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Stresses in Multilayered Thin Films

Published online by Cambridge University Press:  29 November 2013

Robert C. Cammarata ,
John C. Bilello ,
A. Lindsay Greer ,
Karl Sieradzki  and
Steven M. Yalisove
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Extract

Almost all thin films deposited on a substrate are in a state of stress. Fifty years ago pioneering work concerning the measurement of thin-film stresses was conducted by Brenner and Senderoff. They electroplated a metal film onto a thin metal substrate strip fixed at one end and measured the deflection of the free end of the substrate with a micrometer. Using a beam-bending analysis, they were able to calculate a residual stress from the measured deflection of the bimetallic film-substrate system. A variety of other, more sensitive methods of measuring the curvature of the surface of a film-substrate system have since been developed using, for example, capacitance measurements and interferometry techniques.

When a monochromatic x-ray beam is incident onto a curved single crystal, the diffraction condition is satisfied only for regions of the crystal where the inclination angle with respect to the incident beam exactly matches the Bragg angle. When a parallel beam plane-wave source is used, the diffracted beam from a particular set of (hkl) planes gives rise to a single narrow-contour band. If the crystal is rocked by an angle ω, the contour band will move by a certain distance D. The radius of curvature R of the crystal lattice planes is given by

where θ is the Bragg angle. Equal rocking angles produce equivalent D values for uniform curvature, or varied D values for nonuniform curvature. Using this procedure, detailed contour maps of the angular displacement field of the crystal can be mapped in two dimensions.

Type
Mechanical Behavior of Nanostructured Materials
Information
MRS Bulletin , Volume 24 , Issue 2 , February 1999 , pp. 34 - 38
Copyright
Copyright © Materials Research Society 1999

