Analysis of the Emission Characteristics of Field Cathodes Using Regression Models

  • N. V. EgorovEmail author
  • A. Yu. Antonov
  • M. I. Varayun’


The paper considers an approach to the construction and study of the emission (volt-ampere) characteristics of a system with a field electron cathode by regression analysis methods. A three-parameter model of the field electron emission signal is proposed. Estimates of the parameters of the current dependence on voltage are obtained in the framework of mathematical modeling. Estimation is carried out using a quadratic functional for linear and nonlinear models. Model selection should be determined by the analysis of so-called “regression residuals”, which are influenced by measurement errors. The validity of the application of both the linear and weighted nonlinear least-squares methods is shown as a result of mathematical modeling.


field electron emission volt-ampere characteristic regression model least-squares method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. V. Egorov and E. P. Sheshin, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 11 (2), 285 (2017).CrossRefGoogle Scholar
  2. 2.
    N. V. Egorov and E. P. Sheshin, Auto-Electronic Emission. Principles and Instruments (Intellekt, Dolgoprudnyi, 2011) [in Russian].Google Scholar
  3. 3.
    R. H. Fowler and L. W. Nordheim, Proc. R. Soc. A 119 (781), 173 (1928).CrossRefGoogle Scholar
  4. 4.
    G. G. Sominskii, et al., Izv. Vyssh. Uchebn. Zaved., Radiofiz. 58 (7), 567 (2016).Google Scholar
  5. 5.
    D. A. Shiffler, et al., J. Appl. Phys. 118, 083302 (2015).CrossRefGoogle Scholar
  6. 6.
    A. Yu. Antonov, M. I. Varayun’, I. M. Gribkova, and E. Yu. Pigul’, in Proc. Int. Conference “Stability and Control Processes” in Memory of V. I. Zubov (SCP 2015) (St. Petersburg, 2015), p. 144.Google Scholar
  7. 7.
    N. V. Egorov and A. A. Almazov, Vacuum 52, 295 (1999).CrossRefGoogle Scholar
  8. 8.
    M. I. Varayun’ and V. A. Klemeshev, in Proc. 10th Int. Vacuum Electron Sources Conference (IVESC 2014) (St. Petersburg, 2014), p. 1.Google Scholar
  9. 9.
    J. He, P. H. Cutler, and N. M. Miskovsky, Appl. Phys. Lett. 59 (13), 1644 (1991).CrossRefGoogle Scholar
  10. 10.
    N. V. Egorov, et al., Tech. Phys. 54 (6), 916 (2009).CrossRefGoogle Scholar
  11. 11.
    N. V. Egorov, L. I. Antonova, and A. Yu. Antonov, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 6 (6), 906 (2012).CrossRefGoogle Scholar
  12. 12.
    V. A. Golubkov, V. A. Ilyin, M. A. Kuznetsova, and A. V. Serkov, in Proc. IEEE North West Russia Section Young Researchers in Electrical and Electronic Engineer-ing Conference (EIConRusNW 2016) (St. Petersburg, 2016), p. 45.Google Scholar
  13. 13.
    R. G. Forbes, J. H. B. Deane, A. Fischer, and M. S. Mousa, Jordan J. Phys. 8 (6), 125 (2015).Google Scholar
  14. 14.
    V. S. Fomenko, Emission Properties of Materials. Handbook (Naukova Dumka, Kiev, 1981) [in Russian].Google Scholar
  15. 15.
    J. Paulini, T. Klein, and G. Simon, J. Phys. D: Appl. Phys. 26, 1310 (1993).CrossRefGoogle Scholar
  16. 16.
    E. Z. Demidenko, Linear and Nonlinear Regressions (Finansy i Statistika, Moscow, 1981) [in Russian].Google Scholar
  17. 17.
    N. R. Draper and H. Smith, Applied Regression Analysis (John Wiley and Sons, New York, 1981).Google Scholar
  18. 18.
    E. P. Sheshin, Surface Structure and Auto-Emission Properties of Carbon Materials (Moscow Institute of Physics and Technology, Fizmatkniga, Moscow, 2001) [in Russian].Google Scholar
  19. 19.
    A. Yu. Antonov and M. I. Varayun’, in Proc. 14th Int. Baltic Conference on Atomic Layer Deposition (BALD 2016) (St. Petersburg, 2016), p. 41.Google Scholar
  20. 20.
    M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. 8 (1), 3 (1998).CrossRefGoogle Scholar
  21. 21.
    E. E. Lifantova, M. I. Varayun’, and A. Yu. Antonov, in Proc. 2016 Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR 2016) (St. Petersburg, 2016).Google Scholar
  22. 22.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes. The Art of Scientific Computing (Cambridge Univ. Press, Cambridge, 2007).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • N. V. Egorov
    • 1
    • 2
    Email author
  • A. Yu. Antonov
    • 1
    • 2
  • M. I. Varayun’
    • 1
    • 2
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.St. Petersburg Electrotechnical University “LETI”St. PetersburgRussia

Personalised recommendations