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X-Ray Diffraction Determination of Stresses in Thin Films

Published online by Cambridge University Press:  22 February 2011

T. Vreeland Jr.
Affiliation:
California Institute of Technology, Pasadena, CA 91125
A. Dommann
Affiliation:
California Institute of Technology, Pasadena, CA 91125
C.-J. Tsai
Affiliation:
California Institute of Technology, Pasadena, CA 91125
M.-A. Nicolet
Affiliation:
California Institute of Technology, Pasadena, CA 91125
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Abstract

This paper presents the methodology employed in the determination of the stress tensor for thin crystalline films using x-ray rocking curves. Use of the same equipment for the determination of the average stress in poly- or non-crystalline thin films attached to a crystalline substrate is also discussed. In this case the lattice curvature of the substrate is determined by measurement of the shift In the Bragg peak with lateral position in the substrate.

Strains in single crystal layers may be measured using Bragg diffraction from the layers and from the substrate or a reference crystal, with the highest strain sensitivity of any known technique. The difference in Bragg angles for a strained and an unstrained crystal is related to the change in d spacing of the Bragg planes, and the elastic strain is related to'this angular difference. The separation of two peaks on an x-ray rocking curve is generally not equal to the difference in Bragg angles of two diffracting crystals, so diffractometer measurements must be carefully Interpreted in order to obtain x-ray strains in crystalline films (x-ray strains are strains relative to the reference crystal). The unstrained d spacings of the film and the d spacings of the reference crystal must be known to obtain the elastic strains in the film, from which the stress tensor is determined.

Type
Research Article
Copyright
Copyright © Materials Research Society 1989

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References

1. Bonse, V. and Hartmann, I., Z. Kristallogr. 156, 256 (1981).Google Scholar
2. DuNond, J. W. M., Phys. Rev. 52, 812 (1973).Google Scholar
3. Speriosu, V. S., J. Appl. Phys. 52, 6094 (1981).10.1063/1.328549CrossRefGoogle Scholar
4. Zachariasen, W. H., Theory of X-ray Diffraction in Crystals, (Wiley, New York, 1945).Google Scholar
5. Speriosu, V. S. and Vreeland, T. Jr., J. Appl. Phys. 56, 1591 (1984)10.1063/1.334169Google Scholar
6. Vreeland, Thad Jr., J. Mater. Res. 1, 712 (1986).10.1557/JMR.1986.0712Google Scholar
7. Wie, C. R., Tombrello, T., and Vreeland, T. Jr., J. Appl. Phys. 59, 3742 (1986).10.1063/1.336759Google Scholar
8. Fewster, P. F. and Curling, C. J., J. Appl. Phys. 62, 4154 (1987). An incorrect boundary condition was used in the calculations which introduced a small error in their results. The correct boundary condition is given in [7].10.1063/1.339133CrossRefGoogle Scholar
9. Wie, C. R., Choi, Y., Chen, J. F., Vreeland, T. Jr. and Tsai, C.-J., (unpublished) to be presented at the Spring MRS meeting, April 1989.Google Scholar
10. Vreeland, T., Jr. and Paine, B. M., J. Vac. Sci. Technol., A4, 3151 (1986).Google Scholar
11. Chu, X. and Tanner, B. K., Appl. Phys. Lett., 49, 1773 (1986).10.1063/1.97240CrossRefGoogle Scholar
12. Wie, C. R., to appear in J. Appl. Phys.Google Scholar
13. Hearmon, R. F. S., Applied Anisotronic Elasticity, (Oxford University Press, 1961).Google Scholar
14. Unpublished results, Vreeland, T. Jr., Schwarz, R. B., and Samwer, K. H..Google Scholar