A Technique for Deducing In-Plane Modulus and Coefficient of Thermal Expansion of a Supported Thin Film

[+] Author and Article Information
Martin Y. M. Chiang, Chwan K. Chiang, Wen-li Wu

Polymers Division, NIST, Gaithersburg, MD 20899

J. Eng. Mater. Technol 124(2), 274-277 (Mar 26, 2002) (4 pages) doi:10.1115/1.1448522 History: Received April 25, 2001; Revised November 26, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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Sinha,  A. K., Levinstein,  H. J., and Smith,  T. E., 1978, “Thermal stresses and cracking resistance of dielectric films (SiN, Si3N4, and SiO2) on Si substrates,” J. Appl. Phys., 49, No. 4, pp. 2423–2426.
Takeshita,  S., Taki,  S., and Matsushige,  K., 1990, “Application of Two Dimensional Ultrasonic Spectroscopy to Nondestructive Inspection,” Mater. Eval., 48, No. 12, pp. 1473–1477.
Asada,  H., Kishi,  Y., and Hirose,  Y., 1993, “Measurement of Young’s moduli of TiC-coated film by X-ray method,” Thin Solid Films, 236, pp. 247–252.
Rouzaud,  A., Barbier,  E., Ernoult,  J., and Quesnel,  E., 1995, “A method for elastic modulus measurements of magnetron sputtered thin films dedicated to mechanical applications,” Thin Solid Films, 270, pp. 270–274.
Wu,  W. L., and Liou,  H. C., 1998, “Study of ultra-thin hydrogen silsesquioxane films using x-ray reflectivity,” Thin Solid Films, 312, pp. 73–77.
Retajczyk,  T. F., and Sinha,  A. K., 1980, “Elastic stiffness and thermal expansion coefficients of various refractory silicides and silicon nitride films,” Thin Solid Films, 70, pp. 241–247.
Stoney,  G. G., 1909, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. London, Ser. A, 82, pp. 172–175.
Pottiger,  M. T., Coburn,  J. C., and Edman,  J. R., 1994, “The effect of orientation on thermal expansion behavior in polyimide films,” J. Polym. Sci., Part B: Polym. Phys., 32, pp. 825–837.
Zhao,  J. H., Ryan,  T., and Ho,  P. S., 1999, “Measurements of elastic modulus, Poisson ratio, and coefficient of thermal expansion of on-wafer submicron films,” J. Appl. Phys., 85, pp. 6421–6424.
de Lima,  M. M., Lacerda,  R. G., Vilcarromero,  J., and Marques,  F. C., 1999, “Coefficient of thermal expansion and elastic modulus of thin films,” J. Appl. Phys., 86, No. 9, pp. 4936–4942.
Kim,  J. S., Paik,  K. W., and Oh,  S. H., 1999, “The multiplayer-modified Stony’s formular for laminated polymer composites on a silicon substrate,” J. Appl. Phys., 86, No. 10, pp. 5474–5479.
Freund, L. B., 1996, “The mechanics of free-standing strained film/compliant substrate systems,” MRS Symposium Proceedings, Vol. 436, pp. 393–404.
Roark, R. J., and Young, W. C., 1975, Formulas for Stress and Strain, 5th edition, McGraw-Hill, New York.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in Fortran, Cambridge University Press.
ABAQUS version 5.8, 1999, Hibbit, Karlsson and Sorensen, Providence, RI. Certain commercial code is identified in this paper in order to specify adequately the analysis procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology (NIST) nor does it imply that they are necessarily the best available for the purpose.


Grahic Jump Location
Ranges of the relative uncertainty propagation factor for CTE (Mα) and the elastic modulus (Me) for certain combinations of film/substrate
Grahic Jump Location
The dependence of the K*/K on the ratios of the film to substrate stiffness and of the film to substrate thickness
Grahic Jump Location
The variation of the normalized radius of curvature as function of the film deformability and film/substrate stiffness ratio. The lines represent the curvature based on Eq. (1) while the symbols are the results of FEA.
Grahic Jump Location
A schematic of the cross-sectional bending of a bimaterial circular plate due to change in temperature




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