Skip to main content

Simulation of Structure and Parameters of Field Emission Cathodes

  • Chapter
  • First Online:
Field Emission Electronics

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

  • 1034 Accesses

Abstract

In this chapter, simulation of a surface potential barrier is presented and method of determining the barrier permeability based on experimental data is proposed. It also presents simulation of current–voltage characteristics, surface structure and distribution of the work function over the surface of metal field-emission cathode for a model configuration of its vertices. Theoretical studies of the physical processes affecting the field-emission current density limits are discussed towards the end of the chapter.

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 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

Institutional subscriptions

References

  1. A.Y. Antonov, V.P. Denissov. Phys. Scr. 59, 235–240 (1999)

    Google Scholar 

  2. A.Y. Antonov, V.P. Denisov, N.V. Egorov, Mathematical modeling of the passage of electrons through a solid-vacuum boundary for small variations in the work function. Poverhnost. (12), 116–118 (1999)

    Google Scholar 

  3. A.Y. Antonov, Mathematical modeling of electron transport across the border solid-vacuum. The Control Processes and stability, in Proceedings of XXIX Scientific Conference of Applied Mathematics and Control Processes Faculty of Saint Petersburg State University, St. Petersburg (1998), pp. 115–118

    Google Scholar 

  4. A.Y. Antonov, The dependence of the electron energy states of the shape of the potential in the semiconductor emitter. The Control Processes and stability, in Proceedings of XXX Scientific Conference of Applied Mathematics and Control Processes Faculty of Saint Petersburg State University, St. Petersburg (1999), pp. 203–207

    Google Scholar 

  5. A.Y. Antonov, An inverse problem of the transparency of the quantum barrier. The Control Processes and stability, in Proceedings of XXXI Scientific Conference of Applied Mathematics and Control Processes Faculty of Saint Petersburg State University, St. Petersburg (2000), pp. 132–136

    Google Scholar 

  6. A.Y. Antonov, V.P. Denisov, Resonant tunneling in processes of electron emission from semiconductors. Europhys. Conf. Abstr. 23G(ECOSS-18), Th-P-066 (1999)

    Google Scholar 

  7. A.Y. Antonov, V.P. Denisov, Potential barrier shape determination from experimental data. Europhys. Conf. Abstr. 23G(ECOSS-18), We-P-060 (1999)

    Google Scholar 

  8. N.V. Egorov, A.Y. Antonov, M.I. Varayun, Determination of transparency of the potential barrier by the variations of the external field. Poverhnost. (11), 107–110 (2004)

    Google Scholar 

  9. N.V. Egorov, A.Y. Antonov, M.I. Varayun, Isolation of the harmonic component of the field emission signal. Poverhnost. (9), 94–98 (2005)

    Google Scholar 

  10. (a) V.P. Denisov. Pis’ma v ZTP. 18(5), 21 (1992); (b) V.P. Denisov, Pis’ma v ZTP. 18(14), 38 (1992)

    Google Scholar 

  11. L.I. Antonov et al. Pis’ma v ZTP. 11, 602 (1985)

    Google Scholar 

  12. L.I. Antonova, V.P. Denissov. Appl. Surf. Sci. 111, 237 (1997)

    Google Scholar 

  13. B.V. Thien, C. Adessi, New mechanism for electron emission from planar cold cathodes. The solid-state field-controlled electron emitters. Phys. Rev. Lett. 85(4), 864–867 (2000)

    Google Scholar 

  14. M.I. Varayun, Mathematical modeling of the tip of the electron emission structures. Thesis for the degree of Candidate of Physics and Mathematics Sciences, St. Petersburg (2002)

    Google Scholar 

  15. M.I. Varayun, A.Y. Antonov, V.P. Denisov, Mathematical modeling of a field emission cathode, in Proceedings of the X International Meeting: Accelerators -2001. St. Petersburg State University, St. Petersburg (2001), pp. 346–349

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  18. L.D. Landau, E.M. Lifshitz, Quantum mechanics. Non-relativistic theory, M.: Nauka (1974), 752 p

