Advertisement

Modern Developments in Theoretical Research of Field Emission

  • Nikolay EgorovEmail author
  • Evgeny Sheshin
Chapter
Part of the Springer Series in Advanced Microelectronics book series (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.

Keywords

Current-voltage characteristic Fowler–Nordheim plot Emission area Work function Electric field calculation Field electron emission Thermal-field emission Field emission spectroscopy Electron energy distribution Field emission of semiconductors Phenomenological theory Surface diffusion Building-up emitter process Nottingham effect 

References

  1. 1.
    I.M Hoffmann, Investigation of electrostatic emission of tungsten in a wide range of current densities. FTT 4, 2005 (1962)Google Scholar
  2. 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. 3.
    M. Green (ed.), Surface properties of solids. Mir 432 (1972)Google Scholar
  4. 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. 5.
    A.G.J. Oostrom, Philips Res. Rep. Suppl. 1, 1–162 (1966)Google Scholar
  6. 6.
    G.R. Condon, J.A. Panitz, J. Vac. Sci. Technol. B 16, 23 (1998)Google Scholar
  7. 7.
    J. Plšek, D.V. Zhukov, Z. Knor, The average work function and emission area in the Fowler–Nordheim equation. Czech. J. PhysGoogle Scholar
  8. 8.
    G. Binnig, G. Rohrer, Scanning tunnel microscope. World Sci. 10, 26–33 (1985)Google Scholar
  9. 9.
    A. Modinos, Theoretical analysis of field emission data. Solid-State Electron. 45, 809–816 (2001)ADSCrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 11.
    M. Drechsler, E. Henkel, Z. Angew. Phys. 6, 341 (1954)Google Scholar
  12. 12.
    P.H. Cutler, J. He, N.M. Miskovsky et al. J. Vac. Sci. Technol. B. 11, 387–391 (1993)Google Scholar
  13. 13.
    A. Modinos, J.P. Xanthahis, Energy-broadening of field-emitted electrons due to Coulomb collisions. Surf. Sci. 249, 373 (1991)Google Scholar
  14. 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. 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. 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. 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. 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. 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. 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. 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. 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. 23.
    R.G. Forbes, C.J. Edgcombe, U. Valdre, Some comments on models for field enhancement. Ultramicroscopy 95, 57–65 (2003)CrossRefGoogle Scholar
  24. 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. 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)ADSCrossRefGoogle Scholar
  26. 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)ADSCrossRefGoogle Scholar
  27. 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)ADSCrossRefGoogle Scholar
  28. 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)ADSCrossRefGoogle Scholar
  29. 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)ADSCrossRefGoogle Scholar
  30. 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)CrossRefGoogle Scholar
  31. 31.
    W.P. Dyke, Field emission. A new practical electron source. IRE Trans. Mil. Electron. 38–45 (1960)Google Scholar
  32. 32.
    A. Modinos, Field, thermionic and secondary electron emission spectroscopy. M. Nauka, 320 (1990)Google Scholar
  33. 33.
    M.I. Elinson (ed.), The cold cathodes. Sov. Radio 386 (1974)Google Scholar
  34. 34.
    W.W. Dolan, W.P. Dyke, Temperature and field emission of electrons from metals. Phys. Rev. 95, 327–332 (1954)Google Scholar
  35. 35.
    E.L. Murphy, R.H. Good, Thermionic emission, field emission and transition region. Phys. Rev. 102(6), 1464–1473 (1956)ADSCrossRefGoogle Scholar
  36. 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. 37.
    E. Guth, C.J. Mullin, Electron emission of metals in electric field. Phys. Rev. 61(5–6), 339–348 (1942)Google Scholar
  38. 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. 39.
    S.G. Christov, General theory of electron emission from metals. Phys. Stat. Sol. 17(1), 11–26 (1966)ADSCrossRefGoogle Scholar
  40. 40.
    F.I. Itskovich, On the theory of field emission from metals. Part I. ZETP, 50(5), 1425–1437 (1966)Google Scholar
  41. 41.
    F.I. Itskovich, On the theory of field emission from metals. Part II. ZETP 52(6), 1720–1735 (1967)Google Scholar
  42. 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. 43.
    S.C. Miller Jr., R.H. Good Jr., Phys. Rev. 92, 13–67 (1953)Google Scholar
  44. 44.
    M.I. Elinson, G.F. Vasiliev, Field emission. M. Fizmatgiz, 272 (1958) Google Scholar
  45. 45.
    L.N. Dobretsov, M.V. Gomoyunova, Emission elekcronics. M. Nauka, 364 (1964)Google Scholar
  46. 46.
    R. Fischer, H. Neumann, Field emission from Semiconductors. M. Nauka, 215 (1971)Google Scholar
  47. 47.
    V.T. Cherepin, M.A. Vasiliev, Methods and tools for the analysis of material surface Handbook (Naukova Dumka, Kiev, 1982), p. 400Google Scholar
  48. 48.
    J.E. Henderson, R.E. Badley, Phys. Rev. 38(3), 590 (1931)Google Scholar
  49. 49.
    J.E. Henderson, R.K. Dahlstrom, Phys. Rev. 55(5), 473 (1939)ADSCrossRefGoogle Scholar
  50. 50.
    J.E. Henderson, R.K. Dahlstrom, F.R. Abott, Phys. Rev. 41(1), 261 (1932)Google Scholar
  51. 51.
    L. Feldman, D. Meyer, Basics of analysis of surfaces and thin films. M. Mir, 344 (1989)Google Scholar
  52. 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. 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. 54.
    L.W. Swanson, L.C. Crouser, Phys. Rev. 163, 632 (1967)Google Scholar
  55. 55.
    A.B. El-Karen, J.C. Wolfe, J.E. Wolfe, J. Appl. Phys. 48, 4749 (1977)Google Scholar
  56. 56.
    J.W. Gadzuk, E.W. Plummer. Phys. Rev. 3, 2125.58 (1971)Google Scholar
  57. 57.
    A.E. Bell, L.W. Swanson, Phys. Rev. B. 19, 3353 (1979)Google Scholar
  58. 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. 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. 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. 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 pGoogle Scholar
  62. 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. 63.
    N.V. Egorov, On the possibility of narrow collimated electron beams. ZTP. 52(12), 2440–2442 (1982)Google Scholar
  64. 64.
    N.V. Egorov, A.G. Karpov, Diagnostic information and expert systems. SPb. (St. Petersburg State University Publishing House, Russia, 2002) 472 pGoogle Scholar
  65. 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. 66.
    A.G. Zhdan, M.I. Elinson et al., Raditehnika i Elektronika. 7, 570 (1962)Google Scholar
  67. 67.
    M.I. Elinson et al., Raditehnika i Elektronika. 10, 1288 (1965)Google Scholar
  68. 68.
    Y.A. Frenkel, ZETP. 8, 1893 (1938)Google Scholar
  69. 69.
    W. Franz, Ergeb. exapt, Naturwiss. 27, 1 (1953)Google Scholar
  70. 70.
    W. Franz, Handb. Phys. 17, 155 (1956)ADSGoogle Scholar
  71. 71.
    R.J. Hodgkinson, Proc. Phys. Soc. 82(58), 1010 (1963)Google Scholar
  72. 72.
    Y.A. Frankel. ZETP. 7, 1069 (1937)Google Scholar
  73. 73.
    R. Stratton, Phis. Rev. 126, 2002 (1962)Google Scholar
  74. 74.
    M. Sanchez, Helv. Phys. Acta. 36, 1 (1963)Google Scholar
  75. 75.
    H. Frohlich, B.V. Paranjape, Proc. Phys. Soc. 69(21), 866 (1956)Google Scholar
  76. 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. 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. 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. 79.
    V.M. Zhukov, Processes on the surface under field emission. SPb (VVM, Russia, 2007), 295 p.Google Scholar
  80. 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. 81.
    B. Honigman, Growth and shape of the crystals. M. IIL, 224 (1961)Google Scholar
  82. 82.
    C. Herring, Structure and properties of solid surface. ed. By R. Gomer, S.S. Smith (University of Chicago Press, USA, 1953), pp. 5–72Google Scholar
  83. 83.
    C. Herring, The physics of powder metallurgy. ed. by W.E. Kingston (McGrow Book Co., N.Y., 1953), p. 143Google Scholar
  84. 84.
    W.W. Mullins, Theory of thermal growing. J. Appl. Phys. 28(3), 333–339 (1957)ADSCrossRefGoogle Scholar
  85. 85.
    W.W. Mullins, Flattening of nearly plane solid surface to capillarity. J. Appl. Phys. 30(1), 77–83 (1959)ADSCrossRefGoogle Scholar
  86. 86.
    J.L. Boling, W.W. Dolan, Blunting of tungsten needles by surface diffusion. J. Appl. Phys. 29(3), 556–559 (1958)ADSCrossRefGoogle Scholar
  87. 87.
    E.W. Mueller, Oberflachenwanderung von Wolfram auf dem eigenen Kristallgitter. Z. f. Phys. 126(7–9), 642–665 (1949)Google Scholar
  88. 88.
    R.C. Sanwald, J.J. Hren, Surf. Sci. 52, 697 (1975)Google Scholar
  89. 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)ADSCrossRefGoogle Scholar
  90. 90.
    Y.I. Frenkel, On the surface atoms crawling and natural facet roughness. ZTP. 16(1), 39–50 (1947)Google Scholar
  91. 91.
    E.W. Mueller, Weitere Beobachtung mit dem Feldelektronenmicrosko. Z. Phys. 108, 668–680 (1938)Google Scholar
  92. 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. 93.
    I.L. Sokolskaya, Surface migration of tungsten atoms in an electric field. ZTP. 26, 1177–1184 (1956)Google Scholar
  94. 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. 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. 96.
    S.C. Miller Jr., R.H. Good Jr., A WKB-Type approximation to the Schrodinger equation. Phys. Rev. 91(1), 174–179 (1953)ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Saint Petersburg State UniversitySt. PetersburgRussia
  2. 2.MIPTDolgoprudny, Moscow regionRussia

Personalised recommendations