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Modeling of exact viscoelastic stresses in bilayer systems due to thermal and/or lattice mismatch: Maxwell model

Published online by Cambridge University Press:  31 May 2011

Hsiang-Chun Hsueh ,
Donyau Chiang  and
Sanboh Lee
Hsiang-Chun Hsueh
Affiliation:
Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300, Taiwan
Donyau Chiang
Affiliation:
Instrument Technology Research Center, National Applied Research Laboratories, Hsinchu 30076, Taiwan
Sanboh Lee*
Affiliation:
Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300, Taiwan
*
a)Address all correspondence to this author. e-mail: sblee@mx.nthu.edu.tw
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Abstract

The exact solution of viscoelastic stresses in the bilayer system due to thermal and/or lattice mismatch is derived if both layers are Maxwell materials. When the thickness of one layer is much smaller than that of the other layer, the viscoelastic stresses in the bilayer system can be reduced to that of the thin film/substrate system. The relative film thickness and the position in the thin film/substrate systems are included in this solution. The average film stress decreases with increasing the normalized time and finally approaches zero in a long time. As the relative film thickness is equal to or less than 0.001, the average film stresses of the zeroth-order approximation, first-order approximation, and Hsueh and Lee model [J. Appl. Phys.91, 2760 (2002)] are close to that of exact solution. Nevertheless, as the relative film thickness is larger than 0.001, the accuracies of the zeroth-order approximation, first-order approximation, and Hsueh and Lee model are dependent on the normalized time and relative film thickness.

Keywords

SimulationThin filmThermal stresses
Type
Articles
Information
Journal of Materials Research , Volume 26 , Issue 11 , 14 June 2011 , pp. 1392 - 1398
Copyright
Copyright © Materials Research Society 2011

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