Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Straggling in thin silicon detectors

Hans Bichsel

Hans Bichsel

  • 1211 22nd Avenue East, Seattle, Washington 98112

Rev. Mod. Phys. 60, 663 – Published 1 July, 1988

DOI: https://doi.org/10.1103/RevModPhys.60.663

Abstract

Experimental and theoretical data for dielectric functions, x-ray absorption coefficients, and generalized oscillator strengths needed for a description of the energy-loss spectrum of fast charged particles in solid silicon are given. Theories used to calculate spectra of total energy loss ("straggling spectra") are described. The convolution method is used to calculate straggling functions for thin silicon absorbers. They are compared with those obtained from other theories (Landau). For relativistic particles (γ>100), the Vavilov-Shulek theories give incorrect functions for absorbers of thicknesses t<1 mm. The conversion of energy-loss spectra into ionization spectra is discussed, and the latter are compared with experimental functions. Good agreement is found between calculated and observed functions for electrons, mesons, protons, and their antiparticles and for α particles. From this agreement, the error (1σ) of the theoretical values of the most probable energy loss Δp and the full width at half maximum, w, is estimated to be less than ±1%.

References (140)

  1. Abramowitz, M., and I. A. Stegun, 1964, Eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematical Series No. 55 (U.S. GPO, Washington, D.C.)
  2. Ahlen, S. P., 1980, Rev. Mod. Phys. 52, 121
  3. Aitken, D. W., W. L. Lakin, and H. R. Zulliger, 1969, Phys. Rev. 179, 393
  4. Allison, W. W. M., and J. H. Cobb, 1980, Annu. Rev. Nucl. Part. Sci. 30, 253
  5. Anholt, R., 1979, Phys. Rev. A 19, 1004
  6. Antončik, E., G. di Cola, and L. Farese, 1970, Radiat. Eff. 5, 1
  7. Ashley, J. C., 1982, J. Electron. Spectrosc. Relat. Phenom. 28, 177
  8. Ashley, J. C., R. H. Ritchie, and W. Brandt, 1972, Phys. Rev. A 8, 2402
  9. Aspnes, D. E., and A. A. Studna, 1983, Phys. Rev. B 27, 985
  10. Baily, R., C. J. S. Damerell, R. L. English, A. R. Gillman, A. L. Lintern, S. J. Watts, and F. J. Wickens, 1983, Nucl. Instrum. Methods 213, 201
  11. Bak, J. F., A. Burenkov, J. B. B. Petersen, E. Uggerhøj, S. P. Møller, and P. Siffert, 1987, Nucl. Phys. B 288, 681
  12. Bearden, J. A., and A. F. Burr, 1967, Rev. Mod. Phys. 39, 125
  13. Bellamy, E. H., R. Hofstadter, W. L. Lakin, J. Cox, M. L. Perl, W. T. Toner, and T. F. Zipf, 1967, Phys. Rev. 164, 417
  14. Berger, M. J., S. M. Seltzer, S. E. Chappell, J. C. Humphreys, and J. W. Motz, 1969, Nucl. Instrum. Methods 69, 181
  15. Bethe, H., 1930, Ann. Phys. (Leipzig) 5, 325
  16. Bethe, H. A., L. M. Brown, and M. C. Walske, 1950, Phys. Rev. 79, 413
  17. Bichsel, H., 1968, in Fundamentals, Vol. I of Radiation Dosimetry, edited by F. H. Attix and W. C. Roesch (Academic, New York/London), p. 157
  18. Bichsel, H., 1970a, Phys. Rev. B 1, 2854
  19. Bichsel, H., 1970b, Nucl. Instrum. Methods A 78, 277
  20. Bichsel, H., 1972, in American Institute of Physics Handbook, 3rd ed., edited by D. E. Gray (McGraw-Hill, New York), p. 8-142
  21. Bichsel, H., 1974, Phys. Rev. A 9, 571
  22. Bichsel, H., 1985a, Nucl. Instrum. Methods A 235, 174
  23. Bichsel, H., 1985b, Radiat. Protection Dosimetry 13, 91
  24. Bichsel, H., 1987, Helv. Phys. Acta 60, 771
  25. Bichsel, H., K. M. Hanson, and M. E. Schillaci, 1982, Phys. Med. Biol. 27, 959
  26. Bichsel, H., and M. Inokuti, 1976, Radiat. Res. 67, 613
  27. Bichsel, H., R. F. Mozley, and W. A. Aron, 1957, Phys. Rev. 105, 1788
  28. Bichsel, H., and L. E. Porter, 1982, Phys. Rev. A 25, 2499
  29. Bichsel, H., and R. P. Saxon, 1975, Phys. Rev. A 11, 1286
  30. Bichsel, H., and S. Yu, 1972, IEEE Trans. Nucl. Sci. 19 (6), 172
  31. Bloch, F., 1933, Z. Phys. 81, 363
  32. Blunck, O., and S. Leisegang, 1950, Z. Phys. 128, 500
  33. Blunck, O., and K. Westphal, 1951, Z. Phys. 130, 641
  34. Börsch-Supan, W., 1961, J. Res. Nat. Bur. Stand., Sec. B 65, 245
  35. Bohr, N., 1948, Dan. Mat. Fys. Medd. 18, No. 8 (second edition, 1953)
  36. Brenner, D. J., M. Zaider, J. F. Dicello, and H. Bichsel, 1981, in Proceedings of the 7th Symposium on Microdosimetry, edited by J. Booz, H. G. Ebert, and H. D. Hartfiel (Harwood, London), p. 677
  37. Brown, F. C., R. Z. Bachrach, and M. Skibowski, 1977, Phys. Rev. B 15, 4781
  38. Chechin, V. A., L. P. Kotenko, G. I. Merson, and V. C. Yermilova, 1972, Nucl. Instrum. Methods 98, 477
  39. Chechin, V. A., and V. C. Ermilova, 1976, Nucl. Instrum. Methods 136, 551
  40. Chen, C. H., A. E. Meixner, and R. M. Kincaid, 1980, Phys. Rev. Lett. 44, 951
  41. Choi, B.-H., E. Merzbacher, and G. S. Khandelwal, 1973, At. Data 5, 291
  42. Clementi, E., and D. L. Raimondi, 1963, J. Chem. Phys. 38, 2686
  43. Cobb, J. H., W. W. M. Allison, and J. N. Bunch, 1976, Nucl. Instrum. Methods 133, 315
  44. Croitoru, N., P. G. Rancoita, and A. Seidman, 1985, Nucl. Instrum. Methods A 234, 443
  45. Davidović, D. M., B. L. Moiseiwitsch, and P. H. Norrington, 1978, J. Phys. B 11, 847
  46. Dehmer, J. L., M. Inokuti, and R. P. Saxon, 1975, Phys. Rev. A 12, 102
  47. Del Grande, N. K., 1986, private communication
  48. Eisen, F. H., G. J. Clark, J. Bøttiger, and J. M. Poate, 1972, Radiat. Eff. 13, 93
  49. Ermilova, V. C., L. P. Kotenko, and G. I. Merzon, 1977, Nucl. Instrum. Methods 145, 555
  50. Ershov, O. A., and A. P. Lukirskii, 1966, Fiz. Tverd. Tela Leningrad 8, 2137 [Sov. Phys. Solid State 8, 1699 (1967)]
  51. Esbensen, H., O. Fich, J. A. Golovchenko, S. Madsen, H. Nielsen, H. E. Schiøtt, E. Uggerhøj, C. Vraast-Thomsen, G. Charpak, S. Majewski, G. Odyniec, G. Petersen, F. Sauli, J. P. Ponpon, and P. Siffert, 1978, Phys. Rev. B 18, 1039
  52. Evans, R. D., 1967, The Atomic Nucleus, eleventh printing (McGraw-Hill, New York)
  53. Fano, U., 1963, Annu. Rev. Nucl. Sci. 13, 1
  54. Fano, U., and J. W. Cooper, 1968, Rev. Mod. Phys. 40, 441
  55. Ferrell, R. A., 1956, Phys. Rev. 101, 554
  56. Findlay, D. J. S., and A. R. DuSautoy, 1980, Nucl. Instrum. Methods 174, 531
  57. Gähwiller, C., and F. C. Brown, 1970, Phys. Rev. B 2, 1918
  58. Geretschläger, M., 1987, Nucl. Instrum. Methods B 28, 289
  59. Gerward, L., 1981, J. Phys. B 14, 3389
  60. Gerward, L., 1982, High Precision X-Ray Attenuation Coefficients Measured by an Energy Dispersive Method. Revised Values for Si, Cu and Graphite (Technical University of Denmark, Lyngby), LTF III Report No. 40
  61. Hall, G., 1984, Nucl. Instrum. Methods 220, 356
  62. Hancock, S., F. James, J. Movchet, P. G. Rancoita, and L. Van-Rossum, 1983, Phys. Rev. A 28, 615
  63. Hancock, S., F. James, J. Movchet, P. G. Rancoita, and L. Van-Rossum, 1984, Nucl. Instrum. Methods Phys. Res. B 1, 16
  64. Hanke, C. C., and H. Bichsel, 1970, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 38, No. 3
  65. Heitler, W., 1944, The Quantum Theory of Radiation, 2nd ed. (Oxford University, London)
  66. Henins, I., and J. A. Bearden, 1964, Phys. Rev. A 135, 890
  67. Herman, F., and S. Skilman, 1963, Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs)
  68. Herring, J. R., and E. Merzbacher, 1957, J. Elisha Mitchell Sci. Soc. 73, 267
  69. Hinz, H.-J., 1979, "Elektronenenergieverlustmessungen an Si, Ge und A1....," Dissertation (Universität Hamburg)
  70. Hinz, H.-J., and H. Raether, 1979, Thin Solid Films 58, 281
  71. Hunter, W. R., 1966, in Optical Properties and Electronic Structure of Metals and Alloys, Proceedings of the International Colloquium on the Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North-Holland, Amsterdam), p. 136
  72. Hunter, W. R., 1985, private communication
  73. ICRU, 1979, Average Energy Required to Produce an Ion Pair (International Commission on Radiation Units and Measurements, Bethesda, MD), Report No. 31. Sec. IX, p. 1
  74. ICRU, 1984, Stopping Powers for Electrons and Positrons (International Commission on Radiation Units and Measurements, Bethesda, MD), Report No. 37
  75. Inokuti, M., 1971, Rev. Mod. Phys. 43, 297
  76. Inokuti, M., Y. Itikawa, and J. E. Turner, 1978, Rev. Mod. Phys. 50, 23
  77. Inokuti, M., T. Baer, and J. L. Dehmer, 1978, Phys. Rev. A 17, 1229
  78. Inokuti, M., and D. Y. Smith, 1982, Phys. Rev. B 25, 61
  79. Ispirian, K. A., A. T. Margarian, and A. M. Zverev, 1974, Nucl. Instrum. Methods 117, 125
  80. Jackson, J. D., and R. L. McCarthy, 1972, Phys. Rev. B 6, 4131
  81. Jellison, G. E., and F. A. Modine, 1983, Phys. Rev. B 27, 7466
  82. Julliot, C., and M. Cantin, 1978, Nucl. Instrum. Methods 157, 235
  83. Kellerer, A. M., 1968, Mikrodosimetrie (Strahlenbiologisches Institut der Universität München), G. S. F. Bericht B-1
  84. Knop, G., A. Minten and B. Nellen, 1961, Z. Phys. 165, 533
  85. Kohlhaas, E., and F. Scheiding, 1969, in Proceedings of the 5th International Congress on X-Ray Optics and Microanalysis, Tübingen, edited by G. Möllenstedt and K. H. Gaukler (Springer, Berlin), p. 193
  86. Kolata, J. J., T. M. Amos, and Hans Bichsel, 1968, Phys. Rev. 176, 484
  87. Lægsgaard, Erik, 1982, private communication
  88. Landau, L., 1944, J. Phys. (Moscow) VIII, 201
  89. Lapique, F., and F. Piuz, 1980, Nucl. Instrum. Methods 175, 297
  90. Laulainen, N., and H. Bichsel, 1972, Nucl. Instrum. Methods 104, 531
  91. Lennard, W. N., H. Geissel, K. B. Winterbon, D. Phillips, T. K. Alexander, and J. S. Forster, 1986, Nucl. Instrum. Methods A 248, 454
  92. L'Hoir, A., 1984, Nucl. Instrum. Methods 223, 336
  93. Lindhard, J., and A. Winther, 1964, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 34, No. 4
  94. Livingston, M. S., and H. A. Bethe, 1937, Rev. Mod. Phys. 9, 245
  95. Louie, S. G., J. R. Chelikowski, and M. L. Cohen, 1975, Phys. Rev. Lett. 34, 155
  96. Maccabee, H. D., and D. G. Papworth, 1969, Phys. Lett. A 30, 241
  97. Maccabee, H. D., M. R. Raju, and C. A. Tobias, 1968, Phys. Rev. 165, 469
  98. Manson, S. T., 1972, Phys. Rev. A 6, 1013
  99. McGuire, E. J., 1986, Phys. Rev. A 33, 3572
  100. McGuire, E. J., J. M. Peek, and L. C. Pitchford, 1982, Phys. Rev. A 26, 1318
  101. Miller, J. H., L. H. Toburen, and S. T. Manson, 1983, Phys. Rev. A 27, 1337
  102. Møller, S. P., 1986, "Experimental investigations of energy loss and straggling together with inner shell-excitations of relativistic projectiles in solids," Ph.D. thesis (University of Aarhus)
  103. Møller, S. P., et al., 1982, private communication
  104. Nagata, K., T. Doke, J. Kikuchi, N. Hasebe, and A. Nakamoto, 1975, Jpn. J. Appl. Phys. 14, 697
  105. Ogle, W., P. Goldstone, C. Gruhn, and C. Maggiore, 1978, Phys. Rev. Lett. 40, 1242
  106. Perez, J. Ph., J. Sevely, and B. Jouffrey, 1977, Phys. Rev. A 16, 1061
  107. Philipp, H. R., 1972, J. Appl. Phys. 43, 2835
  108. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1986, Numerical Recipes (Cambridge University, New York), p. 191
  109. Raether, H., 1980, Excitation of Plasmons and Interband Transitions by Electrons, Springer Tracts in Modern Physics, Vol. 88 (Springer, Berlin/Heidelberg/New York)
  110. Ritsko, J. J., S. E. Schnatterly, and P. C. Gibbons, 1974, Phys. Rev. Lett. 32, 671
  111. Rohrlich, F., and B. C. Carlson, 1954, Phys. Rev. 93, 38
  112. Schimmerling, W., S. Kaplan, T. S. Subramanian, W. J. McDonald, G. Gabor, A. Sadoffi, and E. Alpen, 1983, in Proceedings of the 8th Symposium on Microdosimetry, edited by J. Booz and H. G. Ebert (Commission of the European Communities, Luxembourg), p. 311
  113. Scott, W. T., 1963, Rev. Mod. Phys. 35, 231
  114. Seltzer, S. M., and M. J. Berger, 1985, Nucl. Instrum. Methods B 12, 95
  115. Shiles, E., T. Sasaki, M. Inokuti, and D. Y. Smith, 1980, Phys. Rev. B 22, 1612
  116. Shiles, E., and D. Y. Smith, 1983, private communication
  117. Shulek, P., B. M. Golovin, L. A. Kulyukina, S. V. Medved', and P. Pavlovich, 1966, Yad. Fiz. 4, 564 [Sov. J. Nucl. Phys. 4, 400 (1967)]
  118. Sternheimer, R. M., 1966, Phys. Rev. 145, 247
  119. Sternheimer, R. M., and R. F. Peierls, 1971, Phys. Rev. B 3, 3681
  120. Sternheimer, R. M., S. M. Seltzer, and M. J. Berger, 1982, Phys. Rev. B 26, 6067
  121. Sternheimer, R. M., M. J. Berger, and S. M. Seltzer, 1984, At. Data Nucl. Data Tables 30, 261
  122. Stiebling, J., and H. Raether, 1978, Phys. Rev. Lett. 40, 1293
  123. Storm, E., and H. I. Israel, 1970, Nucl. Data Tables A 7, 565
  124. Sturm, K., and L. E. Oliveira, 1980, Phys. Rev. B 22, 6268
  125. Symon, K. R., 1948, "Fluctuations in energy lost by high energy charged particles in passing through matter," Ph. D. thesis (Harvard University)
  126. Tabata, T., and R. Ito, 1979, Nucl. Instrum. Methods 158, 521
  127. Talman, R., 1979, Nucl. Instrum. Methods 159, 189
  128. Tarrio, C., and S. E. Schnatterly, 1986a, Bull. Am. Phys. Soc., Ser. 2, 31, 350
  129. Tarrio, C., and S. E. Schnatterly, 1986b, private communication
  130. Tomboulian, D. H., and D. E. Bedo, 1956, Phys. Rev. 104, 590
  131. Tschalär, C., 1968a, Nucl. Instrum. Methods 61, 141
  132. Tschalär, C., 1968b, Nucl. Instrum. Methods 64, 237
  133. Tschalär, C., and Hans Bichsel, 1968, Phys. Rev. 175, 476
  134. Tung, C. J., R. H. Ritchie, J. C. Ashley, and V. E. Anderson, 1976, Inelastic Interactions of Swift Electrons in Solids (Oak Ridge National Laboratory, Oak Ridge), Report No. ORNL-TM-5188
  135. Uehling, E. A., 1954, Annu. Rev. Nucl. Sci. 4, 315
  136. Vavilov, P. V., 1957, Zh. Eksp. Teor. Fiz. 32, 920 [Sov. Phys.-JETP 5, 749 (1957)]
  137. Veigele, Wm. J., 1973, At. Data Tables 5, 51
  138. Viña, L., and M. Cardona, 1984, Phys. Rev. B 29, 6739
  139. Walske, M. C., 1952, Phys. Rev. 88, 1283
  140. Williams, E. J., 1929, Proc. R. Soc. London, Ser. A 125, 420

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation