Skip to main content

Modern Developments in Theoretical Research of Field Emission

  • Chapter
  • First Online:
  • 1058 Accesses

Part of the book series: Springer Series in Advanced Microelectronics ((MICROELECTR.,volume 60))

Abstract

This chapter discusses modern developments in theoretical research of field emission from metals and semiconductors. Emitter shape approximation and methods of electrostatic potential and field strength calculation are considered. It also presents the theory of thermal-field emission (TFE) from metals. Energy distributions of field electrons and TFE electrons emitted from a metal are considered in terms of applications for field emission spectroscopy . Theoretical aspects of phenomena and processes on the emitter surface during field emission are discussed and various theories attempting to explain them are presented.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   199.99
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

Learn about institutional subscriptions

References

  1. I.M Hoffmann, Investigation of electrostatic emission of tungsten in a wide range of current densities. FTT 4, 2005 (1962)

    Google Scholar 

  2. M.I. Elinson, F.F. Dobryakova, V.F. Krapivin, On the theory of field and thermionic emission of metals and semiconductors. Radiotehnika i Electronika. 6(8), 1342–1353 (1961)

    Google Scholar 

  3. M. Green (ed.), Surface properties of solids. Mir 432 (1972)

    Google Scholar 

  4. L. Wei, W. Baoping, G. Li, Y. Hanchun, T. Yan, Analysis of the emission performance of field emitter with Laplace interpolation method. Appl. Surf. Sci., 161, 1–8 (2000)

    Google Scholar 

  5. A.G.J. Oostrom, Philips Res. Rep. Suppl. 1, 1–162 (1966)

    Google Scholar 

  6. G.R. Condon, J.A. Panitz, J. Vac. Sci. Technol. B 16, 23 (1998)

    Google Scholar 

  7. J. Plšek, D.V. Zhukov, Z. Knor, The average work function and emission area in the Fowler–Nordheim equation. Czech. J. Phys

    Google Scholar 

  8. G. Binnig, G. Rohrer, Scanning tunnel microscope. World Sci. 10, 26–33 (1985)

    Google Scholar 

  9. A. Modinos, Theoretical analysis of field emission data. Solid-State Electron. 45, 809–816 (2001)

    Article  ADS  Google Scholar 

  10. R.G. Forbes, K.L. Jensen, New results in the theory of Fowler–Nordheim plots and the modelling of hemi-ellipsoidal emitters. Ultramicroscopy 89, 17 (2001)

    Article  Google Scholar 

  11. M. Drechsler, E. Henkel, Z. Angew. Phys. 6, 341 (1954)

    Google Scholar 

  12. P.H. Cutler, J. He, N.M. Miskovsky et al. J. Vac. Sci. Technol. B. 11, 387–391 (1993)

    Google Scholar 

  13. A. Modinos, J.P. Xanthahis, Energy-broadening of field-emitted electrons due to Coulomb collisions. Surf. Sci. 249, 373 (1991)

    Google Scholar 

  14. Y. Suganuma, M. Tomitori, Analysis of electron standing waves in a vacuum gap of scanning tunneling microscopy: Measurement of band bending through energy shifts of electron standing wave. J. Vac. Sci. Technol. B 18(1), 48–54 (2000)

    Google Scholar 

  15. L.N. Kantorovich, A.S. Foster, A.L. Shluger, A.M. Stoneham, Role of image forces in non-contact scanning force microscope images of ionic surfaces. Surf. Sci. 445, 283–299 (2000)

    Google Scholar 

  16. N.M. Miskovsky, S.H. Park, J. He, P.H. Cutler, Energy exchange processes in field emission from atomically sharp metallic emitters. J. Vac. Sci. Technol. B 11(2), 366–371 (1993)

    Google Scholar 

  17. S. Georgieva, D. Vichev, K. Drandarov, Computer simulation of the emission process of some field emission alloy ion sources. Vacuum 47(10), 1143–1144 (1996)

    Google Scholar 

  18. N.V. Egorov, E.M. Vinogradova, Solution of boundary-value problem in bispherical coordinates. in Proceedings of 3-th International Workshop: BDO-96, St. Petersburg, pp. 274–278 (1996)

    Google Scholar 

  19. G. Mesa, E. Dobado-Fuentes, J.J. Saenz, Image charge method for electrostatic calculations in field emission diodes. J. Applied Phys. 79(1), 39–43 (1996)

