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

Published online by Cambridge University Press:  17 March 2004

K. Tillmann
Affiliation:
Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
N. Hüging
Affiliation:
Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
H. Trinkaus
Affiliation:
Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
M. Luysberg
Affiliation:
Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
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Abstract

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.

Type
Quantitative Transmission Electron Microscopy at Jülich, Germany
Copyright
© 2004 Microscopy Society of America

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References

REFERENCES

Ashby, M.F. & Brown, L.M. (1963a). Diffraction contrast from spherically symmetrical coherency strains. Phil Mag A 8, 10831103.Google Scholar
Ashby, M.F. & Brown, L.M. (1963b). On diffraction contrast from inclusions. Phil Mag A 8, 16491676.Google Scholar
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.Google Scholar
Griffith, A. (1921). The phenomena of rupture and flow in solids. Trans Roy Soc London A 221, 163198.Google Scholar
Hartmann, M. & Trinkaus, H. (2002). Evolution of gas-filled nano-cracks in crystalline solids. Phys Rev Lett 88, 055505055510.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Smith, G.H. & Burge, R.E. (1962). The analytical representation of atomic scattering amplitudes for electrons. Acta Cryst 15, 182186.Google Scholar
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.Google Scholar
Wolfram, S. (1996). The Mathematica Book. Cambridge, UK: Cambridge University Press.