Skip to main content

Principles of Solid State Electron Optics

  • Chapter
Confined Electrons and Photons

Part of the book series: NATO ASI Series ((NSSB,volume 340))

Abstract

The science of vacuum electron optics has benefitted tremendously from the close analogy with light optics. This analogy exists on the level of classical motion (geometrical optics), as well as on the level of quantum mechanical motion (wave optics). The last two decades have witnessed a surge of interest in transport phenomena in low-dimensional semiconductor systems. Examples are the study of weak localization and conductance fluctuations in two-dimensional (2D) electron gases, resonant tunneling through confined states in quantum wells, transport through mini-bands in superlattices, and quantum ballistic transport through quantum point contacts. All of these phenomena have an optical analogue, and may be classified as manifestations of solid state electron optics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Hecht and A. Zajac, Optics, (Addison-Wesley, New York, 1974).

    Google Scholar 

  2. L. D. Landau and E. M. Lifshitz, Mechanics, (Pergamon, Oxford, 1976).

    Google Scholar 

  3. H. Busch, Berechnung der Bahn von Kathodenstrahlen im axialsymmetrischen elektromagnetischen Felde, Ann. Phys. Leipzig 81, 974 (1926).

    Article  MATH  Google Scholar 

  4. L. de Broglie, Recherches sur la Théorie des Quanta, Annales de Physique 10, 22 (1925).

    Google Scholar 

  5. E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. 79, 32 (1926).

    Google Scholar 

  6. W. Elsasser, Bemerkungen zur Quantenmechanik freier Elektronen, Naturwiss. 13, 711 (1925).

    Article  MATH  Google Scholar 

  7. C. Davisson and L. H. Germer, Diffraction of Electrons by a Crystal of Nickel, Phys. Rev. 30, 705 (1927).

    Article  Google Scholar 

  8. R. P. Feynman, Space-Time Approach to Non-Relativistic Quantum Mechanics, Rev. Mod. Phys. 20 (1948), 367.

    Article  MathSciNet  Google Scholar 

  9. P. A. M. Dirac, Physikalische Zeitschrift der Sowjetunion, 3, No. 1 (1933).

    Google Scholar 

  10. D. B. Beard and G. B. Beard, Quantum Mechanics with Applications, (Allyn and Bacon, Boston, 1970).

    Google Scholar 

  11. P. Ehrenfest, Einige die Quantenmechanik betreffende Erkundigungsfragen, Zeits. f. Physik 78, 555 (1932).

    Article  Google Scholar 

  12. D. Lenstra and W. van Haeringen, Playing with Electrons and Photons in Rings, in Analogies in Optics and Microelectronics, W. van Haeringen and D. Lenstra, eds., (Kluwer, Dordrecht, 1990), p.3–19.

    Chapter  Google Scholar 

  13. D. Lenstra, Wave-Particle Analogies in Optics and Microelectronics, in: Studies in Mathematical Physics, Proc. Huygens Symposium, E. van Groenen and E. M. de Jager, eds. (North-Holland Amsterdam, 1992).

    Google Scholar 

  14. H. van Houten and C. W. J. Beenakker, Andreev Reflection and the Josephson Effect in a Quantum Point Contact: an Analogy with Phase-Conjugating Resonators, Physica B175, 187 (1991).

    Google Scholar 

  15. B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel and C. T. Foxon, Quantized Conductance of Point Contacts in a Two-Dimensional Electron Gas, Phys. Rev. Lett. 60 (1988) 848.

    Article  Google Scholar 

  16. B.J. van Wees, L.P. Kouwenhoven, E.M.M. Willems, C.J.P.M. Harmans, J.E. Mooij, H. van Houten, C.W.J. Beenakker, J.G. Williamson, and C.T. Foxon, Quantum ballistic and Adiabatic Electron Transport studied with Quantum Point Contacts, Phys.Rev.B 43, 12431 (1991).

    Article  Google Scholar 

  17. D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, One Dimensional Transport and the Quantization of the Ballistic Resistance, J. Phys. C 21, (1988) L209.

    Article  Google Scholar 

  18. A. Yacoby and Y. Imry, Quantization of the Conductance of Ballistic Point Contacts Beyond the Adiabatic Approximation, Phys.Rev.B 41, 5341 (1990).

    Article  Google Scholar 

  19. L. I. Glazman, G. B. Lesovick, D. E. Khmel’nitskii and R. I. Shekhter, Reflectionless Quantum. Transport and Fundamental Ballistic Resistance Steps in Mircoconstrictions, Pis’ma Zh. Teor. Fiz. 48, 218 (1988) [JETP Lett. 48, 238 (1988)].

