Self-consistent density functional calculation of field emission currents from metals

Physical Review Letters

Volumn 85, Issue 8, 2000, Pages 1750-1753

  Gohda, Y ^a   Nakamura, Y ^a   Watanabe, K ^b   Watanabe, S ^a  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CARRIER CONCENTRATION; ELECTRIC CURRENTS; ELECTRIC FIELD EFFECTS; FERMI LEVEL; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; VACUUM;

DENSITY FUNCTIONAL THEORY (DFT); FIELD EMISSION CURRENTS;

FIELD EMISSION CATHODES;

EID: 0034250236     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.1750     Document Type: Article

References (25)

1. T. Utsumi, IEEE Trans. Electron Devices 38, 2276 (1991).
2. R. H. Fowler and L. W. Nordheim, Proc. R. Soc. London A 119, 173 (1928).
3. See, e.g., L.I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1970), Chap. 34, 3rd ed.
4. E. L. Murphy and R. H. Good, Phys. Rev. 102, 1464 (1956).
5. K. L. Jensen, J. Appl. Phys. 85, 2667 (1999).
6. N. D. Lang, A. Yacoby, and Y. Imry, Phys. Rev. Lett. 63, 1499 (1989).
7. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
8. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
9. K. Hirose and M. Tsukada, Phys. Rev. B 51, 5278 (1995).
10. D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980); J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
11. D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980); J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
12. B. V. Noumerov, Mon. Not. R. Astron. Soc. 84, 592 (1924).
13. The Airy functions Ai(-ζ) and Bi(-ζ) are two independent solutions to the differential equation y″ + ζy = 0. The function Ai(-ζ) tends to zero as ζ → -∞, while Bi(-ζ) increases exponentially.
14. C. S. Lent and D. J. Kirkner, J. Appl. Phys. 67, 6353 (1990).
15. In the case where an electric field is applied, electron density in the vacuum region far from the jellium surface decreases as the inverse square root of z. This is a consequence of acceleration of electrons by the electric field and conservation of electric currents. However, the electron density in this region is negligible as can be seen in Fig. 2, and thus F is regarded as constant in this region.
16. J. P. Perdew and Y. Wang, Phys. Rev. B 38, 12 228 (1988).
17. N. D. Lang, Phys. Rev. B 45, 13 599 (1992).
18. N. D. Lang and W. Kohn, Phys. Rev. B 1, 4555 (1970); 3, 1215 (1971); 7, 3541 (1973).
19. N. D. Lang and W. Kohn, Phys. Rev. B 1, 4555 (1970); 3, 1215 (1971); 7, 3541 (1973).
20. N. D. Lang and W. Kohn, Phys. Rev. B 1, 4555 (1970); 3, 1215 (1971); 7, 3541 (1973).
21. s. We note that the same relation is also used in plotting the results of the FN theory.
22. A similar tendency has already been reported by M. G. Ancona, Phys. Rev. B 46, 4874 (1992). However, his analysis also shows a wrong tendency that emission currents are smaller than that of the original FN theory.
23. For precise estimation of the work function, a method other than the FN plot analysis is usually adopted, such as Kelvin probe and photoemission.
24. It is known that the classical image potential reduces the potential barrier height too much, which results in the overestimation of the current density as seen in Fig. 3. If the effect of the shift of the image plane is included [5], this discrepancy will be reduced.
25. P. H. Cutler and D. Nagy, Surf. Sci. 3, 71 (1964).