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Optical evaluation of the flexural rigidity and residual stress in thin membranes: Picosecond tra nsient grating measurements of the dispersion of the lowest-order Lamb acoustic waveguide mode

Published online by Cambridge University Press:  31 January 2011

John A. Rogers  and
Gregory R. Bogart
John A. Rogers
Affiliation:
Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974
Gregory R. Bogart
Affiliation:
Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974
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Abstract

This article describes a convenient, noncontacting technique for determining the flexural rigidity and residual stress in thin membranes. The method was based on transient grating photoacoustics, also known as impulsive stimulated thermal scattering. Crossed laser pulses provided a coherent source of wavelength tunable acoustic modes in the membranes. Diffraction of a probe laser revealed the time dependence of these motions. The measured dispersion of the lowest-order Lamb mode at small acoustic wavevectors, coupled with classical plate theory, allowed the flexural rigidity and the residual stress to be determined. The technique, its accuracy, and spatial mapping capabilities were demonstrated through analysis of membranes designed for masks in next-generation lithography systems based on projected beams of electrons.

Type
Articles
Information
Journal of Materials Research , Volume 16 , Issue 1 , January 2001 , pp. 217 - 225
Copyright
Copyright © Materials Research Society 2001

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References

REFERENCES

1.1. Liddle, J.A., Berger, S.D., Biddick, C.J., Blakey, M.I., Bolan, K.J., Bowler, S.W., Brady, K., Camarda, R.M., Connelly, W.F., Crorken, A., Custy, J., Farrow, R.C., Felker, J.A., Fetter, L.A., Freeman, B., Harriott, L.R., Hopkins, L., Huggins, H.A., Knurek, C.S., Kraus, J.S., Mixon, D.A., Mkrtchyan, M.M., Novembre, A.E., Peabody, M.L., Simpson, W.M., Tarascon, R.G., Wade, H.H., Waskiewicz, W.K., Watson, G.P., Williams, J.K., and Windt, D.L., Jpn J. Appl. Phys. 1 34, 6664 (1995).Google Scholar
2.Harriott, L.R., J. Vac. Sci. Technol. B 15, 2130 (1997).CrossRefGoogle Scholar
3.Wilson, A.D., IBM J. Res. Dev. 37, 299 (1993).CrossRefGoogle Scholar
4.Smith, H.I., and Schattenburg, M.L., IBM J. Res. Dev. 37, 319 (1993).CrossRefGoogle Scholar
5.Kovacs, G.T.A., Micromachined Transducers Sourcebook (McGraw Hill, New York, 1998).Google Scholar
6.Vinci, R.P. and Vlassak, J.J., Annu. Rev. Mater. Sci. 26, 431 (1996).CrossRefGoogle Scholar
7.El Khakani, M.A. and Chaker, M., J. Vac. Sci. Technol. B 11, 2930 (1993).CrossRefGoogle Scholar
8.Windt, D.L., J. Vac. Sci. Technol. B 17, 1385 (1999).CrossRefGoogle Scholar
9.Vlassek, J.J. and Nix, W.D., J. Mater. Res. 7, 3242 (1992).CrossRefGoogle Scholar
10.Allen, M.G., Mehregany, M., Howe, R.T., and Senturia, S.D., Appl. Phys. Lett. 51, 241 (1987).CrossRefGoogle Scholar
11.Maden, M.A., Jagota, A., Mazur, S., and Farris, R.J., J. Am. Ceram. Soc. 77, 625 (1994).CrossRefGoogle Scholar
12.Tong, Q.K., Maden, M.A., Jagota, A., and Farris, R.J., J. Am. Ceram. Soc. 77, 636 (1994).CrossRefGoogle Scholar
13.Manceau, J-F., Robert, L., Bastien, F.O., Oytana, C., and Biwersi, S., J. Microelectromech. Syst. 5, 243 (1996).CrossRefGoogle Scholar
14.Schlax, M.P., Engelstad, R.L., Lovell, E.G., Liddle, J.A., and Novembre, A.E., in 1999 SPIE Symposium on Emerging Lithographic Technologies III (in press).Google Scholar
15.Rogers, J.A., Maznev, A.A., Banet, M.J., and Nelson, K.A., Annu. Rev. Mater. Sci. 30, 117 (2000).CrossRefGoogle Scholar
16.Rogers, J.A. and Nelson, K.A., J. Appl. Phys. 75, 1534 (1994).CrossRefGoogle Scholar
17.Novembre, A.E., Peabody, M.L., Blakey, M.I., Farrow, R.C., Kasica, R.J., Liddle, J.A., Saunders, T., and Tennant, D.M., Proc. SPIE 3412, 350 (1998).CrossRefGoogle Scholar
18.Rogers, J.A., Fuchs, M., Banet, M.J., Hanselman, J.B., Logan, R., and Nelson, K.A., Appl. Phys. Lett. 71, 225 (1997).CrossRefGoogle Scholar
19.Rogers, J.A., J. Acoust, Soc. Am. 104, 2807 (1998).CrossRefGoogle Scholar
20.Gostein, M., Banet, M.J., Joffe, M., Maznev, A., Sacco, R., Rogers, J.A., and Nelson, K.A., Handbook of Semiconductor Metrology (in press).Google Scholar
21.Duggal, A.R., Rogers, J.A., and Nelson, K.A., J. Appl. Phys. 72, 2823 (1992).CrossRefGoogle Scholar
22.Rogers, J.A. and Nelson, K.A., IEEE Trans. UFFC 42, 555 (1995).CrossRefGoogle Scholar
23.Desmet, C., Kawald, U., Mourad, A., Lauriks, W., and Thoen, J., J. Acoust. Soc. Am. 100, 1509 (1996).CrossRefGoogle Scholar
24.Harata, A. and Sawada, T., Jpn. J. Appl. Phys. 32, 2188 (1993).CrossRefGoogle Scholar
25.Nalamwar, A.L. and Epstein, M., J. Appl. Phys. 47, 43 (1976).CrossRefGoogle Scholar
26.Farnell, G.W. and Adler, E.L., in Physical Acoustics, Principles and Methods, edited by Mason, W.P. and Thurston, R.N. (Academic, New York, 1969), Vol. 6, pp. 109–166.Google Scholar
27.Viktorov, I.A., Rayleigh and Lamb Waves (Plenum, New York, 1976).Google Scholar
28.Rogers, J.A., Yang, Y., and Nelson, K.A., Appl. Phys. A 58, 523 (1994).CrossRefGoogle Scholar
29.Mansfield, E.H., The Bending and Stretching of Plates (Cambridge University Press, New York, 1989).CrossRefGoogle Scholar
30.Ugural, A.C., Stresses in Plates and Shells, 2nd ed. (McGraw Hill, New York, 1999).Google Scholar
31.Rogers, J.A., Dhar, L., and Nelson, K.A., Appl. Phys. Lett. 65, 312 (1994).CrossRefGoogle Scholar
32.Cocson, J.K., Hau, C.S., Lee, P.M., Poon, C.C., Zhong, A.H., Rogers, J.A., and Nelson, K.A., Polymer 36, 4069 (1995).CrossRefGoogle Scholar
33.Mehregany, M., Howe, R.T., and Senturia, S.D., J. Appl. Phys. 62, 3579 (1987).CrossRefGoogle Scholar
34.Knureck, C. (unpublished).Google Scholar
35.Simmons, G. and Wang, H., Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed. (M.I.T. Press, Cambridge, MA, 1971).Google Scholar
36.Queslel, J.E. and Mark, J.E., in Encyclopedia of Polymer Science and Engineering, 2nd ed., edited by Mark, H.F., Bikales, N.M., Overberger, C.G., Menges, G., and Kroschwitz, J.I. (Wiley, New York, 1986), Vol. 5, pp. 365–408.Google Scholar
37.Maznev, A.A., Rogers, J.A., and Nelson, K.A., Opt. Lett. 23, 1319 (1998).CrossRefGoogle Scholar