    Google Scholar 

  20. Y. Ohkavara, T. Naijo, T. Washio, S. Oshio, H. Ito, H. Saitoh. Field emission properties of AlZnO whiskers modified by amorphous carbon and related films. Jpn. J. Appl. Phys. 40(12), 7013–7017 (2001)

    Google Scholar 

  21. K.L. Jensen, J.E. Yater, Advanced emitters for next generation rf amplifiers. J. Vac. Sci. Technol. B, 16(4), 2038–2049 (1998)

    Google Scholar 

  22. M.S. Yermoshina, Mathematical modeling of electron emission from a point cathode of complex configuration. Kand. Diss. SPb. 112 p (2004)

    Google Scholar 

  23. R.G. Forbes, C.J. Edgcombe, U. Valdre, Some comments on models for field enhancement. Ultramicroscopy 95, 57–65 (2003)

    Article  Google Scholar 

  24. P.J. Birdseye, D.A. Smith, G.D.W. Smith, Analogue investigation of electric field distribution and ion trajectories in the field ion microscope. J. Phys. D: Appl. Phys. 7 (1974)

    Google Scholar 

  25. W.W. Dolan, W.P. Dyke, J.K. Trolan, The field emission initiated vacuum area. II. The resistively heated emitter. Phys. Rev. 91(5), 1054–1057 (1953)

    Article  ADS  Google Scholar 

  26. J.R. Barbour, W.W. Dolan, J.K. Trolan et al., Space-charge effects in field emission. Phys. Rev. 92(1), 45–51 (1953)

    Article  ADS  Google Scholar 

  27. J.K. Trolan, J.R. Barbour, E.E. Martin, W.P. Dyke, Electron emission from a lattice step on clean tungsten. Phys. Rev. 100(6), 1646–1649 (1955)

    Article  ADS  Google Scholar 

  28. W.P. Dyke, F.M. Charbonnier, R.W. Straer et al., Electrical stability and life of the heated field emission cathode. J. Appl. Phys. 31(5), 790–805 (1960)

    Article  ADS  Google Scholar 

  29. J.R. Barbour, F.M. Charbonnier, W.W. Dolan et al., Determination of surface tension and surface migration constants for tungsten. Phys. Rev. 117(6), 1452–1459 (1960)

    Article  ADS  Google Scholar 

  30. F.M. Charbonnier, J.R. Barbour, L.F. Garret, W.P. Dyke, Basic and applied studies of field emission at microwave frequencies. Proc. IEEE 51(7), 991–1004 (1963)

    Article  Google Scholar 

  31. W.P. Dyke, Field emission. A new practical electron source. IRE Trans. Mil. Electron. 38–45 (1960)

    Google Scholar 

  32. A. Modinos, Field, thermionic and secondary electron emission spectroscopy. M. Nauka, 320 (1990)

    Google Scholar 

  33. M.I. Elinson (ed.), The cold cathodes. Sov. Radio 386 (1974)

    Google Scholar 

  34. W.W. Dolan, W.P. Dyke, Temperature and field emission of electrons from metals. Phys. Rev. 95, 327–332 (1954)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  36. R.H. Good, E.W. Mueller, Field emission. In Handbuch der Physik (ed. By S. Flugge), Bd. 21, 176–231 (Springer, Berlin, 1956)

    Google Scholar 

  37. E. Guth, C.J. Mullin, Electron emission of metals in electric field. Phys. Rev. 61(5–6), 339–348 (1942)

    Google Scholar 

  38. M.I. Elinson, The emission of electrons under the influence of strong electric fields. Dokt. Diss., L: LPI n. MI Kalinin (1961)

    Google Scholar 

  39. S.G. Christov, General theory of electron emission from metals. Phys. Stat. Sol. 17(1), 11–26 (1966)

    Article  ADS  Google Scholar 

  40. F.I. Itskovich, On the theory of field emission from metals. Part I. ZETP, 50(5), 1425–1437 (1966)

    Google Scholar 

  41. F.I. Itskovich, On the theory of field emission from metals. Part II. ZETP 52(6), 1720–1735 (1967)

    Google Scholar 

  42. I.S. Andreev, The study of electron emission from the metal in its transition from cold to thermionic. J. Tech. Phys. 22, 1428–1441 (1952)

    Google Scholar 

  43. S.C. Miller Jr., R.H. Good Jr., Phys. Rev. 92, 13–67 (1953)

    Google Scholar 

  44. M.I. Elinson, G.F. Vasiliev, Field emission. M. Fizmatgiz, 272 (1958)

    Google Scholar 

  45. L.N. Dobretsov, M.V. Gomoyunova, Emission elekcronics. M. Nauka, 364 (1964)

    Google Scholar 

  46. R. Fischer, H. Neumann, Field emission from Semiconductors. M. Nauka, 215 (1971)

    Google Scholar 

  47. V.T. Cherepin, M.A. Vasiliev, Methods and tools for the analysis of material surface Handbook (Naukova Dumka, Kiev, 1982), p. 400

