Skip to main content

Quantitative Transmission Electron Microscopy Analysis of the Pressure of Helium-Filled Cracks in Implanted Silicon

  • K. Tillmann (a1), N. Hüging (a1), H. Trinkaus (a1) and M. Luysberg (a1)

The pressure of crack-shaped cavities formed in silicon upon implantation with helium and subsequent annealing is quantitatively determined from the measurement of diffraction contrast features visible in transmission electron micrographs taken under well-defined dynamical two-beam conditions. For this purpose, simulated images, based on the elastic displacements associated with a Griffith crack, are matched to experimental micrographs, thus yielding unambiguous quantitative data on the ratio p/μ of the cavity pressure to the silicon matrix shear modulus. Experimental results demonstrate cavity radii of some 10 nm and p/μ values up to 0.22, which may be regarded as sufficiently high for the emission of dislocation loops from the cracks.

Corresponding author
Corresponding author. E-mail:
Hide All


Ashby, M.F. & Brown, L.M. (1963a). Diffraction contrast from spherically symmetrical coherency strains. Phil Mag A 8, 10831103.
Ashby, M.F. & Brown, L.M. (1963b). On diffraction contrast from inclusions. Phil Mag A 8, 16491676.
Fichtner, P.F.P., Kaschny, J.R., Behar, M., Yankow, R.A., Mücklich, A., & Skorupa, W. (1999). Nucleation and growth of platelet bubble structures in helium implanted silicon. Nucl Inst and Meth 148, 329333.
Griffith, A. (1921). The phenomena of rupture and flow in solids. Trans Roy Soc London A 221, 163198.
Hartmann, M. & Trinkaus, H. (2002). Evolution of gas-filled nano-cracks in crystalline solids. Phys Rev Lett 88, 055505055510.
Hashimoto, H., Howie, A., & Whelan, M.J. (1962). Anomalous electron absorption effects in metal foils: Theory and comparison with experiment. Proc Roy Soc A 269, 80103.
Hellwege, K.-H. (1982). Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. 17. Berlin: Springer.
Hirsch, P.B., Howie, A., Nicholson, R.B., Pashley, D.W., & Whelan, M.J. (1965). Electron Microscopy of Thin Crystals. London: Butterworth.
Hirsch, P.B., Howie, A., & Whelan, M.J. (1960). A kinematical theory of diffraction contrast of electron transmission microscope images of dislocations and other defects. Phil Trans A 252, 499528.
Hirth, J.P. & Lothe, J. (1968). Theory of Dislocations. New York: Pergamon Press.
Holländer, B., Lenk, S., Mantl, S., Trinkaus, H., Kirch, D., Luysberg, M., Hackbarth, T., Herzog, H.J., & Fichtner, P.F.P. (2001). Strain relaxation of pseudomorphic SiGe/Si(100) heterostructures after hydrogen or helium ion implantation for virtual substrate fabrication. Nucl Inst and Meth in Phys Res B 175–177, 357367.
Howe, J.M. (1997). Interfaces in Materials. New York: John Wiley & Sons, Inc.
Howie, A. & Whelan, M.J. (1960). Diffraction contrast of electron microscope images of crystal lattice defects. In Proc Eur Reg Conf on Electron Microscopy, De Nederlandse Vereniging voor Electronenmicroscopie, pp. 181183. Delft, The Netherlands.
Howie, A. & Whelan, M.J. (1961). Diffraction contrast of electron microscope images of crystal lattice defects. II. The development of a dynamical theory. Proc Roy Soc London A 263, 217237.
Hüging, N. (2002). Untersuchung elastischer Verzerrungsfelder und struktureller Defekte in mit Heliumionen implantiertem silizium. Diploma thesis. Research Centre Zulich, Ltd., 1110.
Janssens, K.G.G., van der Biest, O., van Hellemont, J., & Maes, H.E. (1997). Assessment of the quantitative characterization of localized strain using electron diffraction contrast imaging. Ultramicroscopy 69, 151167.
Kumikov, V.K. & Khokonov, K.B. (1983). On the measurement of surface free energy and surface tension of solid metals. J Appl Phys 54, 13461350.
Luysberg, M., Kirch, D., Trinkaus, H., Holländer, B., Lenk, S., Mantl, S., Herzog, H.J., Hackbarth, T., & Fichtner, P.F.P. (2002). Effect of helium ion implantation and annealing on the relaxation behavior of pseudomorphic SiGe buffer layers on Si(100) substrates. J Appl Phys 69, 42904295.
Mura, T. (1982). Micromechanics of Defects in Solids. The Hague, The Netherlands: Martinus Nijhoff Publishers.
Oliviero, E., Beaufort, M.F., & Bardot, J.F. (2001). Dislocations induced by bubble formation in high energy He implantation in silicon. J Appl Phys 89, 53325338.
Smith, G.H. & Burge, R.E. (1962). The analytical representation of atomic scattering amplitudes for electrons. Acta Cryst 15, 182186.
Trinkaus, H., Holländer, B., Rongen, S., Mantl, S., Herzog, H.J., Kuchenbecker, J., & Hackbarth, T. (2000). Strain relaxation mechanisms for hydrogen-implanted SiGe/Si(100) heterostructures. Appl Phys Lett 76, 35523553.
Wolfram, S. (1996). The Mathematica Book. Cambridge, UK: Cambridge University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Microscopy and Microanalysis
  • ISSN: 1431-9276
  • EISSN: 1435-8115
  • URL: /core/journals/microscopy-and-microanalysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 4
Total number of PDF views: 5 *
Loading metrics...

Abstract views

Total abstract views: 51 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th November 2017. This data will be updated every 24 hours.