Thermo-induced curvature and interlayer shear stress analysis of MEMS double-layer structure

  • Long ZhangEmail author
  • Xiaomin Zhang
  • Jiyun Song
  • Hengwei Zheng
Original Article


The interlayer stress and delamination failure mechanism of the multilayer membrane structure of microelectromechanical systems under thermal coupling condition are basic research topics in modern micro-optoelectronics. To address the deficiency of the classical plate membrane model in analyzing interlayer stress, this work proposed a more reasonable beam membrane model, deduced the thermo-induced curvature and interlayer shear stress equation of the two-layer system and analyzed the influences of heating power, film/base thickness ratio, and relaxation time. In addition, the finite element model established by Comsol Multiphysics is compared with the classical plate membrane model and beam membrane model. Numerical results showed that the curvatures of the traditional polymer and hybrid structures increased with power, and that the value of the beam membrane model was greater than that of the plate membrane model. The curvature of the hybrid structure increased with film thickness. When the thickness ratio was 0.5, the curvature of the traditional polymer structure reached its maximum value. The finite element results are consistent with the beam membrane model, indicating that the beam membrane model has higher accuracy. When film relaxation time increased to the order of \(10^{-3}\,\hbox {s}\) magnitude, the thermal mismatch stress and curvature of the two structures increased considerably. Shear force increased exponentially with distance from the center of the interface and reached its maximum value at the interface end. These results can provide references for the safety design of optical switches.


Thermal optical switch Generalized thermoelasticity Multilayer structure Thermo-induced curvature Interlayer shear force 



This work was supported by the National Natural Science Foundation of China (No. 11602042), Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2018jcyjAX0514) and Research Foundation of Chongqing University of Science and Technology (ck2017zkyb020).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Long Zhang
    • 1
    • 2
    • 3
    Email author
  • Xiaomin Zhang
    • 2
  • Jiyun Song
    • 2
  • Hengwei Zheng
    • 1
  1. 1.Department of Theoretical and Applied MechanicsChongqing University of Science and TechnologyChongqingPeople’s Republic of China
  2. 2.Department of Engineering MechanicsChongqing UniversityChongqingPeople’s Republic of China
  3. 3.School of Electronic Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

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