    Google Scholar 

  20. C. W. J. Beenakker and H. van Houten, Magnetotransport and Nonadditivity of Point-Contact Resistances in Series, Phys. Rev. B 39, 10445 (1989).

    Article  Google Scholar 

  21. L. W. Molenkamp, A. A. M. Staring, C. W. J. Beenakker, R. Eppenga, C. E. Timmering, J. G. Williamson, C. J. P. M. Harmans, and C. T. Foxon, Electron-Beam Collimation with Quantum. Point Contacts, Phys.Rev.B 41 1274 (1990).

    Article  Google Scholar 

  22. A. Szafer and A. D. Stone, Theory of Quantum Conduction through a Constriction, Phys.Rev.Lett. 62, 300 (1989).

    Article  Google Scholar 

  23. For a review see C. W. J. Beenakker and H. van Houten, Quantum transport in semiconductor nanostructures, Solid State Physics 44 1 (1990).

    Article  Google Scholar 

  24. E. A. Montie, E. C. Cosman, G. W. Hooft, M. B. van der Mark, and C. W. J. Beenakker, Observation of the Optical Analogue of Quantized Conductance of a Point Contact, Nature 350, 594 (1991)

    Article  Google Scholar 

  25. see also Physica B 175, 149 (1991).

    Google Scholar 

  26. H. van Houten and C. W. J. Beenakker, Quantum Point Contacts and Coherent Electron Focusing, in: Analogies in Optics and Microelectronics, W. van Haeringen and D. Lenstra, eds. (Kluwer, Dordrecht, 1990).

    Google Scholar 

  27. H. van Houten, B. J. van Wees, J. E. Mooij, C. W. J. Beenakker, J. G. Williamson, and C. T. Foxon, Coherent Electron Focusing in a Two-Dimensional Electron Gas, Europhys. Lett. 5, 721 (1988).

    Article  Google Scholar 

  28. E. Sivan, M. Heiblum, C. P. Umbach, and H. Shtrikman, Electrostatic Lens in the Ballistic Regime, Phys.Rev.B 41, 7937 (1990).

    Article  Google Scholar 

  29. J. Spector, H. L. Störnier, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. Electron Focusing in Two-Dimensional Systems by Means of an Electrostatic Lens, 56, 1290 (1990)

    Google Scholar 

  30. J. Spector, J. S. Weiner, H. L. Störnier, K. W. Baldwin, L. N. Pfeiffer, and K. W. West, Ballistic Electron Optics, Surf. Sci. 263, 240 (1992).

    Article  Google Scholar 

  31. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, Frustrated Total Internal Reflection: A Demonstration and Review, Am. J. Phys. 54, 601 (1986).

    Article  Google Scholar 

  32. R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, Analogies between Electron and Photon Tunneling, Physica B175, 257 (1991).

    Google Scholar 

  33. W. A. Harrison, Solid State Theory, (McGraw-Hill, New York, 1970).

    Google Scholar 

  34. S. Washburn, A. B. Fowler, H. Schmid, and D. Kern, Possible Observation of Transmission Resonances in GaAs-AlGaAs Transistors, Phys. Rev. B 38, 1554 (1988).

    Article  Google Scholar 

  35. G. Breit and E. Wigner, Capture of Slow Neutrons, Phys. Rev. 49, 519 (1936).

    Article  MATH  Google Scholar 

  36. R. Tsu and L. Esaki, Tunneling in a Finite Superlattice, Appl. Phys. Lett. 22, 562 (1973).

    Article  Google Scholar 

  37. L. L. Chang, L. Esaki and R. Tsu, Resonant Tunneling in Semiconductor Double Barriers, Appl. Phys. Lett. 24, 593 (1974).

    Article  Google Scholar 

  38. M. Büttiker, Coherent and Sequential Tunneling in Series Barriers, IBM J. Res. Dev. 32, 63 (1988).

    Article  Google Scholar 

  39. E. Burstein and S. Lundqvist, eds. Tunneling Phenomena in Solids, (Plenum, New York, 1969).

    Google Scholar 

  40. V. Kalmeyer and R. B. Laughlin, Differential Conductance in Three-Dimensional Resonant Tunneling, Phys. Rev. B 35, 9805 (1987).

    Article  Google Scholar 

  41. W. Xue and P. A. Lee, Two-Dimensional Resonant Tunneling, Phys. Rev. B 38, 3913 (1988).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media New York

About this chapter

Cite this chapter

van Houten, H., Beenakker, C.W.J. (1995). Principles of Solid State Electron Optics. In: Burstein, E., Weisbuch, C. (eds) Confined Electrons and Photons. NATO ASI Series, vol 340. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1963-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-1963-8_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5807-7

  • Online ISBN: 978-1-4615-1963-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics