Fast numerical calculation of X-ray diffraction from crystal microsystems

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Resumo

In the kinematical approximation, a method for rapid numerical calculation of X-ray diffraction from thin crystalline microsystems has been developed. The speed of calculating of reciprocal space maps using this approach is three to four orders of magnitude higher than calculations based on the Takagi–Taupin equations or two-dimensional recurrence relations. Within the framework of the obtained solutions, numerical simulation of X-ray reciprocal space mapping was performed for three models of crystal chips of microsystems.

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Sobre autores

V. Punegov

Federal Research Center “Komi Scientific Center, the Ural Branch of the Russian Academy of Sciences”

Email: vpunegov@dm.komisc.ru

Institute of Physics and Mathematics

Rússia, Syktyvkar

D. Malkov

Federal Research Center “Komi Scientific Center, the Ural Branch of the Russian Academy of Sciences”

Autor responsável pela correspondência
Email: vpunegov@dm.komisc.ru

Institute of Physics and Mathematics

Rússia, Syktyvkar

Bibliografia

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  3. Schifferle V., Dommann A., Neels A. // Sci. Technol. Adv. Mater. 2017. V. 18. P. 219. https://doi.org/10.1080/14686996.2017.1282800
  4. Punegov V.I., Pavlov K.M., Karpov A.V., Faleev N.N. // J. Appl. Cryst. 2017. V. 50. P. 1256. https://doi.org/10.1107/S1600576717010123
  5. Punegov V.I., Kolosov S.I. // J. Appl. Cryst. 2022. V. 55. P. 320. https://doi.org/10.1107/S1600576722001686
  6. Punegov V.I., Kolosov S.I., Pavlov K.M. // Acta Cryst. A. 2014. V. 70. P. 64. https://doi.org/10.1107/S2053273313030416
  7. Punegov V.I., Kolosov S.I., Pavlov K.M. // J. Appl. Cryst. 2016. V. 49. P. 1190. https://doi.org/10.1107/S1600576716008396
  8. Takagi S. // Acta Cryst. 1962. V. 15 P. 1311. https://doi.org/10.1107/S0365110X62003473
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2. Fig. 1. Schematic representation of X-ray diffraction from a MEMS chip consisting of an upper curved part of thickness Lz1 and a lower perfect or gradient region of the crystal of thickness Lz2. The width of the incident and reflected X-ray beam is w, the illumination of the surface of the structure has the size Lx. PSD is a position sensitive detector.

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3. Fig. 2. RSM calculation map from the first MEMS chip model – a curved Si crystal with a thickness of 4 µm. The lateral width of the crystal is Lx = 135 µm.

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4. Fig. 3. RSM calculation map from the second MEMS chip model with a curved top part with a thickness of 2 μm. The bottom layer is an undeformed crystal with a thickness of Lz2 = 2 μm.

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5. Fig. 4. RSM calculation map from the third MEMS chip model with a curved top. The bottom layer has a one-dimensional deformation gradient along the crystal depth.

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6. Fig. 5. Lateral qx-sections (a) and vertical qz-sections (b) of RSM maps from the first (1), second (2) and third (3) MEMS chip models.

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