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La Rivista del Nuovo Cimento (1978-1999)

, Volume 15, Issue 1, pp 1–57 | Cite as

Electron scattering in microstructure processes

  • G. Messina
  • A. Paoletti
  • S. Santangelo
  • A. Tucciarone
Article

Conclusions

The study of electron beam penetration in solids is fundamental to understanding the basic processes in a variety of applications, such as microscopy, electron probe microanalysis and microlithography. The physics of electron scattering in solids has been discussed in sect. 2, in order to obtain a useful theoretical description of the electron transport problem. Due to the complexity of the electron scattering process strong simplifications have been proposed. The single-scattering approach of Everhart and the diffusion sphere approach of Archard, described in sect. 3, have the merit of modelling, in a very simple way, two extreme cases, large-angle single scattering and diffusion: the real situation can be considered as being intermediate between the two. Presently, the most basic approach to the study the electron penetration in solids is the Monte Carlo method. MC calculations consider the behaviour of individual electrons. The trajectory of an electron through the solid is calculated step by step, assuming it is scattered through randomly determined angles, on the basis of the equations used to approximate the physical processes. The great success of Monte Carlo calculations relies upon three factors: a) its adaptability to systems having a variety of geometries, with reference to size, shape or internal structure; b) the number of different output data available from MC calculations, in the form of plots of electron trajectories, energy and angular distributions of forward and backward scattered electrons; c) the physical insight into the problem, allowed by the capability of treating the process directly in terms of its basic mechanisms. The accuracy of such calculations depends on the accuracy of the modelling of the scattering, MC results being, in any case, more accurate than analytical treatments.

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References

  1. [1]
    G. Wentzel: Z. Phys., 40, 590 (1927).ADSCrossRefGoogle Scholar
  2. [2]
    R. E. Burge and G. H. Smith: Proc. Phys. Soc. London, 79, 673 (1962).ADSCrossRefGoogle Scholar
  3. [3]
    F. Lenz: Z. Naturforsch. A, 9, 185 (1954).ADSCrossRefGoogle Scholar
  4. [4]
    C. J. Joachain: Quantum Collision Theory (Elsevier Science Publisher, Amsterdam 1975).Google Scholar
  5. [5]
    E. G. Williams: Proc. R. Soc. A, 169, 531 (1939).ADSCrossRefGoogle Scholar
  6. [6]
    S. Leisegang: Z. Phys., 132, 183 (1952).ADSCrossRefGoogle Scholar
  7. [7]
    B. P. Nigam, M. K. Sundaresan and Ta-You Wu: Phys. Rev., 115, 491 (1959).MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    H. Bethe: Handb. Phys., 24, 519 (1933).Google Scholar
  9. [9]
    R. D. Birkoff: Handb. Phys., 34, 53 (1958).ADSGoogle Scholar
  10. [10]
    G. Love, M. G. C. Cox and V. D. Scott: J. Phys. D, 10, 7 (1977).ADSCrossRefGoogle Scholar
  11. [11]
    T. E. Everhart and P. H. Hoff: J. Appl. Phys., 42, 5837 (1971).ADSCrossRefGoogle Scholar
  12. [12]
    M. J. Berger and S. M. Seltzer: Nuclear Science Series Report No. 39 NAS-NCR Publication No. 1133 (National Academy of Sciences, Washington, D. C, 1964), p. 205.Google Scholar
  13. [13]
    P. Duncumb and C. da Casa: Conference on Electron Probe Microanalysis (Institute of Physics and Physical Society, London, 1967).Google Scholar
  14. [14]
    R. H. Ritchie, F. W. Garber, Y. Nakai and R. D. Firkhoff: Adv. Radiat. Biol., 3, 1 (1969) (Academic Press, New York).Google Scholar
  15. [15]
    C. J. Powell: Rev. Mod. Phys., 48, 33 (1976).ADSCrossRefGoogle Scholar
  16. [16]
    T. S. Rao-Sahib and D. B. Wittry: J. Appl. Phys., 45, 5060 (1974).ADSCrossRefGoogle Scholar
  17. [17]
    J. J. Thomson: Conduction of Electricity Through Gases (Cambridge University Press, Cambridge, England, 1906).Google Scholar
  18. [18]
    T. E. Everhart: J. Appl. Phys., 31, 1483 (1960).ADSCrossRefGoogle Scholar
  19. [19]
    G. D. Archard: J. Appl. Phys., 32, 1505 (1961).ADSCrossRefGoogle Scholar
  20. [20]
    H. A. Bethe, M. B. Rose and L. P. Smith: Proc. Am. Phil. Soc, 78, 573 (1938).Google Scholar
  21. [21]
    S. G. Tomlin: Proc. Phys. Soc, 82, 465 (1963).ADSCrossRefGoogle Scholar
  22. [22]
    V. E. Cosslett: Br. J. Appl. Phys., 15, 107 (1964).ADSCrossRefGoogle Scholar
  23. [23]
    H. Kanter: Br. J. Appl. Phys., 15, 555 (1964).ADSCrossRefGoogle Scholar
  24. [24]
    H. W. Thummel: Durchgang von Elektronen- und Betastrahlung durch Materieschichten (Passage of electron and beta rays rough films of matter) (Akademie-Verlag, Berlin, German Democratic Rep., 1974), Chapt. 9–11.Google Scholar
  25. [25]
    H. Niedrig: Scanning Electron Microsc, 1, 29 (1981).Google Scholar
  26. [26]
    H. Niedrig: Electron Beam Interactions with Solids, SEM, Inc., AMF O’Hare (Chicago), IL 60666, U.S.A., p. 51.Google Scholar
  27. [27]
    R. W. Nosker: J. Appl. Phys., 40, 1872 (1969).ADSCrossRefGoogle Scholar
  28. [28]
    J. S. Greeneich and Van Duzer: IEEE Trans. Electron Devices, ED-21, 286 (1974).CrossRefGoogle Scholar
  29. [29]
    R. J. Hawryluk, A. M. Hawryluk and H. I. Smith: J. Appl. Phys., 45, 2251 (1974).CrossRefGoogle Scholar
  30. [30]
    M. H. Kalos and P. A. Whitlock: Monte Carlo Methods (John Wiley & Sons, 1985).Google Scholar
  31. [31]
    R. Y. Rubinstein: Simulation and The Monte Carlo Method (John Wiley & Sons, 1981).Google Scholar
  32. [32]
    D. F. Kyser and K. Murata: Proceedings of the VI International Conference on Electron and Ion Beam Science and Technology (The Electrochemical Society, Princeton, N. J., 1974).Google Scholar
  33. [33]
    K. Murata, T. Matsukawa and R. Shimizu: Jpn. J. Appl. Phys., 10, 678 (1971).ADSCrossRefGoogle Scholar
  34. [34]
    K. Murata: J. Appl. Phys., 45, 4110 (1974).ADSCrossRefGoogle Scholar
  35. [35]
    K. Murata: Electron Beam Interactions with Solids, SEM, Inc., AMF O’Hare (Chicago), IL 60666, U.S.A., p. 311.Google Scholar
  36. [36]
    L. A. Kulchetsky and G. D. Latychev: Phys. Rev., 61, 254 (1942).ADSCrossRefGoogle Scholar
  37. [37]
    M. Green: Proc. Phys. Soc., 82, 204 (1963).ADSCrossRefGoogle Scholar
  38. [38]
    I. R. McDonald, A. M. Lamki and C. F. G. Delaney: J. Phys. D., 4, 1210 (1971).ADSCrossRefGoogle Scholar
  39. [39]
    K. Murata: J. Appl. Phys., 57, 575 (1985).ADSCrossRefGoogle Scholar
  40. [40]
    K. Murata, M. Kotera, K. Nagami and S. Namba: IEEE Trans. Electron Devices, ED-32, 1694 (1985).CrossRefGoogle Scholar
  41. [41]
    I. Adesida, T. E. Everhart and R. Shimizu: J. Vac. Sci. Technol., 16, 1743 (1979).ADSCrossRefGoogle Scholar
  42. [42]
    S. Horiguchi, M. Suzuki, T. Kobayashi, H. Yoshino and Y. Sakakibara: Appl. Phys. Lett., 39, 512 (1981).ADSCrossRefGoogle Scholar
  43. [43]
    R. J. Hawryluk, A. M. Hawryluk and H. I. Smith: J. Appl. Phys., 53, 5985 (1982).ADSCrossRefGoogle Scholar
  44. [44]