    Google Scholar 

  19. L.N. Dobretsov, M.V. Gomoyunova. Emission electronics, M.: Nauka (1964), 364 p

    Google Scholar 

  20. T. Pang, A numerical method for quantum tunneling. Comput. Phys. 9, 602–606 (1995)

    Google Scholar 

  21. K.-Y. Kim, B. Lee, Superlattices Microstruct. 24(6), 389 (1997)

    Article  ADS  Google Scholar 

  22. P. Niedermann, N. Sankarraman, R.J. Noer, O. Fisher. J. Appl. Phys. 59, 892–896 (1986)

    Google Scholar 

  23. V.M. Zhukov, S.A. Polezhaev. Radiotehnika i elektronika. 33(10), 2153–2162 (1988)

    Google Scholar 

  24. A. Modinos, J.P. Xanthahis, Energy floating of field-emitted electrons due to Coulomb scattering. Surf. Sci. 249(1–3), 373–378 (1991)

    Article  ADS  Google Scholar 

  25. D. Nicolaescu, Physical basis for applying the F-NJ-E relationship to experimental I-V data. J. Vac. Sci. Technol. B 11(2), 392–395 (1993)

    Article  Google Scholar 

  26. A. Seidl, M. Takai, A. Hosono, S. Yura, S. Okuda, Geometry effects arising from anodization of field emitters. J. Vac. Sci. Technol. B. 18(2), 929–932 (2000)

    Google Scholar 

  27. M.I. Elinson, G.F. Vasiliev. Field emission. M.: Fizmatgiz (1958), 272 p

    Google Scholar 

  28. N.V. Egorov, V.M. Zhukov, C.A. Polezhaev, Metal tip producing for scanning tunneling microscopy, in Proceedings of 148. WE-Heraeus-Seminar: STM-Related Spectroscopies of Semiconductor Interfaces, Bad Honnef (1995), pp. 5–7

    Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  31. 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 

  32. 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 

  33. K.A. Nikiforov, Mathematical modeling of the field electron emission from a metal-dielectric systems. Dissertation for the degree of Candidate of Sciences, St. Petersburg (2005)

    Google Scholar 

  34. C.A. Spindt, C.E. Holland, P.R. Schwoebel, I. Brodie. J. Vac. Sci. Technol. B. 16, 758 (1998)

    Google Scholar 

  35. E. Mueller, T. Tson, Ion microscopy. M.: Metallurgy (1972), 360 p

    Google Scholar 

  36. J. Rena, S. Ranganathan (eds.), The field-ion microscopy. M.: Mir (1971), 210 p

    Google Scholar 

  37. A.L. Suvorov, T.L. Razinkova, V.A. Kuznetsov, Computers in field ion microscopy. Phys. Stat. Sol. 61A, 11 (1980)

    Google Scholar 

  38. A.L. Suvorov, Structure and properties of the surface atomic layers of metal. M.: Energoatomizdat (1990), 296 p

    Google Scholar 

  39. A.L. Suvorov, T.L. Razinkova, V.A. Kuznetsov, Computer simulation of field electro images. Surf. Sci. 52, 697 (1975)

    Google Scholar 

  40. K.A. Nikiforov, N.V. Egorov, Modelling of the surface structure and the numerical calculation of a current density of field emission metal cathode. Vestnik St. Petersburg State University, Ser.10. Applied mathematics, computer science, management processes. 2, 39–45

    Google Scholar 

  41. I.M. Gribkova, Mathematical modeling of the image field in an electron microscope. Bachelor work, St. Petersburg (2009), 37 p. I.M. Gribkova, Mathematical modeling of the image field in an electron microscope. The Control Processes and stability, ed. by N.V. Smirnov, G.S. Tamasyan, in Proceedings of XXXIX Scientific Conference of Applied Mathematics and Control Processes Faculty of Saint Petersburg State University, Publishing House of St. Petersburg state University, St. Petersburg (2008), pp. 116–121

    Google Scholar 

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

    Google Scholar 

  43. M. Drechsler, E. Henkel, Feldemissions-Stromdichten und Oberflachenfeldstarken bei Feldemissionsmikroskopen sowie Methoden zur Bestimmung des Spitzenrauius, der Spitzenform, der Vergrosserung und des Auflosungsvermogens. Z. Angew. Phys. 6, 341–346 (1954)

    Google Scholar 

  44. W.P. Dyke, J.K. Trolan, Field Emission: large current densities, space charge and vacuum arc. Phys. Rev. 89(4), 799–808 (1953)

    Google Scholar 

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

    Google Scholar 

  46. G.E. Vibrans, Vacuum voltage breakdown as thermal instability of the emitting protrusions. J. Appl. Phys. 35(10), 2855–2857 (1964)

    Article  ADS  Google Scholar 

  47. V.M. Zhukov, Stability of the surface of the tip emitters when exposed to thermo and field. Stability and control processes, ed. by D.A. Ovsyannikov, L.A. Petrosyanm in Proceedings of the International Conference Volume 1: Section 1–5, 11. St. Petersburg State University, Research Institute of the VM and PU, OOO VVM, St. Petersburg (2005), pp. 161–164

    Google Scholar 

  48. Y.V. Andrianov, V.N. Bazdyrev, D.A. Borisov, V.M. Zhukov, Spontaneous growth of field emission current in a microwave field. ZTP. 61(9), 183–185 (1991)

    Google Scholar 

  49. V.L. Egorov, Y.V. Chentsov, Field emission cathodes in modern electron microscopes. In: Proceedings of the State Optic Inst. L. Publishing House of the State Optic Inst, vol. 58, pp. 68–87 (1985)

    Google Scholar 

  50. N.V. Egorov, K.A. Nikiforov, C-C. Shen, Reconstruction of the surface of the field electron emitter. Poverhnost. X-ray Synchrotron Neutron. (10), 100–106 (2009)

    Google Scholar 

  51. K. Nikiforov, Simulation of the crystal structure of the surface of a metal cathode. The control processes and stability, ed. by N.V. Smirnov, V.N. Starkov, in Proceedings of XXXV Scientific Conference of Applied Mathematics and Control Processes Faculty of Saint Petersburg State University, Publishing House of St. Petersburg state University, St. Petersburg (2004), pp. 244–247

    Google Scholar 

  52. V.S. Fomenko, The Emission Properties of the Materials. Directory, 4th edn. Revised and complementary (Naukova Dumka, Kiev, 1981), 340 p

    Google Scholar 

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

    Google Scholar 

  54. L.A. Rudnicki, On the work function of the electron and the donor-acceptor properties of non-ideal adsorption particles and coated metal surfaces. Math. USSR Acad. Sci. Ser. Nat. 26, 1240–1246 (1982)

    Google Scholar 

  55. V. Linnik, The method of least squares, and the theoretical foundations of mathematical and statistical processing of observations. L.: Fizmatgiz (1962), p. 352

    Google Scholar 

  56. M.I. Elinson (ed.), The cold cathodes. M.: Sov. radio (1974), 386 p

    Google Scholar 

  57. T.I. Lewis, Theoretical interpretation of field emission experiments. Phys. Rev. 101(6), 1694–1698 (1956)

    Article  ADS  Google Scholar 

  58. W.B. Nottingham, Remarks on energy losses attending thermionic emission of electrons from metals. Phys. Rev. 59(11), 907–908 (1941)

    Article  ADS  Google Scholar 

  59. O.W. Richardson, Extraction of electrons from cold conductors in intense electric fields. Proc. Roy. Soc. 117, 719–730 (1928)

    Google Scholar 

  60. 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 

  61. V.A. Gorkov, M.I. Elinson, G.L. Yakovlev, Theoretical and experimental research in the fore-arc phenomena of field emission. Radiotehnika i Elektronika. 7(9), 1501–1510 (1962)

    Google Scholar 

  62. A. van Oostrom, Dependence of the critical field strength for vacuum breakdown of tungsten on the field emitting area, in Proceeding III International Symposium on Discharges and Electrical insulation in Vacuum, Paris (1968), pp. 174–180

    Google Scholar 

  63. D. Lee, The influence of Nottingham effect on temperature of field emitting surface, in Proceedings of Insulation of High Voltages in Vacuum, Boston (1965), pp. 96–98

    Google Scholar 

  64. A.S. Kompaneets, Effect of space charge on the field emission. DAN USSR 128(6), 1160–1162 (1959)

    Google Scholar 

  65. Y.V. Zubenko, I.L. Sokolskaya, G.N. Fursey. ZTP. 34(5), 911–912 (1964)

    Google Scholar 

  66. N.V. Egorov, V.M. Zhukov, On the mechanism of formation of “rings” on the field emission cathodes images. Abstracts, in 21st All-Union. Conference for emission electronics, L. (1990), p. 240

    Google Scholar 

  67. N.V. Egorov, A.G. Karpov, Diagnostic Information and Expert Systems (St. Petersburg State University Publishing House, St. Petersburg, 2002), 472 p

    Google Scholar 

  68. N.V. Egorov, B.V. Yakovlev, Evolution of the surface of liquid metal in a strong electric field. Poverhnost. (8–9), 36–41 (1994)

    Google Scholar 

  69. R. Klein, L. Leder, Filed emission from Niobium in the normal and Superconducting State. Phys. Rev. 124(4), 15–18 (1961)

    Google Scholar 

  70. H. Bergeret, A. Septier, Finding of cathode heating owing to Nottingham effect. CR Acad. Sci. 277(17), 489–492 (1973)

    Google Scholar 

  71. L.M. Baskin, V.A. Godyak, O.I. Lvov et al., Effect of space charge of relativistic electrons in the field emission. ZTP. 42(6), 1282–1287 (1972)

    Google Scholar 

  72. N.E. Alexeevskiy, The impact of the emission current on the critical parameters of tantalum. DAN USSR. 242(4), 816 (1978)

    Google Scholar 

  73. V.M. Zhukov, Processes on the Surface Under Field Emission (VVM, St. Petersburg, 2007), 295 p

    Google Scholar 

  74. D.A. Ovsyannikov, N.V. Egorov, Mathematical Modeling of Systems of Formation of Electron and Ion Beams (St. Petersburg State University, St. Petersburg, 1998), 276 p

    Google Scholar 

  75. N.V. Egorov, The physical model of the processes occurring in the field emission diode in the magnetic field. Lett. ZTP 8, 1038–1041 (1982)

    Google Scholar 

  76. V.E. Ptitsyn, G.N. Fursei, N.V. Egorov et al., Egorov et al. Effect of magnetic field on the field electron emission from tungsten. Lett. ZTP 5, 116–119 (1979)

    Google Scholar 

  77. V.E. Ptitsyn, G.N. Fursei, N.V. Egorov et al., The temperature dependence of the magnetic field emission effects in metals. Lett. ZTP 6, 619–622 (1980)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  79. I. Brodie, Temperature of strongly field emmiting surface. Int. J. Electron. 18, 223–232 (1965)

    Google Scholar 

  80. L.W. Swanson, L.C. Crouser, F.M. Charbonnier, Energy exchanges attending field emission. Phys. Rev. 151(1), 327–340 (1966)

    Article  ADS  Google Scholar 

  81. T.E. Stern, B.S. Gossling, R.H. Fowler, Further studies in the emission of electrons from cold metals. Roy. Soc. Proc. A. 124, 699–723 (1929)

    Google Scholar 

  82. 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 

  83. N.B. Eisenberg, On the role of the space charge in spherical electronic projectors. ZTP. 24(11), 2079–2082 (1964)

    Google Scholar 

  84. N.B. Eisenberg, On the influence of the space charge in the form of characteristics lnJ(1/Va) of field emission cathodes. Radiotehnika i Elektronika. 9(12), 2147–155 (1964)

    Google Scholar 

  85. A.S. Kompaneets, Effect of space charge on the field emission. Radiotehnika i Elektronika. V.5. 6 y 3JK56. N8, 1315–1317 (1960)

    Google Scholar 

  86. R.P. Poplavskiy, The potential distribution in a spherical capacitor in the case of saturation current. ZTP 20, 149–159 (1950)

    Google Scholar 

  87. V.A. Godyak, L.V. Dubovoy, G.R. Zabolotskaya, Calculation of the field emission current that limited by space charge. ZETP. 57(11), 1795–1798 (1969)

    Google Scholar 

  88. A.N. Tikhonov, V.J. Arsenin, Methods of solving of ill-posed problems. M.: Nauka (1974), 286 p

    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). Simulation of Structure and Parameters of Field Emission Cathodes. In: Field Emission Electronics. Springer Series in Advanced Microelectronics, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-56561-3_4

Download citation

Publish with us

Policies and ethics