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Aberration-corrected self-interference of split higher order Laue zone line for measuring the z-dependent strain profile

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Abstract

A common characteristic in semiconductor nanostructures is the lattice strain originating from the lattice mismatch between layers of different compositions. Three-dimensional strain measurement in crystals using transmission electron microscopy (TEM) techniques has been the subject of intense works for decades. This information is required for the strain-bandgap engineering being used by our current fast computers and necessary for future quantum computers. However, the missing information was the 3rd dimension that is the atomic displacement and how it changes along the electron-beam direction. The strain information along the electron-beam direction is in the phase of the diffracted beam, which has been obtained recently by the novel technique of self-interference of split higher order Laue zone line (SIS-HOLZ). SIS-HOLZ has been made possible by the correction of the beam aberrations having its analytical and experimental details reported here for the atomic displacement profile existing at the interface of a Si and Si/Si0.8Ge0.2 superlattice.

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References

  1. M. Chun, Y. Sun, U. Aghoram, and S.E. Thompson: Strain: A solution for higher carrier mobility in nanoscale MOSFETs. Annu. Rev. Mater. Res. 39, 203–229 (2009).

    Article  Google Scholar 

  2. Y. Sun, S.E. Thompson, and T. Nishida: Strain Effect in Semiconductors: Theory and Device Applications (Springer, London, 2010); pp. 235–266.

    Book  Google Scholar 

  3. P.W. Deelman, L.F. Edge, and C.A. Jackson: Metamorphic materials for quantum computing. MRS Bull. 41 (03), 224–230 (2016).

    Article  Google Scholar 

  4. M.J. Hÿtch, E. Snoeck, and R. Kilaas: Quantitative measurement of displacement and strain fields from hrem micrographs. Ultramicroscopy 74 (3), 131–146 (1998).

    Article  Google Scholar 

  5. M.J. Hÿtch and L. Potez: Geometric phase analysis of high-resolution electron microscopy images of antiphase domains: Example Cu3Au. Philos. Mag. 76 (6), 1119–1138 (1997).

    Article  Google Scholar 

  6. K. Saitoh, H. Nakahara, and N. Tanaka: Improvement of the precision of lattice parameter determination by nano-beam electron diffraction. Microscopy 69 (5), 533–539 (2013).

    Article  Google Scholar 

  7. P. Favia, M.B. Gonzales, E. Simoen, P. Verheyen, D. Klenov, and H. Bender: Nanobeam diffraction: Technique evaluation and strain measurement on complementary metal oxide semiconductor devices. J. Electrochem. Soc. 158 (4), H438–H446 (2011).

    Article  CAS  Google Scholar 

  8. A. Armigliato, R. Balboni, G. Carnevale, G. Pavia, D. Piccolo, S. Frabboni, A. Benedetti, and A.G. Cullis: Application of convergent beam electron diffraction to two-dimensional strain mapping in silicon devices. Appl. Phys. Lett. 82 (13), 2172–2174 (2003).

    Article  CAS  Google Scholar 

  9. Z. Lu, F. Pyczak, S. Krämer, H. Biermann, and H. Mughrabi: Fast and reliable evaluation of lattice distortions from convergent-beam electron diffraction patterns. Philos. Mag. 83 (20), 2383–2397 (2003).

    Article  CAS  Google Scholar 

  10. F. Houdellier, C. Roucau, L. Clement, J. Rouvière, and M. Casanove: Quantitative analysis of HOLZ line splitting in CBED patterns of epitaxially strained layers. Ultramicroscopy 106 (10), 951–959 (2006).

    Article  CAS  Google Scholar 

  11. K. Saitoh, Y. Yasuda, M. Hamabe, and N. Tanaka: Automated characterization of bending and expansion of a lattice of a Si substrate near a SiGe/Si interface by using split HOLZ line patterns. J. Electron Microsc. 59 (10), 367–378 (2010).

    Article  CAS  Google Scholar 

  12. L. Clément, R. Pantel, L.T. Kwakman, and J.L. Rouvière: Strain measurements by convergent-beam electron diffraction: The importance of stress relaxation in lamella preparations. Appl. Phys. Lett. 84 (5), 651–653 (2004).

    Article  Google Scholar 

  13. D. Cooper, J.P. Barnes, J.M. Hartmann, A. Béché, and J.L. Rouvière: Dark field electron holography for quantitative strain measurements with nanometer-scale spatial resolution. Appl. Phys. Lett. 95 (5), 053501–053503 (2009).

    Article  Google Scholar 

  14. A. Béché, J.L. Rouvière, J.P. Barnes, and D. Cooper: Dark field electron holography for strain measurement. Ultramicrpscopy 111, 227–238 (2011).

    Article  Google Scholar 

  15. A. Béché, J.L. Rouvière, J. Barnes, and D. Cooper: Strain measurement at the nanoscale: Comparison between convergent beam electron diffraction, nano-beam electron diffraction, high resolution imaging and dark field electron holography. Ultramicroscopy 131, 10–23 (2013).

    Article  Google Scholar 

  16. R. Vincent, T. Walsh, and M. Pozzi: Iterative phase retrieval from kinematic rocking curves in CBED patterns. Ultramicroscopy 76 (3), 125–137 (1999).

    Article  CAS  Google Scholar 

  17. E. Javon, A. Lubk, R. Cours, S. Reboh, N. Cherkashin, F. Houdellier, C. Gatel, and M.J. Hÿtch: Dynamical effects in strain measurements by dark-field electron holography. Ultramicroscopy 147, 70–85 (2014).

    Article  CAS  Google Scholar 

  18. A. Lubk, E. Javon, N. Cherkashin, S. Reboh, C. Gatel, and M.J. Hÿtch: Dynamic scattering theory for dark-field electron holography of 3D strain fields. Ultramicroscopy 136, 42–49 (2014).

    Article  CAS  Google Scholar 

  19. C. Alfonso, L. Alexandre, C. Leroux, G. Jurczak, W. Saikaly, A. Charai, and J.M. Penisson: HOLZ lines splitting on SiGe/Si relaxed samples: Analytical solutions for the kinematical equation. Ultramicroscopy 110 (4), 285–296 (2010).

    Article  CAS  Google Scholar 

  20. R. Vincent, A.R. Preston, and M.A. King: Measurement of strain in silver halide particles by convergent beam electron diffraction. Ultramicroscopy 24 (4), 409–419 (1988).

    Article  CAS  Google Scholar 

  21. R. Herring, M. Norouzpour, K. Saitoh, N. Tanaka, and T. Tanji: Determination of three-dimensional strain state in crystals using self-interfered split HOLZ lines. Ultramicroscopy 156, 37–40 (2015).

    Article  CAS  Google Scholar 

  22. R. Herring, G. Pozzi, T. Tanji, and A. Tonomura: Interferometry using convergent electron diffracted beams plus an electron biprism (CBED + EBI). Ultramicroscopy 60 (1), 153–169 (1995).

    Article  CAS  Google Scholar 

  23. R. Herring, G. Pozzi, T. Tanji, and A. Tonomura: Realization of a mixed type of interferometry using convergent-beam electron diffraction and an electron biprism. Ultramicroscopy 50 (1), 94–100 (1993).

    Article  Google Scholar 

  24. C. Gatel, F. Houdellier, and M.J. Hÿtch: Direct Measurement of Aberrations by Convergent-beam Electron Holography (CHEF) (14th European Microscopy Congress, Aachen, Germany, 2008).

    Book  Google Scholar 

  25. P.B. Hirsch, A. Howie, R. Nicholson, D. Pashley, and M.J. Whelan: Electron Microscopy of Thin Crystals (BUTTERWORTH, London, 1965).

    Google Scholar 

  26. E. Ungersboeck, S. Dhar, G. Karlowatz, S. Sverdlov, H. Kosina, and S. Selberherr: The effect of general strain on the band structure and electron mobility of silicon. IEEE Trans. Electron Devices 54 (9), 2183–2190 (2007).

    Article  CAS  Google Scholar 

  27. S. Rozeveld and J. Howe: Determination of multiple lattice parameters from convergent-beam electron diffraction patterns. Ultramicroscopy 50 (1), 41–56 (1993).

    Article  CAS  Google Scholar 

  28. L. Alexandre, K. Rousseau, C. Alfonso, W. Saikaly, L. Fares, C. Grosjean, and A. Charai: Optimized FIB silicon samples suitable for lattice parameters measurements by convergent beam electron diffraction. Micron 39 (3), 294–301 (2008).

    Article  CAS  Google Scholar 

  29. H. Lichte: Electron holography: Optimum position of the biprism in the electron microscope. Ultramicroscopy 64 (1), 79–86 (1996).

    Article  CAS  Google Scholar 

  30. R. Herring: Coherence of k-space electrons: Application to TDS electrons by DBI. Microscopy 62, 1–10 (2013).

    Article  Google Scholar 

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ACKNOWLEDGMENT

NSERC support is greatly appreciated as is the help of Arthur Blackburn, Research Scientist of UVic’s Advanced Microscopy Facility.

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Correspondence to Mana Norouzpour.

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Norouzpour, M., Herring, R. Aberration-corrected self-interference of split higher order Laue zone line for measuring the z-dependent strain profile. Journal of Materials Research 32, 996–1008 (2017). https://doi.org/10.1557/jmr.2016.518

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  • DOI: https://doi.org/10.1557/jmr.2016.518

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