Skip to main content
SpringerLink
Log in

Physical Basis for Field Emission

  • Chapter
  • First Online:
Mathematical Modeling of Emission in Small-Size Cathode

Part of the book series: Heat and Mass Transfer ((HMT))

  • 354 Accesses

Abstract

In this chapter, without claiming to be original, we recall some basic notions of the solid-state physics which will be used to construct the mathematical model of the field emission cathode. More detailed descriptions of these facts can be found in any literature on the solid-state physics. Our description is based on [2, 3, 23, 27, 28, 30, 41, 42]. In this chapter, we also present some known notions from the theory of field emission based on the papers and monographs [4, 10,11,12, 17, 20, 34, 36, 37, 39, 43] and several others which will be mentioned in the course of presentation.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Notes

  1. 1.

    The Wentzel–Kramers–Brillouin method.

  2. 2.

    This quantity does not play any role in studying the problem of field emission.

References

  1. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Books on Mathematics. Dover Publications, NY (1965)

    MATH  Google Scholar 

  2. Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Cengage Learning (1976)

    Google Scholar 

  3. Bonch-Bruevich, V.L., Kalashnikov, S.G.: Semiconductor Physics. Nauka, Moscow (1990). (in Russian)

    Google Scholar 

  4. Charbonnier, F.M., Strayer, R.W., Swanson, L.W., Martin, E.E.: Nottingham effect in field and t-f emission: heating and cooling domains, and inversion temperature. Phys. Rev. Lett. 13(13), 397–401 (1964)

    Article  ADS  Google Scholar 

  5. Christov, S.G.: General theory of electron emission from metals. Phys. Status Ssolidi (B) 17(1), 11–26 (1966)

    Article  ADS  Google Scholar 

  6. Chung, M.S., Cutler, P.H., Miskovscky, N.M., Sullivan, T.E.: Energy exchange processes in electron emission at high fields and temperature. J. Vacuum Sci. Technol. B 12(2), 727–736 (1994)

    Article  ADS  Google Scholar 

  7. Chung, M.S., Hyun, S.S.: Derivation of the average energy of the field electrons emitted from semiconductors. J. Korean Phys. Soc. 38(6), 758–761 (2001)

    Google Scholar 

  8. Chung, M.S., Jang, Y.J., Mayer, A., Cutler, P.H., Miskovscky, N.M., Weis, B.L.: Energy exchange in field emission from semiconductors. J. Vacuum Sci. Technol. B 26, 800–805 (2008)

    Article  ADS  Google Scholar 

  9. Chung, M.S., Jang, Y.J., Mayer, A., Cutler, P.H., Miskovscky, N.M., Weis, B.L.: Theoretical analysis of the energy exchange and cooling in field emission from the conduction band of the n-type semiconductor. J. Vacuum Sci. Technol. B 27, 692–697 (2009)

    Article  ADS  Google Scholar 

  10. Ding, M.: Field emission from silicon: Ph.D. thesis. Massachusetts Institute of Technology (2001)

    Google Scholar 

  11. Egorov, N., Sheshin, E.: Field Emission Electronics. Springer (2017)

    Google Scholar 

  12. Elinson, M.I., Vasil’ev, G.F.: Field Emission. Fizmatgiz, Moscow (1958). (in Russian)

    Google Scholar 

  13. Fleming, G.M., E., H.J.: The energy losses attending field current and thermoionic emission of electrons from metals. Phys. Rev. 58, 887–894 (1940)

    Article  ADS  Google Scholar 

  14. Flügge, S. (ed.): Electron-Emission and Gas Discharges I, Encyclopedia of Physics, vol. XXI. Springer, Berlin (1956)

    Google Scholar 

  15. Forbes, R.G.: Simple good appeoximations for the special elliptic functions in standart fowler-nordheim tunneling theory for a Schottky-Nordheim barrier. Appl. Phys. Lett. 89 (2006)

    Article  ADS  Google Scholar 

  16. Forbes, R.G.: On the need for a tunneling pre-factor in Fowler-Nordheim tunneling theory. J. Appl. Phys. 103 (2008)

    Article  ADS  Google Scholar 

  17. Forbes, R.G., Deane, J.H.B.: Reformulation of the standart theory of Fowler-Nordheim tunneling and cold field electron emission. Proc. Royal Soc. A 463, 2907–2927 (2007)

    Article  ADS  Google Scholar 

  18. Fowler, R.H., Nordheim, L.: Electron emission in intense electric fields. Proc. Royal Soc. Lond. Ser. A 119(781), 173–181 (1928)

    Article  ADS  Google Scholar 

  19. Fröman, H., Fröman, P.O.: JWKB Approximation: Contributions to the Theory. North-Holland Pub, Amsterdam (1965)

    MATH  Google Scholar 

  20. Furcey, G.: Field Emission in Vacuum Microelectronics. Springer (2005)

    Google Scholar 

  21. Glazov, V.M., Chizhevskaia, S.N., Glagoleva, N.N.: Liquid Semiconductors. Springer (1969)

    Google Scholar 

  22. Grigoriev, I.S., Meilikhov, E.Z., Radzig, A.A.: Handbook of Physical Quantities. CRC Press (1997)

    Google Scholar 

  23. Grundmann, M.: The Physics of Semiconductors: An Introduction Including Nanophysics and Applications. Springer (2016)

    Google Scholar 

  24. Hantzsche, E.: Theory of cathode spot phenomena. Physica B+C 104, 3–16 (1981)

    Article  ADS  Google Scholar 

  25. Hantzsche, E.: The thermo-field emission of electrons in arc discharges. Beiträge aus der Plasmaphysik 22(4), 325–346 (1982)

    Article  Google Scholar 

  26. Hantzsche, E.: The state of the theory of vacuum arc cathodes. Beiträge aus der Plasmaphysik 23(1), 77–94 (1983)

    Article  ADS  Google Scholar 

  27. Hofmann, P.: Solid State Physics : An Introduction. Wiley (2015)

    Google Scholar 

  28. Kasap, S., Capper, P. (eds.): Springer Handbook of Electronic and Photonic Materials. Springer, US (2007)

    Google Scholar 

  29. Kemble, E.C.: The Fundamental Principles of Quantum Mechanics. McGraw-Hill, NY (1937)

    Google Scholar 

  30. Kittel, C.: Introduction to Solid State Physics. Wiley (2005)

    Google Scholar 

  31. Lafferty, J.M. (ed.): Vacuum Arcs: Theory and Application. Wiley, NY (1980)

    Google Scholar 

  32. Landau, L.D., Lifshitz, E.M.: Quantum Mechanics-Nonrelativistic Theory (Course of Theoretical Physics). Pergamon Press (1981)

    Google Scholar 

  33. Lee, T.H.: T-f theory of electron emission in high-current arcs. J. Appl. Phys. 30(2), 166–171 (1959)

    Article  ADS  Google Scholar 

  34. Levine, P.H.: Thermoelectric phenomena associated with electron-field emission. J. Appl. Phys. 33(2), 582–587 (1962)

    Article  ADS  Google Scholar 

  35. Miller, S.C., Good, R.H.: A WKB-type approximation to the Schrödinger equation. Phys. Rev. 91(1), 174–179 (1953)

    Article  ADS  MathSciNet  Google Scholar 

  36. Modinos, A.: Field, Thermionic, and Secondary Electron Emission Spectroscopy. Springer, US (1984)

    Book  Google Scholar 

  37. Murphy, E.L., Good, R.H.: Thermionic emission, field emission, and the transition region. Phys. Rev. 102(6), 1464–1473 (1956)

    Article  ADS  Google Scholar 

  38. Nottingham, W.B.: Remarks on energy losses attending thermionic emission of electrons from metals. Phys. Rev. (1941)

    Google Scholar 

  39. Paulini, J., Klein, T., Simon, G.: Thermo-field emission and the Nottingham effect. J. Phys. D: Appl. Phys. 26(8), 1310–1315 (1993)

    Article  ADS  Google Scholar 

  40. Richardson, O.: Thermionic phenomena and the laws which govern them. In: Nobel Lecture, pp. 224–236. Stockholm (1929)

    Google Scholar 

  41. Shalimova, K.V.: Physics of Semiconductors. Energoatomizdat, Moscow (1985). (in Russian)

    Google Scholar 

  42. Stilbans, L.S.: Physics Semiconductors. Soviet radio, Moscow (1967). (in Russian)

    Google Scholar 

  43. Stratton, R.: Theory of field emission from semiconductors. Phys. Rev. 125(1), 67–82 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  44. Vainshtein, I.A., Zatsepin, A.F., Kortov, V.S.: Applicability of the empirical varshni relation for the temperature dependence of the width of the band gap. Phys. Solid State 41(6), 905–908 (1999)

    Article  ADS  Google Scholar 

  45. Vallée, O., Soares, M.: Airy Functions and Applications to Physics. Imperial College Press, London (2004)

    Book  Google Scholar 

  46. Varshni, Y.P.: Temperature dependence of the energy gap in semiconductors. Physica 34(1), 149–154 (1967)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    Vladimir Danilov, Roman Gaydukov & Vadim Kretov

Authors
  1. Vladimir Danilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roman Gaydukov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vadim Kretov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Danilov .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Danilov, V., Gaydukov, R., Kretov, V. (2020). Physical Basis for Field Emission. In: Mathematical Modeling of Emission in Small-Size Cathode. Heat and Mass Transfer. Springer, Singapore. https://doi.org/10.1007/978-981-15-0195-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-0195-1_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-0194-4

  • Online ISBN: 978-981-15-0195-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation