Issues »  Volume 38, Issue 1

Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

V. B. Molodkin$^{1}$, S. I. Olikhovskii$^{1}$, E. G. Len$^{1}$, Ye. M. Kyslovskyy$^{1}$, O. V. Reshetnyk$^{1}$, T. P. Vladimirova$^{1}$, B. V. Sheludchenko$^{1}$, E. S. Skakunova$^{1}$, V. V. Lizunov$^{1}$, E. V. Kochelab$^{1}$, I. M. Fodchuk$^{2}$, V. P. Klad’ko$^{3}$

$^{1}$G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03680 Kyiv-142, Ukraine
$^{2}$Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi Str., 50012 Chernivtsi, Ukraine
$^{3}$V.E. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 41 Nauky Ave., 03028 Kyiv, Ukraine

Received: 10.11.2015. Download: PDF

A short review of basic principles and limitations in obtaining the analytical expressions for the coherent and diffuse scattering intensities measured by the triple-crystal diffractometer (TCD) are presented. Explicit analytical expressions are given for both the diffuse components of TCD profiles and the reciprocal-lattice maps measured within the Bragg diffraction geometry from crystals containing microdefects of several types. These formulas are derived by using the generalized dynamical theory of X-ray scattering by imperfect crystals with randomly distributed microdefects. Some examples demonstrating possibilities of the developed theory for quantitative characterization of structural imperfections in real single crystals are represented. In particular, characteristics of the complicated microdefect structures fabricated in various silicon crystals grown by Czochralski technique and floating-zone melting method are determined by analytical treatment of the measured TCD profiles, rocking curves, and reciprocal space maps.

Key words: dynamical scattering, triple-crystal diffractometer, double-crystal diffractometer, microdefects.

URL: http://mfint.imp.kiev.ua/en/abstract/v38/i01/0099.html

DOI: https://doi.org/10.15407/mfint.38.01.0099

PACS: 61.05.cc, 61.05.cp, 61.72.Dd, 61.72.J-, 68.35.Gy, 81.40.Ef, 81.40.Wx

Citation: V. B. Molodkin, S. I. Olikhovskii, E. G. Len, Ye. M. Kyslovskyy, O. V. Reshetnyk, T. P. Vladimirova, B. V. Sheludchenko, E. S. Skakunova, V. V. Lizunov, E. V. Kochelab, I. M. Fodchuk, and V. P. Klad’ko, Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals, Metallofiz. Noveishie Tekhnol., 38, No. 1: 99—138 (2016)

REFERENCES
  1. P. Eisenberger, N. G. Alexanropoulos, and P. M. Platzmann, Phys. Rev. Lett., 28, No. 23: 1519 (1972) Crossref
  2. B. C. Larson and W. G. Schmatz, Phys. Rev. B, 10, No. 6: 2307 (1974) Crossref
  3. A. Iida and K. Kohra, phys. status solidi (a), 51, No. 2: 533 (1979) Crossref
  4. A. Iida, phys. status solidi (a), 54, No. 2: 701 (1979) Crossref
  5. A. M. Afanas'ev, M. V. Koval'chuk, E. F. Lobanovich, R. M. Imamov, P. A. Aleksandrov, and M. K. Melkonyan, Kristallografiya, 26, Iss. 1: 28 (1981) (in Russian)
  6. E. K. Kov'ev, V. V. Ratnikov, and L. M. Sorokin, Fizika Tverdogo Tela, 23, No. 6: 1626 (1981) (in Russian)
  7. P. Zaumseil and U. Winter, phys. status solidi (a), 70, No. 2: 497 (1982) Crossref
  8. P. Zaumseil and U. Winter, phys. status solidi (a), 73, No. 2: 455 (1982) Crossref
  9. A. A. Lomov, P. Zaumseil, and U. Winter, Acta Crystallogr. A, 41, No. 3: 223 (1985) Crossref
  10. R. N. Kyutt, A. A. Sitnikova, and L. M. Sorokin, Fizika Tverdogo Tela, 27, No. 3: 673 (1985) (in Russian)
  11. V. Holý and J. Kubĕna, phys. status solidi (b), 170, Iss. 1: 9 (1992) Crossref
  12. L. A. Charniy, A. N. Morozov, V. T. Bublik, K. D. Scherbachev, I. V. Stepantsova, and V. M. Kaganer, J. Cryst. Growth, 118: 163 (1992) Crossref
  13. V. Holý, U. Pietch, and T. Baumbach, High-Resolution X-Ray Scattering from Thin Films and Multilayers (Berlin–Heideiberg: Springer: 1998)
  14. P. F. Fewster, X-Ray Scattering from Semiconductors (London: Imperial College Press: 2000)
  15. V. B. Molodkin, S. I. Olikhovskii, M. E. Osinovskii, V. V. Kochelab, A. Yu. Kazimirov, M. V. Koval'chuk, and F. N. Chukhovskiy, Metallofizika, 6, No. 3: 7 (1984) (in Russian)
  16. V. B. Molodkin, V. V. Nemoshkalenko, S. I. Olikhovskii, E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. P. Krivitsky, V. F. Machulin, I. V. Prokopenko, G. E. Ice, and B. C. Larson, Metallofiz. Noveishie Tekhnol., 20, No. 11: 29 (1998)
  17. V. B. Molodkin, M. Ando, E. N. Kislovskii, S. I. Olikhovskii, T. P. Vladimirova, O. V. Reshetnyk, E. G. Len, E. A. Evgrafova, and E. V. Pervak, Metallofiz. Noveishie Tekhnol., 24, No. 4: 541 (2002)
  18. S. I. Olikhovskii, V. B. Molodkin, E. M. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, E. G. Len, G. E. Ice, R. I. Barabash, R. Köhler, and D. O. Grigoriev, Metallofiz. Noveishie Tekhnol., 27, No. 7: 949 (2005)
  19. S. I. Olikhovskii, V. B. Molodkin, E. M. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, G. E. Ice, R. I. Barabash, R. Köhler, and D. O. Grigoriev, Metallofiz. Noveishie Tekhnol., 27, No. 9: 1251 (2005)
  20. V. B. Molodkin, S. I. Olikhovskii, and M. E. Osinovskii, Metallofizika, 5, No. 1: 3 (1983) (in Russian)
  21. V. B. Molodkin, S. I. Olikhovskii, E. N. Kislovskii, E. G. Len, and E. V. Pervak, phys. status solidi (b), 227: 429 (2001) Crossref
  22. S. I. Olikhovskii, V. B. Molodkin, E. N. Kislovskii, E. G. Len, and E. V. Pervak, phys. status solidi (b), 231: 199 (2002) Crossref
  23. V. S. Wang and R. J. Matyi, J. Appl. Phys., 72, Iss. 11: 5158 (1992) Crossref
  24. M. A. Krivoglaz, X-Ray and Neutron Scattering in Nonideal Crystals (Berlin: Springer: 1996) Crossref
  25. P. H. Dederichs, Phys. Rev. B, 4: 1041 (1971) Crossref
  26. R. Bloch, D. Bahr, J. Olde, L. Brügemann, and W. Press, Phys. Rev. B, 42: 5093 (1990) Crossref
  27. T. P. Vladimirova, R. F. Seredenko, V. B. Molodkin, S. I. Olikhovskii, and E. N. Kislovskii, Metallofiz. Noveishie Tekhnol., 29, No. 6: 711 (2007) (in Ukrainian)
  28. V. B. Molodkin, S. I. Olikhovskii, E. N. Kislovskii, T. P. Vladimirova, E. S. Skakunova, R. F. Seredenko, and B. V. Sheludchenko, Phys. Rev. B, 78, No. 22: 224109 (2008) Crossref
  29. V. P. Klad'ko, L. I. Datsenko, J. Bak-Misiuk, V. F. Machulin, I. V. Prokopenko, V. B. Molodkin, S. I. Olikhovskii, and Z. V. Maksimenko, J. Phys. D: Applied Physics, 34, No. 10A: A87 (2001) Crossref
  30. E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. B. Molodkin, S. I. Olikhovskii, B. V. Sheludchenko, R. F. Seredenko, and E. S. Skakunova, Metallofiz. Noveishie Tekhnol., 29, No. 5: 701 (2007) (in Ukrainian)
  31. A. P. Shpak, V. B. Molodkin, S. I. Olikhovskii, Ye. M. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, E. G. Len, A. I. Nizkova, V. M. Venger, and S. V. Dmitriev, phys. status solidi (b), 204, No. 8: 2651 (2007) Crossref
  32. V. B. Molodkin, S. I. Olikhovskii, E. S. Skakunova, E. G. Len, E. N. Kislovskii, O. V. Reshetnyk, T. P. Vladimirova, V. V. Lizunov, L. N. Skapa, S. V. Lizunova, E. V. Fuzik, N. G. Tolmachev, B. K. Ostafiychuk, V. M. Pylypiv, and O. Z. Garpul'. Metallofiz. Noveishie Tekhnol., 37, No. 8: 1017 (2015) Crossref
  33. E. S. Skakunova, Metallofiz. Noveishie Tekhnol., 37, No. 4: 555 (2015) Crossref
  34. J. Chikawa, Y. Asaeda, and I. Fujimoto, J. Appl. Phys., 41: 1922 (1970) Crossref
  35. V. Holý, and J. Kubĕna, phys. status solidi (b), 141, No. 1: 35 (1987) Crossref
  36. V. V. Nemoshkalenko, V. B. Molodkin, E. N. Kislovskii, S. I. Olikhovskii, T. A. Grishchenko, M. T. Kogut, and E. V. Pervak, Metallofiz. Noveishie Tekhnol., 22, No. 2: 42 (2000) (in Russian)
  37. V. G. Bar'yahtar, V. V. Nemoshkalenko, V. B. Molodkin, A. P. Shpak, D. Chikava, K. Kohra, R. N. Kyutt, S. I. Olikhovskii, A. I. Nizkova, T. A. Grishchenko, E. N. Kislovskii, M. T. Kogut, and M. V. Koval'chuk, Metallofizika, 15, No. 12: 72 (1993) (in Russian)
  38. C. Bergmann, A. Gröschel, J. Will, and A. Magerl, J. Appl. Phys., 118: 015707 (2015) Crossref
  39. V. B. Molodkin, S. I. Olikhovskii, E. G. Len, E. N. Kislovskii, V. P. Kladko, O. V. Reshetnyk, T. P. Vladimirova, and B. V. Sheludchenko, phys. status solidi (a), 206, No. 8: 1761 (2009) Crossref
  40. A. Borgesi, B. Pivac, A. Sasella, and A. Stella, J. Appl. Phys., 77: 4169 (1995) Crossref
  41. V. B. Molodkin, S. I. Olikhovskii, Ye. M. Kyslovskyy, E. G. Len, O. V. Reshetnyk, T. P. Vladimirova, V. V. Lizunov, and S. V. Lizunova, Semiconductor Physics, Quantum Electronics and Optoelectronics, 13, No. 4: 353 (2010)
  42. A. P. Shpak, V. B. Molodkin, S. I. Olikhovskii, Ye. M. Kyslovskyy, O. V. Reshetnyk, T. P. Vladimirova, E. G. Len, A. I. Nizkova, V. M. Venger, and S. V. Dmitriev, phys. status solidi (a), 204, No. 8: 2651 (2007) Crossref
  43. P. M. Petroff and A. J. R. de Kock, J. Cryst. Growth, 30: 117 (1975) Crossref
  44. H. Föll, V. Gösele, and B. O. Kolbesen, J. Cryst. Growth, 52, No. 2: 907 (1981) Crossref
  45. P. J. Roksnoer and M. M. B. van der Boom, J. Cryst. Growth, 53, No. 3: 563 (1981) Crossref
  46. P. J. Roksnoer, J. Cryst. Growth, 68, No. 2: 596 (1984) Crossref
  47. V. B. Molodkin, S. I. Olikhovskii, Ye. M. Kyslovskyy, T. P. Vladimirova, E. V. Kochelab, O. V. Reshetnyk, V. V. Dovganyuk, I. M. Fodchuk, T. V. Lytvynchuk, V. P. Klad'ko, and Z. Świątek, phys. status solidi (a), 208, No. 11: 2552 (2011) Crossref
  48. E. N. Kislovskii, V. B. Molodkin, S. I. Olikhovskii, E. G. Len, B. V. Sheludchenko, S. V. Lizunova, T. P. Vladimirova, E. V. Kochelab, O. V. Reshetnik, V. V. Dovganyuk, I. M. Fodchuk, T. V. Litvinchuk, and V. P. Klad'ko, J. Surface Investigation. X-Ray, Synchrotron and Neutron Techniques, 7, No. 3: 523 (2013) Crossref

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