Length of Free Path of Slow Electrons in a Solid Depending on Their Energy

V. O. Tin’kov

G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

Received: 05.01.2006. Download: PDF

The main methods of calculation of the inelastic mean free path (IMFP), $\lambda$, of inelastically-scattered electrons versus their energy $E_{0}$ are reviewed. Mechanisms, which influence on the character of $\lambda($E_{0}$)$-dependence of IMFP, are considered for electron—electron scattering within the framework of the free electron-gas model approximation. Within the framework of the examined model, the IMFPs, $\lambda$, is calculated for pure Pt, Co and a Pt$_{80}$Co$_{20}$ alloy in a wide range of energies – $Е_0 = 10 − 1600$ eV. The obtained results are compared with experimental data on IMFPs, $\lambda$, for $3d$-metals (Fe $\rightarrow$ Cu) and $5d$-metals (Pt, Au). As revealed, the high divergence of experimental dependence and semi-empirical calculations for IMFP, $\lambda_{exp}$, is in the low-energy range of $Е_0$. As shown, a most correct definition of IMFP, $\lambda(Е_0)$, may be obtained by approximation of experimental data, if any, by $\lambda = A / E_{0}^{2} + BE_{0}^{1/2}$ relation (where $A$, $B$ are fitting parameters).

Keywords: electron free length path, damping length, electron—electron scattering, free electron-gas model, interzone transitions, plasmons, dielectric response function.

PACS: 72.15.Lh, 73.20.Mf, 73.50.Mx, 73.50.Gr, 79.20.Hx, 79.20.Uv, 82.80.Pv

DOI: https://doi.org/10.15407/ufm.07.02.117

Citation: V. O. Tin’kov, Length of Free Path of Slow Electrons in a Solid Depending on Their Energy, Usp. Fiz. Met., 7, No. 2: 117—134 (2006) (in Russian), doi: 10.15407/ufm.07.02.117

References (32)  
  1. M. O. Vasylyev and S. I. Sidorenko, Diffusion and Surface Segregation (Kyiv: Ministry Education of Ukraine: 1998).
  2. P. Beccat, Y. Gauthier, R. Baudoing-Savois, and J. C. Bertolini, Surf. Sci., 238: 105 (1990). Crossref
  3. M. A. Vasiliev, J. Phys. D: Appl. Phys., 30: 3037 (1997).
  4. Surface Analysis Methods in Materials Science (Eds. D. J. O'Connor, B. A. Sexton, and R. St. C. Smart) (2nd ed.) (Berlin: Springer: 2003).
  5. V. T. Cherepin, M. A. Vasil'ev, Metody i pribory dlya analiza poverkhnosti materialov: Spravochnik (Kiev: Naukova dumka: 1982).
  6. I. F. Koval', V. N. Lysenko, P. V. Mel'nik, N. G. Nakhodkin, Atlas ionizatsionnykh spektrov (Kiev: Vishcha shkola: 1989).
  7. Primenenie elektronnoy spektroskopii dlya analiza poverkhnostey (Red. Kh. Ibakh) (Riga: Zinatne: 1980).
  8. M. P. Seah, Practical Surface Analysis by Auger and X-Ray Photoelectron Spectroscopy (Eds. D. Briggs and M. P. Seah) (Chichester: Wiley: 1990), p. 201.
  9. C. J. Powell, J. Electron Spectrosc. Relat. Phenom., 47: 197 (1988).
  10. A. Jablonski and J. C. Powell, Surf. Sci. Reports, 47: 33 (2002). Crossref
  11. M. P. Seah and W. A. Dench, Surf. Interface Anal., 1, No. 1: 2 (1979).
  12. D. Penn, Phys. Rev., 35, No. 2: 482 (1987). Crossref
  13. B. Lesiak, A. Jablonski, J. Zemek, P. Lejcek et al., Surf. Interface Anal., 30: 217 (2000).
  14. C. J. Powell and A. Jablonski, J. Phys. Chem. Ref. Data, 28, No. 1: 19 (1987).
  15. T. P. Ershova, V. V. Korablev, Yu. A. Morozov, FTT, 22, № 7: 2199 (1980).
  16. D. Payns, Elementarnye vozbuzhdeniya v tverdykh telakh (Moskva: Mir: 1965).
  17. M. A. Vasil'ev, A. G. Blashchuk, V. A. Tin'kov, Metallofiz. noveyshie tekhnol., 25, No. 12: 1617 (2003).
  18. M. A. Vasylyev, S. P. Chenakin, and V. A. Tinkov, Vacuum, 78: 19 (2005).
  19. M. A. Vasylyev, V. A. Tinkov, A. G. Blaschuk, J. Luyten, and C. Creemers, Appl. Surf. Sci.: (2006) (to be published).
  20. P. J. Cumpson and M. P. Seah, Surf. Interface Anal., 25: 430 (1997). Crossref
  21. P. J. Cumpson, Surf. Interface Anal., 25: 447 (1997). Crossref
  22. W. H. Gries, Surf. Interface Anal., 24: 38 (1996). Crossref
  23. H. Bethe, Ann. der Physik, 5: 325 (1930).
  24. D. R. Penn, J. Electron Spectrosc. Relat. Phenom., 9: 29 (1976).
  25. S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interface Anal., 11: 577 (1988).
  26. S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interface Anal., 25: 25 (1997).
  27. S. Tanuma, C. J. Powell, and D. R. Penn, Surf. Interface Anal., 35: 268 (2003).
  28. W. B. Pearson, A Handbook of Lattice Spacings and Structure of Metals and Alloys (New York: Pergamon: 1958).
  29. A. P. Shpak, M. A. Vasil'ev, V. A. Tin'kov, Metallofiz. Noveishie Tekhnol., 26, No. 6: 765 (2004).
  30. M. A. Vasil'ev, V. A. Tin'kov, S. V. Chervonnyy, Uspehi Fiz. Met., 7, No. 1: 41 (2006).
  31. A. Jablonski, B. Lesiak, J. Zemek, and P. Jiricek, Surf. Sci., 595: 1 (2005). Crossref
  32. A. G. Blashchuk, M. A. Vasil'ev, V. A. Tin'kov, Metallofiz. Noveishie Tekhnol., 25, No. 3: 363 (2003).