholar 

  50. F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Nat. Photonics 4, 611 (2010)

    Article  ADS  Google Scholar 

  51. C. Klingshirn et al., Phys. Status Solidi B 247, 1424 (2010)

    Article  ADS  Google Scholar 

  52. C. Klingshirn, B.K. Meyer, A. Waag, A. Hoffmann, J. Geurts, Zinc Oxide: From Fundamental Properties Towards Novel Applications, Springer Series in Materials Science, vol. 120 (Springer, Berlin, 2010)

    Book  Google Scholar 

  53. P.Y. Yu, M. Cardona, Fundamentals of Semiconductors, 4th edn. (Springer, Heidelberg, 2010)

    Book  Google Scholar 

  54. M. Helfrich et al., J. Cryst. Growth 323, 187 (2011)

    Article  ADS  Google Scholar 

  55. A. Kuc, N. Zibouche, T. Heine, Phys. Rev. B 83, 245213 (2011)

    Article  ADS  Google Scholar 

  56. K.F. Mak, K. He, J. Shan, T.F. Heinz, Nat. Nanotech. 7, 494 (2012)

    Article  ADS  Google Scholar 

  57. K.S. Novoselov et al., Nature 490, 192 (2012)

    Article  ADS  Google Scholar 

  58. Q.H. Wang et al., Nat. Nanotechnol. 7, 699 (2012)

    Article  ADS  Google Scholar 

  59. D. Xiao et al., Phys. Rev. Lett. 108, 196802 (2012)

    Article  ADS  Google Scholar 

  60. C.Z. Ning, Semiconductor nanowire lasers, in Advances in Semiconductor Lasers, Semiconductors and Semimetals, vol. 86, 455, ed. by J.J. Coleman, A.C. Bryce, C. Jagadish (Academic, Elsevier, Burlington, 2012)

    Chapter  Google Scholar 

  61. Y. Shirasaki, G.J. Supran, M.G. Bawendi, V. Bulovic, Nat. Photonics 7, 13 (2013)

    Article  ADS  Google Scholar 

  62. Y. Shimazaki et al., Nat. Phys. 11, 1032 (2015)

    Article  Google Scholar 

  63. F. Wu, F. Qu, A.H. MacDonald, Phys. Rev. B 91, 075310 (2015)

    Article  ADS  Google Scholar 

  64. A. Castellanos-Gomez, Nat. Photonics 10, 202 (2016)

    Article  ADS  Google Scholar 

  65. K.F. Mak, J. Shan, Nat. Photonics 10, 216 (2016)

    Article  ADS  Google Scholar 

  66. S. Mokkapati, C. Jagadish, Opt. Express 24, 17345 (2016)

    Article  ADS  Google Scholar 

  67. K.S. Novoselov et al., Science 353, aac9439 (2016)

    Article  Google Scholar 

  68. S. Tarucha et al., Spin qubits with semiconductor quantum dots, in Principles and Methods of Quantum Information Technologies, Lecture Notes in Physics, vol. 911 ed. by Y. Yamamoto, K. Semba (Springer, Tokyo, 2016)

    Chapter  Google Scholar 

  69. S. Dufferwiel et al., Nat. Photonics 11, 497 (2017)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Baden-WĂĽrttemberg, Germany

    Heinz Kalt & Claus F. Klingshirn

Authors
  1. Heinz Kalt
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  2. Claus F. Klingshirn
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Corresponding author

Correspondence to Heinz Kalt .

Problems

Problems

17.1

Calculate the effective density of states per unit volume at 300 K for electrons and holes in bulk GaAs and the density of states per unit area in a GaAs QW. Calculate the corresponding density per volume for \(l_{z}\,{=}\,10\,\text {nm}\).

17.2

Calculate the positions of the first three quantized electron levels for a GaAs quantum well assuming infinitely high barriers and the realistic band discontinuity to Al\(_{0.40}\)Ga\(_{0.60}\)As and compare them.

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Kalt, H., Klingshirn, C.F. (2019). Low-Dimensional Semiconductor Structures. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_17

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