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Fermi energy of electrons in a thin metallic plate


A strict analytical expression for the Fermi energy of electrons in a thin metallic plate as a function of the plate thickness at a given electron density has been derived for the first time. The derivation has been carried out taking into account the size quantization in the free-electron approximation at zero temperature.

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  1. 1.

    K. Oura, V. G. Lifshits, A. A. Saranin, A. V. Zotov, and M. Katayama, Surface Science: An Introduction (Springer, Berlin, 2003; Nauka, Moscow, 2006).

    Google Scholar 

  2. 2.

    D. V. Buturovich, D. V. Vyalykh, M. V. Kuz’min, M. A. Mittsev, and S. L. Molodtsov, Fiz. Tverd. Tela (St. Petersburg) 48(10), 1890 (2006) [Phys. Solid State 48 (10), 2008 (2006)].

    Google Scholar 

  3. 3.

    D. V. Buturovich, M. A. Kuz’min, M. V. Loginov, and M. A. Mittsev, Fiz. Tverd. Tela (St. Petersburg) 50(1), 168 (2008) [Phys. Solid State 50 (1), 173 (2008)].

    Google Scholar 

  4. 4.

    J.-H. Chou, Q. Niu, and Z. Zhang, Phys. Rev. Lett. 80, 3582 (1998).

    ADS  Article  Google Scholar 

  5. 5.

    K. P. Bohnen and K. M. Ho, Surf. Sci. Rep. 19, 99 (1993).

    ADS  Article  Google Scholar 

  6. 6.

    F. K. Schulte, Surf. Sci. 55, 427 (1976).

    ADS  Article  Google Scholar 

  7. 7.

    A. Kiejna, J. Peisert, and P. Scharoch, Surf. Sci. 432, 54 (1999).

    ADS  Article  Google Scholar 

  8. 8.

    P. J. Feibelman, Phys. Rev. B: Condens. Matter 27, 1991 (1983).

    ADS  Article  Google Scholar 

  9. 9.

    P. J. Feibelman and D. R. Hamann, Phys. Rev. B: Condens. Matter 29, 6463 (1984).

    ADS  Article  Google Scholar 

  10. 10.

    S. Ciraci and I. P. Batra, Phys. Rev. B: Condens. Matter 33, 4294 (1986).

    ADS  Article  Google Scholar 

  11. 11.

    I. P. Batra, S. Ciraci. G. P. Srivastava, J. S. Nelson, and C. Y. Fong, Phys. Rev. B: Condens. Matter 34, 8246 (1986).

    ADS  Article  Google Scholar 

  12. 12.

    J. C. Boetteger, U. Brikenheuer, N. Rõsch, and S. B. Trickey, Int. J. Quantum Chem., Symp. 28, 675 (1994).

    Article  Google Scholar 

  13. 13.

    J. C. Boetteger, Phys. Rev. B: Condens. Matter 53, 13133 (1996).

    ADS  Article  Google Scholar 

  14. 14.

    K. M. Ho and K. P. Bohnen, Phys. Rev. B: Condens. Matter 32, 3446 (1985).

    ADS  Article  Google Scholar 

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Correspondence to V. D. Dymnikov.

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Original Russian Text © V.D. Dymnikov, 2011, published in Fizika Tverdogo Tela, 2011, Vol. 53, No. 5, pp. 847–852.

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Dymnikov, V.D. Fermi energy of electrons in a thin metallic plate. Phys. Solid State 53, 901–907 (2011).

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  • Fermi Energy
  • Plate Thickness
  • Macroscopic Characteristic
  • Metallic Plate
  • Jellium Model