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Elastic flexure of bilayered beams subject to strain differentials

Published online by Cambridge University Press:  31 January 2011

T-J. Chuang  and
S. Lee
T-J. Chuang
Affiliation:
Ceramics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899–8521
S. Lee
Affiliation:
Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043
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Abstract

The residual stresses present in a thin film and the curvature formed at its substrate during deposition have been a great concern to electrochemists and process engineers. Here a new hybrid analytical method is presented to reanalyze the flexural problem subjected to a strain differential in the general case. It was shown that the present solutions for ultrathin films agree with Stoney's equation. Moreover, single or dual neutral axes resulted, depending on materials and thickness ratios between the film and the substrate. Quantitative differences with others in the solutions of deformed curvature and residual stress are discussed in a representative case of GaAs top coat/Si substrate wafers.

Type
Articles
Information
Journal of Materials Research , Volume 15 , Issue 12 , December 2000 , pp. 2780 - 2788
Copyright
Copyright © Materials Research Society 2000

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References

REFERENCES

1.Vincenzini, P., Forum on New Materials, Vol. H, Surface Engineering (Techna Srl, Faenza, Italy, 1999).Google Scholar
2.Stoney, G.G., Proc. R. Soc. London 82, 172 (1909).Google Scholar
3.Chu, S.N.G, Macrander, A.T., Strage, K.E., and Johnston, W.D. Jr, J. Appl. Phys. 57, 249 (1985).CrossRefGoogle Scholar
4.Moyan, I.C. and Segmuller, C., J. Appl. Phys. 60(10), 2980 (1986).Google Scholar
5.Timoshenko, S., J. Opt. Soc. 11, 233 (1925).CrossRefGoogle Scholar
6.Davidenkov, N.N., Sov. Phys. Solid State 2, 2595 (1961).Google Scholar
7.Chu, S.N.G, J. Electrochem. Soc. 145, 3621 (1998).CrossRefGoogle Scholar
8.Chuang, T-J., Lee, S., and Wang, W-L. (unpublished work, National Tsing Hua University, Hsinchu, Taiwan, 1997).Google Scholar
9.Hibbeler, R.C., Mechanics of Materials Macmillian, New York, 1991), Sec. 6.4, Composite Beams, p. 281.Google Scholar
10.Timoshenko, S., Strength of Materials, Part I, Elementary Theory and Problems, 3rd ed., (D. Van Nostrand Co., Inc., Princeton, NJ, 1955), Sec. 47, p. 217.Google Scholar
11.Jou, J-H., Res. Rep on General Formula for Internal Stresses and Curvature Radius in Multilayer Structures—Consideration of Processing Condition RJ 6058 (60191) in Physics (IBM Research Division, San Jose, CA, 1988).Google Scholar
12.Tu, K.N., Mayer, J.W., and Feldman, L.C., Electronic Thin Film Science For Electrical Engineers and Materials Scientists (Macmillian, New York, 1992), Chap. 4.Google Scholar