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Finite Element Calculations of Strains in Passivated Metal Lines

Published online by Cambridge University Press:  10 February 2011

I. Eppler
Affiliation:
Institut fü Festkörperforschung, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
H. Schroeder
Affiliation:
Institut fü Festkörperforschung, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
W. Schilling
Affiliation:
Institut fü Festkörperforschung, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
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Abstract

Passivated metal lines, commonly used in integrated circuits, show thermally induced strains and stresses due to the mismatch of the thermal expansion coefficients of the lines and their surroundings. These strains depend on the geometry and the elastic constants of both, line and surroundings (i.e. substrate and passivation) and - for the case of an array of parallel lines - on the repetition distance of the lines. For a given set of these parameters the strains and stresses can be obtained from finite element calculations using a model with plane strain conditions.

In order to obtain the dependences of the strains from these parameters systematic finite element calculations have been made for an infinite array of parallel lines with variations of the geometries and the elastic constants.

Since only the volume mean values of the metal strains can be measured easily (X-ray, wafer curvature method (metal stress)), the dependences of these mean values on the different parameters are presented.

Type
Research Article
Copyright
Copyright © Materials Research Society 1997

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References

REFERENCES

[1] Mura, T., Micromechanics of defects in solids (Martinus Nijhoff Publishers 1982)Google Scholar
[2] Korhonen, M. A., Black, R. D., and Li, Che-Yu, J. Appl. Phys. 69 (3), 1748 (1991)Google Scholar
[3] Greenebaum, B., Sauter, A. I., Flinn, P. A. and Nix, W. D., Appl. Phys. Lett. 58, p. 1845 (1987)Google Scholar
[4] Sauter, A. I. and Nix, W. D. in “Thin Films: Stresses and Mechanical Properties II” edited by Doerner, M. F., Oliver, W. C., Pharr, G. M. and Brotzen, F. R. (Mater. Res. Soc. Proc. 188, San Francisco, CA, 1990) pp. 1520 Google Scholar
[5] Jones, R. E. and Basehore, M. L., Appl. Phys. Lett. 50, p. 725 (1987)Google Scholar
[6] Burges, U., Eppler, I., Schilling, W., Schroeder, H., Trinkaus, H., Proc of Third Int. Work shop on “Stress-induced Phenomena in Metallization” Stanford (USA), June 1995, AIP Conf. Proc., in pressGoogle Scholar
[7] Beckers, D., Schroeder, H., Eppler, I., Schilling, W. in “Thin Films: Stresses and Mechanical Properties VI” edited by Gerberich, W. W., Gao, H., Sundgren, J. E. and Baker, S. P. (Mater. Res. Soc. Proc. 436, San Francisco, CA, 1996)Google Scholar
[8] Schrem, E., PERMAS Handbook for Linear Static Analysis, Intes Publications UM 404, REV B, Stuttgart 1988 Google Scholar