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References

1.Hoffman, R.W., in Physics of Thin Films, vol. 3, edited by Hass, G. and Thun, R.E. (Academic Press, New York, 1966) p. 211.Google Scholar
2.Thornton, J.A., Tabock, J., and Hoffman, D.W., Thin Solid Films 64 (1979) p. 111.CrossRefGoogle Scholar
3.Doerner, M.F. and Nix, W.D., CRC Critical Rev. Solid State Mater. Sci. 14 (1988) p. 225.CrossRefGoogle Scholar
4.Windischmann, H., CRC Critical Rev. Solid State Mater. Sci. 17 (1992) p. 547.CrossRefGoogle Scholar
5.Parfitt, L.J., Rek, Z.U., Yalisove, S.M., and Bilello, J.C., in Thin Films-Structure and Morphology, edited by Moss, S.C., Ila, D., Cammarata, R.C., Chason, E.H., Einstein, T.L., and Williams, E.D. (Mater. Res. Soc. Symp. Proc. 441, Pittsburgh, 1997) p. 385.Google Scholar
6.Brenner, A. and Senderoff, S., J. Res. Natl. Bur. Stand. 42 (1949) p. 105.CrossRefGoogle Scholar
7.Fingan, J.D. and Hoffman, R.W., in 8th Natl. Symp. on Vacuum Technology Transactions (Pergamon Press, New York, 1961) p. 935.Google Scholar
8.Hoffman, D.W. and Kukla, C.M., J. Vac. Sci. Technol. A 3 (1985) p. 2600.CrossRefGoogle Scholar
9.Flinn, P.A., Gardner, D.S., and Nix, W.D., IEEE Trans. Electron. Devices 34 (1987) p. 689.CrossRefGoogle Scholar
10.Nix, W.D., Metall. Trans. A 20 (1989) p. 2217.CrossRefGoogle Scholar
11.Volkert, C.A., J. Appl. Phys. 70 (1991) p. 3521.CrossRefGoogle Scholar
12.Renniger, M., Phys. Lett. 1 (1962) p. 104.CrossRefGoogle Scholar
13.Renniger, M., Z. Phys. 19 (1965) p. 20.Google Scholar
14.Bonse, U. and Hart, M., Z. Phys. 18 (1965) p. 154.CrossRefGoogle Scholar
15.Bonse, U. and Hart, M., Acta Crystallogr Sec. A 24 (1968) p. 240.Google Scholar
16.Kuo, C.L., Emamian, M., and Bilello, J.C., Rev. Sci. Instrum. 55 (1984) p. 107.CrossRefGoogle Scholar
17.Kuo, C.L., Vanier, P.E., and Bilello, J.C., J. Appl. Phys. 55 (1984) p. 375.CrossRefGoogle Scholar
18.Tao, J., Lee, L.H., and Bilello, J.C., J. Electron. Mater. 20 (1991) p. 819.CrossRefGoogle Scholar
19.Floro, J.A., Chason, E., Lee, S.R., Twesten, R.D., Hwang, R.Q., and Freund, L.B., J. Electron. Mater. 26 (1997) p. 969.CrossRefGoogle Scholar
20.Zhao, Z.B., Hershberger, J., Yalisove, S.M., and Bilello, J.C., in Thin Films: Stresses and Mechanical Properties VII, edited by Cammarata, R.C., Busso, E.P., Nastasi, M.A., and Oliver, W.C. (Mater. Res. Soc. Symp. Proc. 505, Warrendale, PA, 1998) p. 519.Google Scholar
21.Parfitt, L.J., PhD thesis, University of Michigan, 1997.Google Scholar
22.Keller, R.R., Maier, H.J., Renner, H., Mughrabi, H., and Preston, A., Philos. Mag. 74 (1996) p. 23.Google Scholar
23.Marra, W.C., Eisenberger, P., and Cho, A.Y., J. Appl. Phys. 50 (1979) p. 6947.CrossRefGoogle Scholar
24.Noyan, I.C. and Cohen, J.B., Residual Stress: Measurement by Diffraction and Interpretation (Springer-Verlag, New York, 1987).CrossRefGoogle Scholar
25.Feidenhans'l, R., Surf. Sci. Rep. 10 (1989) p. 105.CrossRefGoogle Scholar
26.Fuossa, P.H. and Brennan, S., Annu. Rev. Mater. Sci. 20 (1990) p. 365.CrossRefGoogle Scholar
27.Cui, S.F., Mai, Z.H., Wu, L.S., Wang, C.Y., and Dai, D.Y., Rev. Sci. Instrum. 62 (1991) p. 2419.CrossRefGoogle Scholar
28.Doerner, M.F. and Brennan, S., J. Appl. Phys. 63 (1988) p. 126.CrossRefGoogle Scholar
29.Toney, M.F. and Brennan, S., Phys. Rev. B 39 (1989) p. 7963.CrossRefGoogle Scholar
30.Bain, J.A., Chyung, L.J., Brennan, S., and Clemens, B.M., Phys. Rev. B 44 (1991) p. 1184.CrossRefGoogle Scholar
31.Clemens, B.M. and Bain, J.A., MRS Bulletin XVII (7) (1992) p. 46.CrossRefGoogle Scholar
32.Noyan, I.C., Huang, T.C., and York, B.R., CRC Critical Rev. Solid State Mater. Sci. 20 (1995) p. 125.CrossRefGoogle Scholar
