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.

中文翻译：

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MEMS双层结构的热致曲率和层间剪应力分析

微机电系统多层膜结构在热耦合条件下的层间应力和分层破坏机理是现代微光电子学的基础研究课题。为了解决经典板膜模型在分析层间应力方面的不足，该工作提出了一个更合理的梁膜模型，推导了两层系统的热致曲率和层间切应力方程，并分析了加热功率的影响，膜/基层厚度比和松弛时间。另外，将Comsol Multiphysics建立的有限元模型与经典板膜模型和梁膜模型进行了比较。数值结果表明，传统聚合物和杂化结构的曲率随功率的增加而增大，束膜模型的值大于板膜模型的值。混合结构的曲率随着膜厚度的增加而增加。当厚度比为0.5时，传统聚合物结构的曲率达到最大值。有限元计算结果与梁膜模型吻合，表明该模型具有较高的精度。当胶片松弛时间增加到\（10 ^ {-3} \，\ hbox {s} \）大小，两个结构的热失配应力和曲率均显着增加。剪切力随着距界面中心的距离呈指数增长，并在界面末端达到最大值。这些结果可为光开关的安全设计提供参考。