Articles | Volume 15, issue 2
https://doi.org/10.5194/jsss-15-167-2026
https://doi.org/10.5194/jsss-15-167-2026
Regular research article
 | 
02 Sep 2026
Regular research article |  | 02 Sep 2026

Modeling and extraction of residual stresses in some MEMS multilayer systems

Li Long, Frank Long, Bernhard Schwartz, Geert Brokmann, and Thomas Ortlepp

Cited articles

Abadias, G., Chason, E., Keckes, J., Sebastiani, M., Thompson, G. B., Barthel, E., Doll, G. L., Murray, C. E., Stoessel, C. H., and Martinu, L.: Review Article: Stress in thin films and coatings: Current status, challenges, and prospects, J. Vac. Sci. Technol. A., 36, 020801, https://doi.org/10.1116/1.5011790, 2018. a
Chason, E., Shin, J. W., Heame, S. J., and Freund, L. B.: Kinetic model for dependence of thin film stress on growth rate, temperature, and microstructure, J. Appl. Phys., 111, 083520, https://doi.org/10.1063/1.4704683, 2012. a
Chason, E., Engwall, A. M., Rao, Z., and Nishimura, T.: Kinetic model for thin film stress including the effect of grain growth, J. Appl. Phys., 123, 185305, https://doi.org/10.1063/1.5030740, 2018. a, b, c
Chen, K. S., Zhang, X., and Lin, S. Y.: Intrinsic stress generation and relaxation of plasma-enhanced chemical vapor deposited oxide during deposition and subsequent thermal cycling, Thin Solid Films, 434, 190–202, https://doi.org/10.1016/S0040-6090(03)00462-0, 2003. a
Cowan, G.: Statistical Data Analysis, Oxford University Press, ISBN 0-19850156-0, 1998. a
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Short summary
Thin-film multilayers deposited on a wafer induce bending due to residual and thermal stresses that strongly depend on process conditions. The resulting curvature can be measured optically. We present a closed-form analytical model that relates the measured curvature to the residual stresses in individual layers. Using a small set of curvature measurements, layer-resolved residual stresses can be extracted without resource-intensive finite-element model simulations.
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