    Google Scholar 

  48. J.E. Henderson, R.E. Badley, Phys. Rev. 38(3), 590 (1931)

    Google Scholar 

  49. J.E. Henderson, R.K. Dahlstrom, Phys. Rev. 55(5), 473 (1939)

    Article  ADS  Google Scholar 

  50. J.E. Henderson, R.K. Dahlstrom, F.R. Abott, Phys. Rev. 41(1), 261 (1932)

    Google Scholar 

  51. L. Feldman, D. Meyer, Basics of analysis of surfaces and thin films. M. Mir, 344 (1989)

    Google Scholar 

  52. J.D. Caret, B. Feyrbah, B. Heaton et al. The use of electron spectroscopy for surface analysis. H. Ubach (ed.). Riga Zinatne, 315 (1980)

    Google Scholar 

  53. D.A. Orlov, M. Hoppe, U. Weigel, D. Schwalm, A.S. Terechov, A. Wolf, Energy distribution of electrons emitted from GaAs (Cs, O). Appl. Phys. Lett. 78, 2721 (2001)

    Google Scholar 

  54. L.W. Swanson, L.C. Crouser, Phys. Rev. 163, 632 (1967)

    Google Scholar 

  55. A.B. El-Karen, J.C. Wolfe, J.E. Wolfe, J. Appl. Phys. 48, 4749 (1977)

    Google Scholar 

  56. J.W. Gadzuk, E.W. Plummer. Phys. Rev. 3, 2125.58 (1971)

    Google Scholar 

  57. A.E. Bell, L.W. Swanson, Phys. Rev. B. 19, 3353 (1979)

    Google Scholar 

  58. V.A. Korablev, Y. Kudinov, MSh Sugainov, T.A. Baranova, Photoelectron spectroscopy with angular resolution of GaAs with a negative electron affinity. Raditehnika i Elektronika. 32, 321 (1992)

    Google Scholar 

  59. G. Vergara, A. Herrera-Gomez, W.E. Spicer, Electron transverse energy distribution in GaAs negative electron affinity cathodes: Calculation compared to experiment. J. Appl. Phys. 80, 1809 (1966)

    Google Scholar 

  60. N.V. Egorov, V.R. Tolstyakov, Investigation of the effect of the surface state on the emission characteristics of semiconductor photo field cathodes. Surface 8, 23–33 (1996)

    Google Scholar 

  61. D.A. Ovsyannikov, N.V. Egorov, Mathematical modeling of systems for formation of electron and ion beams (Publishing of St. Petersburg State University, Russia, 1998). 276 p

    Google Scholar 

  62. N.V. Egorov, V.R. Tolstyakov, The effect of multi-particle tunneling in the field electron emission from semiconductors. Povrhnoct’ 9, 10–13 (1996)

    Google Scholar 

  63. N.V. Egorov, On the possibility of narrow collimated electron beams. ZTP. 52(12), 2440–2442 (1982)

    Google Scholar 

  64. N.V. Egorov, A.G. Karpov, Diagnostic information and expert systems. SPb. (St. Petersburg State University Publishing House, Russia, 2002) 472 p

    Google Scholar 

  65. M.I. Elinson, Effect of internal electric fields in the semiconductor at its field emission. Raditehnika i Elektronika. 4,140–142 (1959)