33.Malhotra, S. G., Rek, Z.U., Yalisove, S.M., and Bilello, J.C., J. Appl. Phys. 79 (1996) p. 6872.CrossRefGoogle Scholar
34.Malhotra, S. G., Rek, Z.U., Yalisove, S.M., and Bilello, J.C., Thin Solid Films 301 (1997) p. 45.CrossRefGoogle Scholar
35.Malhotra, S. G., Rek, Z.U., Yalisove, S.M., and Bilello, J.C., Thin Solid Films 301 (1997) p. 55.CrossRefGoogle Scholar
36.Hershberger, J., Rek, Z.U., Kustas, F., Yalisove, S.M., and Bilello, J.C. in Applications of Synchrotron Radiation Techniques to Materials Science, edited by Mini, S.M., Stock, S.R., Perry, D.L., and Terminello, L.J. (Mater. Res. Soc. Symp. Proc. 524, Warrendale, PA, 1998) p. 109.Google Scholar
37.Whitacre, J.F., Rek, Z.U., Yalisove, S.M., and Bilello, J.C., in Applications of Synchrotron Radiation Techniques to Materials Science, edited by Mini, S.M., Stock, S.R., Perry, D.L., and Terminello, L.J. (Mater. Res. Soc. Symp. Proc. 524, Warrendale, PA, 1998) p. 115.Google Scholar
38.Johnson, W.C., Metall. Trans. A 18 (1987) p. 1093.CrossRefGoogle Scholar
39.Johnson, W.C. and Voorhees, P.W., Metall. Trans. A 18 (1987) p. 1213.CrossRefGoogle Scholar
40.Johnson, W.C., in Multilayers: Synthesis, Properties, and Non-Electronic Applications, edited by Barbee, T.W. Jr., Spaepen, F., and Greer, L. (Mater. Res. Soc. Symp. Proc. 103, Pittsburgh, 1988) p. 61.Google Scholar
41.Gibbs, J.W., The Scientific Papers of J. Willard Gibbs, vol. 1 (Longmans-Green, London, 1906) p. 55.Google Scholar
42.Shuttleworth, R., Proc. Phys. Soc. London, Sect. A 63 (1950) p. 445.Google Scholar
43.Herring, C., in The Physics of Powder Metallurgy, edited by Kingston, W.E. (McGraw-Hill, New York, 1951) p. 143.Google Scholar
44.Cahn, J.W., Acta Metall. 28 (1980) p. 1333.CrossRefGoogle Scholar
45.Cammarata, R.C., Prog. Surf. Sci. 46 (1994) p. 1.CrossRefGoogle Scholar
46.Brooks, H., in Metal Interfaces (American Society for Metals, Metals Park, OH, 1963) p. 20.Google Scholar
47.Cahn, J.W. and Larché, F., Acta. Metall. 30 (1982) p. 51.CrossRefGoogle Scholar
48.Cammarata, R.C. and Sieradzki, K., Phys. Rev. Lett. 62 (1989) p. 2005.CrossRefGoogle Scholar
49.Kosevich, Yu.A. and Kosevich, A.M., Solid State Commun. 70 (1989) p. 541.CrossRefGoogle Scholar
50.Streitz, F.H., Cammarata, R.C., and Sieradzki, K., Phys. Rev. B 49 (1994) p. 10707.CrossRefGoogle Scholar
51.Shull, A.L. and Spaepen, F., J. Appl. Phys. 80 (1996) p. 6243.CrossRefGoogle Scholar
52.Barnett, S.A. and Shinn, M., Annu. Rev. Mater. Sci. 24 (1994) p. 481.CrossRefGoogle Scholar
53.Cammarata, R.C., Thin Solid Films 248 (1994) p. 82.CrossRefGoogle Scholar
54.Was, G.S. and Foecke, T., Thin Solid Films 286 (1996) p. 1.CrossRefGoogle Scholar
55.Cammarata, R.C., in Handbook of Thin Film Process Technology, edited by Glocker, D. and Shah, S.I. (Institute of Physics, Bristol, 1998) p. F2.Google Scholar
56.Wonnell, S.K., Delaye, J.M., Bibolé, M., and Limoge, Y., J. Appl. Phys. 72 (1992) p. 5195.CrossRefGoogle Scholar
57.Prokes, S.M., Glembocki, O.J., and Godbey, D.J., Appl. Phys. Lett. 60 (1992) p. 1087.CrossRefGoogle Scholar
58.Prokes, S.M. and Wang, K.L., Appl. Phys. Lett. 56 (1990) p. 2628.CrossRefGoogle Scholar
59.Stephenson, G.B., Acta Metall. 36 (1988) p. 2663.CrossRefGoogle Scholar
60.Darken, L.S., Trans. Metall. Soc. AIME 175 (1948) p. 184.Google Scholar
61.Greer, A.L., Defect Diff. Forum 129–130 (1996) p. 163.CrossRefGoogle Scholar
62.Karpe, N., Bøttiger, J., Krog, J.P., Conyers, J.S., Greer, A.L., and Somekh, R.E., Philos. Mag. A75 (1997) p. 461.CrossRefGoogle Scholar
63.Conyers, J.S., Hall, M.J., Greer, A.L., and Somekh, R.E., J. Magn. Magn. Mater. 156 (1996) p. 419.CrossRefGoogle Scholar