    J. Henoc and F. Maurice: CEA Report R-4615 (Atomic Energy Commission, France, 1975).Google Scholar
  45. [45]
    R. Shimizu, Y. Kataoka, T. Matsukawa, T. Ikuta, K. Murata and H. Hashimoto: J. Phys. D, 8, 820 (1975).ADSCrossRefGoogle Scholar
  46. [46]
    R. Shimizu, Y. Kataoka, T. Ikuta, T. Koshikawa and H. Hashimoto: J. Phys. D. A, 9, 101 (1976).ADSCrossRefGoogle Scholar
  47. [47]
    M. Gryzinski: Phys. Rev., 138, 336 (1965).MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    R. Shimizu and T. E. Everhart: Appl. Phys. Lett., 33, 784 (1978).ADSCrossRefGoogle Scholar
  49. [49]
    E. R. Krefting and L. Reimer: Quantitative Analysis with Electron Microprobes and Secondary Ion Mass Spectroscopy, edited by E. Preuss (Zentral-Bibliothek der KFA, Julich, 1973), p. 114.Google Scholar
  50. [50]
    S. Ichimura, M. Aratama and R. Shimizu: J. Appl. Phys., 51, 2853 (1980).ADSCrossRefGoogle Scholar
  51. [51]
    M. Kotera, K. Murata and K. Nagami: J. Appl. Phys., 52, 997, 7403 (1981).ADSCrossRefGoogle Scholar
  52. [52]
    I. Adesida, R. Shimizu and T. E. Everhart: J. Appl. Phys., 51, 5963 (1980).ADSGoogle Scholar
  53. [53]
    R. D. Evans: The Atomic Nucleus (McGraw Hill, New York, N. Y., 1955), p. 576.Google Scholar
  54. [54]
    N. F. Moller: Z. Phys., 70, 786 (786).Google Scholar
  55. [55]
    N. F. Mott: Proc. R. Soc. London Ser. A, 126, 259 (1930).ADSCrossRefGoogle Scholar
  56. [56]
    K. Murata, D. F. Kyser and C. H. Ting: J. Appl. Phys., 52, 4396 (1981).ADSCrossRefGoogle Scholar
  57. [57]
    D. C. Joy: Microel. Eng., 1, 103 (1983).CrossRefGoogle Scholar
  58. [58]
    G. Messina, A. Paoletti, S. Santangelo and A. Tucciaeone: Proceedings of the International Conference on Microlithography ME91, September 17–19, 1991, Rome, Italy.Google Scholar
  59. [59]
    G. Messina, A. Paoletti, S. Santangelo and A. Tucciarone: to be published.Google Scholar
  60. [60]
    M. Parikh: J. Appl. Phys., 50, 4371 (1979) Part I, 4378 (1979) Part II, 4383 (1979) Part. III.ADSCrossRefGoogle Scholar
  61. [61]
    T. H. P. Chang: J. Vac. Sei. Technol., 1, 1271 (1979).Google Scholar
  62. [62]
    M. Parikh and D. F. Kyser: J. Appl. Phys., 50, 1104 (1979).ADSCrossRefGoogle Scholar
  63. [63]
    J. S. Greeneich: Electron Beam Process, in G. R. Brewer (Editor): Electron Beam Technology in Microelectronic Fabrication (Academic Press, New York, N. Y., 1980).Google Scholar
  64. [64]
    S. J. Wind, M. G. Rosenfield, G. Pepper, W. W. Molzen and P. D. Gerber: J. Vac. Sci. Technol. B, 7, 1507 (1989).CrossRefGoogle Scholar
  65. [65]
    S. A. Rishton and D. P. Kern: J. Vac. Sci. Technol. B, 5, 135 (1987).CrossRefGoogle Scholar
  66. [66]
    M. G. Rosenfield, S. J. Wind, W. W. Molzen and P. D. Gerber: Microelectronic Engineering, 11, 617 (1990).CrossRefGoogle Scholar
  67. [67]
    M. Gentili, A. Lucchesini, P. Lugli, G. Messina, A. Paoletti, S. Santangelo, A. Tucciarone and G. Petrocco: J. Vac. Sci. Technol. B, 7, 1586 (1989).CrossRefGoogle Scholar
  68. [68]
    M. G. Rosenfield, S. A. Rishton, D. P. Kern, D. E. Seeger and C. A. Whiting: J. Vac. Sci. Technol. B, 8, 1763 (1990).CrossRefGoogle Scholar
  69. [69]
    G. R. Brewer (Editor): Electron Beam Technology in Microelectronic Fabrication (Academic Press, New York, N. Y., 1980).Google Scholar
  70. [70]
    A. Heuberger: J. Vac. Sci. Technol. B, 6, 107 (1988).CrossRefGoogle Scholar
  71. [71]
    M. Gentili, A. Lucchesini, P. Lugli, G. Messina, A. Paoletti, S. Santangelo, A. Tucciarone and G. Petrocco: Microelectronic Engineering, 9, 147 (1989).CrossRefGoogle Scholar
  72. [72]
    M. Gentili, A. Lucchesini, L. Scopa, P. Lugli, G. Messina, A. Paoletti, S. Santangelo and A. Tucciarone: European Transactions on Telecommunications and Related Technologies, Vol. I, 61 (1990).Google Scholar
  73. [73]
    G. Messina, A. Paoletti, S. Santangelo and A. Tucciarone: Microelectronic Engineering, 11, 625 (1990).CrossRefGoogle Scholar
  74. [74]
    G. A. C. Jones, S. Blythe and H. Ahmed: J. Vac. Sci. Technol. B, 5, 120 (1987).CrossRefGoogle Scholar
  75. [75]
    C. P. Umbach and A. N. Broers: Appl. Phys. Lett., 56, 1504 (1990).CrossRefGoogle Scholar
  76. [76]
    F. Carcegnac, A. M. Haghiri-Gosnet, G. Messina, A. Paoletti, F. Rousseaux, S. Santangelo and A. Tucciarone: Microelectronic Engineering, 13, 197 (1991).CrossRefGoogle Scholar
  77. [77]
    G. Messina, A. Paoletti, S. Santangelo and A. Tucciarone: to be published.Google Scholar
  78. [78]
    G. Messina, A. Paoletti, S. Santangelo and A. Tucciarone: Nuovo Cimento D, 13, 1049 (1991).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1992

Authors and Affiliations

  • G. Messina
    • 1
  • A. Paoletti
    • 2
  • S. Santangelo
    • 1
  • A. Tucciarone
    • 1
    • 2
  1. 1.Istituto di Fisica della Facoltà di IngegneriaUniversità di Reggio CalabriaReggio Calabria
  2. 2.Facoltà di Ingegneria dell’Università di Roma-Tor VergataRoma

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