Skip to main content
Log in

New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

  • Contributed Papers
  • Published:
Microchimica Acta Aims and scope Submit manuscript

Abstract

The study of fast electron interaction with solids in the energy range from 100 eV to several tens of keV is prompted by quickly developing microbeam analysis techniques such as electron probe microanalysis, scanning electron microscopy, electron energy loss spectroscopy and so on. It turned out that for random solids the electron transport problem might be solved on the basis of the generalized radiative field similarity principle. The latter states that the exact differential elastic cross section in the kinetic equation may be replaced by an approximate one provided the conditions of radiative field similarity are fulfilled. Application of the generalized similarity principle to electron scattering in solids has revealed many interesting features of electron transport. Easy to use and effective formulae have been obtained for the angular and energy distribution of electrons leaving a target, total yields of characteristic photons and slow electrons escaping from a sample bombarded by fast primaries, escape probability of Auger electrons as a function of depth etc. The analytical results have been compared with Monte Carlo calculations and experiments in a broad range of electron energies and scattering properties of solids and good agreement has been observed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Reimer, H. Drescher,J. Phys. D: Appl. Phys. 1977,10, 805.

    Google Scholar 

  2. H. Niedrig,J. Appl. Phys. 1982,53, R15.

    Google Scholar 

  3. R. Shimizu,Jpn. J. Appl. Phys. 1983,22, 1631.

    Google Scholar 

  4. P. Streubel, H. Berndt,Surf. Interface Anal. 1984,6, 48.

    Google Scholar 

  5. D. Briggs, M. P. Seah (eds.),Practical Surface Analysis, Vol. 1, Wiley, New York, 1990.

    Google Scholar 

  6. G. Gergely,Surf. Interface Anal. 1981,3, 201.

    Google Scholar 

  7. A. Jablonski, J. Gryko, J. Kraaer, S. Tougaard,Phys. Rev. 1989,B39, 61.

    Google Scholar 

  8. N. T. Bagraev, A. T. Gusarov, V. A. Mashkov,Surf. Sci. 1986,172, L545.

    Google Scholar 

  9. S. Tougaard, J. Kraaer,Phys. Rev. 1991,B43, 1651.

    Google Scholar 

  10. I. M. Bronstein, B. S. Freiman,Vtorichnaya Elektronnaya Emissi, Nauka, Moscow, 1968, p. 75 (Russian).

    Google Scholar 

  11. R. A. Bonham, T. G. Strand,J. Chem. Phys. 1963,39, 2200.

    Google Scholar 

  12. A. C. Yates,Comp. Phys. Comm. 1971,2, 175.

    Google Scholar 

  13. U. Fano, J. A. Stephens,Phys. Rev. 1986,B34, 438.

    Google Scholar 

  14. K. Blum,Density Matrix: Theory and Applications, Plenum Press, New York, 1981.

    Google Scholar 

  15. S. L. Dudarev, M. I. Ryazanov,Sov. Phys. JETP 1985,61, 370.

    Google Scholar 

  16. S. L. Dudarev, M. I. Ryazanov,Acta Cryst. 1988,A44, 51.

    Google Scholar 

  17. W. S. M. Werner, I. S. Tilinin,Appl. Surf. Sci. 1993,70/71, 29.

    Google Scholar 

  18. V. V. Sobolev,Rasseyanie Sveta v Atmospherah Planet, Nauka, Moscow, 1972 (Russian).

    Google Scholar 

  19. K. M. Case, P. F. Zweifel,Linear Transport Theory, Addison-Wesley, Reading, MA, 1967.

    Google Scholar 

  20. W. S. M. Werner, I. S. Tilinin,Surf. Sci. Lett. 1992,268, L319.

    Google Scholar 

  21. I. S. Tilinin, W. S. M. Werner,Phys. Rev. 1992,B46, 13739.

    Google Scholar 

  22. Stopping Powers for Electrons and Positrons,ICRU Report 37, Internat. Com. on Radiation Units and Measurements, Bethesda, MD, 1984.