    Google Scholar 

  66. A.G. Zhdan, M.I. Elinson et al., Raditehnika i Elektronika. 7, 570 (1962)

    Google Scholar 

  67. M.I. Elinson et al., Raditehnika i Elektronika. 10, 1288 (1965)

    Google Scholar 

  68. Y.A. Frenkel, ZETP. 8, 1893 (1938)

    Google Scholar 

  69. W. Franz, Ergeb. exapt, Naturwiss. 27, 1 (1953)

    Google Scholar 

  70. W. Franz, Handb. Phys. 17, 155 (1956)

    ADS  Google Scholar 

  71. R.J. Hodgkinson, Proc. Phys. Soc. 82(58), 1010 (1963)

    Google Scholar 

  72. Y.A. Frankel. ZETP. 7, 1069 (1937)

    Google Scholar 

  73. R. Stratton, Phis. Rev. 126, 2002 (1962)

    Google Scholar 

  74. M. Sanchez, Helv. Phys. Acta. 36, 1 (1963)

    Google Scholar 

  75. H. Frohlich, B.V. Paranjape, Proc. Phys. Soc. 69(21), 866 (1956)

    Google Scholar 

  76. A.F. Yatsenko, On a model photo-field emission from p-type semiconductors. Phys. Stat. Solid. 1(2), 169–175 (1970)

    Google Scholar 

  77. G.N. Fursei, M. Kaplan, O.I. L’vov, On the theory of field emission from semiconductor of p-type. Vestnik Leningrad. Universiteta. Ser. Fisiki I Himii. 16, 167–170 (1968)

    Google Scholar 

  78. L.M. Baskin, O.I. Lvov, G.N. Fursey, Generation features of field emission from semiconductors. Phys. Stat. Sol. B. 47, 49–62 (1971)

    Google Scholar 

  79. V.M. Zhukov, Processes on the surface under field emission. SPb (VVM, Russia, 2007), 295 p.

    Google Scholar 

  80. I.L. Sokolskaya, Application of a field emission microscope to study the surface diffusion and self-diffusion. ed. by Y.E. Geguzina, Procedinds of “Surface diffusion and spreading” Nauka, 108–148 (1969)

    Google Scholar 

  81. B. Honigman, Growth and shape of the crystals. M. IIL, 224 (1961)

    Google Scholar 

  82. C. Herring, Structure and properties of solid surface. ed. By R. Gomer, S.S. Smith (University of Chicago Press, USA, 1953), pp. 5–72

    Google Scholar 

  83. C. Herring, The physics of powder metallurgy. ed. by W.E. Kingston (McGrow Book Co., N.Y., 1953), p. 143

    Google Scholar 

  84. W.W. Mullins, Theory of thermal growing. J. Appl. Phys. 28(3), 333–339 (1957)

    Article  ADS  Google Scholar 

  85. W.W. Mullins, Flattening of nearly plane solid surface to capillarity. J. Appl. Phys. 30(1), 77–83 (1959)

    Article  ADS  Google Scholar 

  86. J.L. Boling, W.W. Dolan, Blunting of tungsten needles by surface diffusion. J. Appl. Phys. 29(3), 556–559 (1958)

    Article  ADS  Google Scholar 

  87. E.W. Mueller, Oberflachenwanderung von Wolfram auf dem eigenen Kristallgitter. Z. f. Phys. 126(7–9), 642–665 (1949)

    Google Scholar 

  88. R.C. Sanwald, J.J. Hren, Surf. Sci. 52, 697 (1975)

    Google Scholar 

  89. F.A. Nichols, W.W. Mullins, Morphological changes of a surface of revolutions due to capillarity-induced surface diffusion. J. Appl. Phys. 36(6), 1826–1835 (1965)

    Article  ADS  Google Scholar 

  90. Y.I. Frenkel, On the surface atoms crawling and natural facet roughness. ZTP. 16(1), 39–50 (1947)

    Google Scholar 

  91. E.W. Mueller, Weitere Beobachtung mit dem Feldelektronenmicrosko. Z. Phys. 108, 668–680 (1938)

    Google Scholar 

  92. M. Benjamin, R.O. Jenkins, The distribution of autoelectronic emission from single crystal metal points. I. Tungsten, Molibdenium, Nickel in the clean state. Proc. Roy. Soc. (A) 95, 262–279 (1940)

    Google Scholar 

  93. I.L. Sokolskaya, Surface migration of tungsten atoms in an electric field. ZTP. 26, 1177–1184 (1956)

    Google Scholar 

  94. V. Zhukov, A.A. Almazov, The spontaneous growth of the field electron emission (FEE) current to rebuild tip emitters. XXI All-union Conf. Emission Electron. L. 1, 241 (1990)

    Google Scholar 

  95. N.V. Egorov, V.M. Zhukov, The effect of increasing the current to rebuild emitting surface of the field electron cathode. Poverhnost. Phys. Chem. Mech. 3, 48–53 (1995)

    Google Scholar 

  96. S.C. Miller Jr., R.H. Good Jr., A WKB-Type approximation to the Schrodinger equation. Phys. Rev. 91(1), 174–179 (1953)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nikolay Egorov .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Egorov, N., Sheshin, E. (2017). Modern Developments in Theoretical Research of Field Emission. In: Field Emission Electronics. Springer Series in Advanced Microelectronics, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-56561-3_3

Download citation

Publish with us

Policies and ethics