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Thermal strains in passivated aluminum and copper conductor lines

Published online by Cambridge University Press:  09 March 2011

Hongqing Zhang ,
G. Slade Cargill III  and
Antoinette M. Maniatty
Hongqing Zhang
Affiliation:
Department of Materials Science & Engineering, Lehigh University, Bethlehem, Pennsylvania 18105
G. Slade Cargill III*
Affiliation:
Department of Materials Science & Engineering, Lehigh University, Bethlehem, Pennsylvania 18105
Antoinette M. Maniatty
Affiliation:
Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180
*
a)Address all correspondence to this author. e-mail: gsc3@lehigh.edu
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Abstract

Line width and line thickness thermal strain components in passivated Al and Cu lines were observed to relax much more than the line length strain component. Although the width-to-thickness ratios were large, 3.5 and 4.4 for Al and Cu lines, respectively, the behaviors of the thermal stresses were far from the equibiaxial. Observed changes in deviatoric strains between room temperature and 190 °C for Al and 300 °C for Cu were consistent with a model in which the changes in line width and line thickness strains were simply related to changes in line length strains by the uniaxial Poisson’s ratio. Changes in line length strains were determined by the differences in metal and substrate thermal expansion coefficients and the magnitudes of temperature changes through retained elastic strain coefficients for Al of 30% for heating and for Cu of 60% for heating and 80% for cooling, with the balance accommodated by relaxation.

Keywords

Stress/strain relationshipThermal stressesx-Ray diffraction
Type
Articles
Information
Journal of Materials Research , Volume 26 , Issue 5 , 14 March 2011 , pp. 633 - 639
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Yeo, I.-S., Ho, P.S., and Anderson, S.G.H.: Characteristics of thermal-stresses in Al(Cu) fine lines: I. Unpassivated line structures. J. Appl. Phys. 78, 945 (1995).CrossRefGoogle Scholar
2.Flinn, P.A. and Chiang, C.: X-ray-diffraction determination of the effect of various passivations on stress in metal-films and patterned lines. J. Appl. Phys. 67, 2927 (1990).CrossRefGoogle Scholar
3.Besser, P.R., Brennan, S., and Bravman, J.C.: An x-ray method for direct determination of the strain state and strain relaxation in micron-scale passivated metallization lines during thermal cycling. J. Mater. Res. 9, 13 (1994).CrossRefGoogle Scholar
4.Besser, P.R., Marieb, T.N., Lee, J., Flinn, P.A., and Bravman, J.C.: Measurement and interpretation of strain relaxation in passivated Al-0.5% Cu lines. J. Mater. Res. 11, 184 (1996).CrossRefGoogle Scholar
5.Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. London, Ser. A 241, 376 (1957).Google Scholar
6.Korhonen, M.A., Black, R.D., and Li, C.-Y.: Stress-relaxation of passivated aluminum line metallizations on silicon substrates. J. Appl. Phys. 69, 1748 (1991).CrossRefGoogle Scholar
7.Sauter, A.I. and Nix, W.D.: Thermal-stresses in aluminum lines bonded to substrates. IEEE Trans. Compon. Hybrids and Manuf. Technol. 15, 594 (1992).CrossRefGoogle Scholar
8.Shen, Y.L.: On the elastic assumption for copper lines in interconnect stress modeling. IEEE Trans. Device Mater. Reliab. 8, 600 (2008).CrossRefGoogle Scholar
9.Wang, P.C., Cargill, G.S. III, Noyan, I.C., Liniger, E.G., Hu, C.-K., and Lee, K.Y.: Thermal and electromigration strain distributions in 10 μm-wide Al conductor lines measured by x-ray microdiffraction, in Materials Reliability in Microelectronics VII, edited by Clement, J.J., Keller, R.R., Krisch, K.S., Sanchez, J.E. Jr., and Suo, Z. (Mater. Res. Soc. Symp. Proc. 473,Pittsburgh, PA, 1997), p. 273.Google Scholar
10.Wang, P.C., Cargill, G.S. III, Noyan, I.C., and Hu, C.-K.: Electromigration-induced stress in aluminum conductor lines measured by x-ray microdiffraction. Appl. Phys. Lett. 72, 1296 (1998).CrossRefGoogle Scholar
11.Tamura, N., Celestre, R.S., MacDowell, A.A., Padmore, H.A., Spolenak, R., Valek, B.C., Chang, N.M., Manceau, A., and Patel, J.R.: Submicron x-ray diffraction and its applications to problems in materials and environmental science. Rev. Sci. Instrum. 73, 1369 (2002).CrossRefGoogle Scholar
12.Zhang, H., Cargill, G.S. III, Ge, Y., Maniatty, A.M., and Liu, W.: Strain evolution in Al conductor lines during electromigration. J. Appl. Phys. 104, 123533 (2008).CrossRefGoogle Scholar
13.Vinci, R.P., Zielinski, E.M., and Bravman, J.C.: Thermal stresses in passivated copper interconnects determined by x-ray analysis and finite element modeling, in Materials Reliability in Microelectronics IV, edited by Børgesen, P., Coburn, J.C., Sanchez, J.E. Jr., Rodbell, K.P., and Filter, W.F. (Mater. Res. Soc. Symp. Proc. 338,Pittsburgh, PA, 1994), p. 289.Google Scholar
14.Vinci, R.P., Marib, T.N., and Bravman, J.C.: Non-destructive evaluation of strains and voiding in passivated copper metallizations, in Thin Films: Stresses and Mechanical Properties IV, edited by Townsend, P.H., Weihs, T.P., Sanchez, J.E. Jr., and Børgesen, P. (Mater. Res. Soc. Symp. Proc. 308,Pittsburgh, PA, 1993), p. 297.Google Scholar
15.Steigerwald, J.M., Murarka, S.P., and Gutmann, R.J.: Chemical Mechanical Planarization of Microelectronic Materials (Wiley-Interscience, 1997).CrossRefGoogle Scholar
16.Ice, G.E. and Larson, B.C.: 3D x-ray crystal microscope. Adv. Eng. Mater. 2, 643 (2000).3.0.CO;2-U>CrossRefGoogle Scholar
17.Chung, J.-S. and Ice, G.E.: Automated indexing for texture and strain measurement with broad-bandpass x-ray microbeams. J. Appl. Phys. 86, 5249 (1999).CrossRefGoogle Scholar
18.Tamura, N., MacDowell, A.A., Celestre, R.S., Padmore, H.A., Valek, B., Bravman, J.C., Spolenak, R., Brown, W.L., Marieb, T., Fujimoto, H., Batterman, B.W., and Patel, J.R.: High spatial resolution grain orientation and strain mapping in thin films using polychromatic submicron x-ray diffraction. Appl. Phys. Lett. 80, 3724 (2002).CrossRefGoogle Scholar
19.Zhang, H.: Thermal and electromigration induced strain and microstructure evolution in metal conductor lines. Ph.D. Thesis, Lehigh University, Pub. No. 3358117 (2009).Google Scholar