  23. J. C. Ashley, C. J. Tung, R. H. Ritchie, V. E. Andersen,IEEE Trans. Nucl. Sci. 1976,NS-23, 1833.

    Google Scholar 

  24. S. Tanuma, C. J. Powell, D. R. Penn,Surf. Interface Anal. 1988,11, 577.

    Google Scholar 

  25. I. S. Tilinin,Sov. Phys. JETP 1988,67, 1570.

    Google Scholar 

  26. I. S. Tilinin,Poverkhnost 1990,8, 10 (Russian).

    Google Scholar 

  27. C. A. Quarles,Phys. Rev. 1976,13A, 1278.

    Google Scholar 

  28. E. H. S. Burhop, W. H. Asaad,Adv. Atom. Mol. Phys. 1972,8, 164.

    Google Scholar 

  29. S. Chandrasekhar,Radiative Transfer, Dover Publications, New York, 1960.

    Google Scholar 

  30. A. L. Tofterup,Surf. Sci. 1986,167, 70.

    Google Scholar 

  31. S. Tougaard,Surf. Interface Anal. 1988,11, 453.

    Google Scholar 

  32. H. A. Bethe,Ann. Phys. 1930,5, 325.

    Google Scholar 

  33. I. S. Tilinin, W. S. M. Werner,Surf. Sci. 1993,290, 119.

    Google Scholar 

  34. M. E. Riley, C. J. MacCallum, F. Biggs,Atom. Data Nucl. Data Tab. 1975,15, 443.

    Google Scholar 

  35. W. S. M. Werner, I. S. Tilinin, M. Hayek, in preparation.

  36. H. Kullenkamf, W. Spyra,Z. Phys. 1954,137, 416.

    Google Scholar 

  37. L. Küchler, H.-J. Hunger,Exp. Tech. Phys. 1982,30, 335.

    Google Scholar 

  38. B. F. I. Schonland,Proc. Roy. Soc. 1923,A104, 235.

    Google Scholar 

  39. J. O. Brand,Ann. Phys. 1936,26, 609.

    Google Scholar 

  40. P. C. R. Palluel,Comp. Rend. Acad. Sci. 1947,224, 1492.

    Google Scholar 

  41. J. G. Trump, R. J. van der Graaf,Phys. Rev. 1949,75, 44.

    Google Scholar 

  42. H. Kullenkampf, K. Rüttiger,Z. Phys. 1954,137, 426.

    Google Scholar 

  43. E. J. Sternglass,Phys. Rev. 1954,93, 345.

    Google Scholar 

  44. H. Kanter,Ann. Phys. 1957,20, 144.

    Google Scholar 

  45. H. E. Bishop,Proc. IV Cong. Intern. Optique des Rayons X et Microanalyse, Paris, 1965, pp. 153–158.

  46. K. A. Wright, J. G. Trump,J. Appl. Phys. 1962,33, 687.

    Google Scholar 

  47. D. Harder, H. Ferber,Phys. Lett. 1964,9, 233.

    Google Scholar 

  48. E. Weinryb, J. Philibert,Comp. Rend. Acad. Sci. 1964,258, 4535.

    Google Scholar 

  49. J. L. Bienlein, G. Schlosser,Z. Phys. 1963,174, 91.

    Google Scholar 

  50. P. Ya. Glasunov, V. G. Guglya,Dokl. Akad. Nauk SSSR 1964,159, 632 (Russian).

    Google Scholar 

  51. L. M. Boyarshinov,Atomnaya Energiya 1966,21, 42 (Russian).

    Google Scholar 

  52. T. Tabata,Phys. Rev. 1967,162, 336.

    Google Scholar 

  53. V. G. Guglya, P. Ya. Glasimov, V. V. Kosukhin,Zh. Tekh. Fiz. 1968,38, 897 (Sov. Phys. Tech. Phys. 1968,13, 675).

    Google Scholar 

  54. P. Verdier, F. Arnal,Comp. Rend. 1968,B267, 1443.

    Google Scholar 

  55. P. J. Ebert, A. P. Lauson, E. M. Lent,Phys. Rev. 1969,183, 422.

    Google Scholar 

  56. T. Tabata, R. Ito, S. Okabe,Nucl. Inst. Meth. 1971,94, 509.

    Google Scholar 

  57. H. Frank,Z. Naturforsch. 1959,14a, 247.

    Google Scholar 

  58. K. Murata,Proc. Symp. on Scanning Electron Microscopy (O. Johari, I. Corvin, eds.), IITRI, Chicago, 1973, pp. 267–276.

    Google Scholar 

  59. I. S. Tilinin,Poverkhnost 1992,2, 5 (Russian).

    Google Scholar 

  60. M. Green,Proc. Phys. Soc. 1964,83, 435.

    Google Scholar 

  61. R. Castaing, J. Descamps,J. Phys. Radium. 1965,16, 304.

    Google Scholar 

  62. L. S. Bircs, R. E. Seebold,Anal. Chem. 1961,33, 687.

    Google Scholar 

  63. I. S. Tilinin,Poverkhnost 1988,8, 5 (Russian).

    Google Scholar 

  64. R. Shimizu,Jpn. J. Appl. Phys. 1983,22, 1631.

    Google Scholar 

  65. G. B. Edelstein, L. V. Kasakov, V. N. Shemelev,Pismma v ZhTF 1980,6, 489 (Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tilinin, I.S., Werner, W.S.M. New developments in theory of fast electron scattering in solids: Applications to microbeam analysis. Mikrochim Acta 114, 485–503 (1994). https://doi.org/10.1007/BF01244576

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01244576

Key words

Navigation