梯度残余应力下多层膜结构的弹性变形

中国机械工程 ›› 2014, Vol. 25 ›› Issue (14): 1867-1871.

梯度残余应力下多层膜结构的弹性变形

董健;蒋恒

浙江工业大学特种装备制造与先进加工技术浙江省重点实验室,杭州,310014

出版日期:2014-07-25 发布日期:2014-08-25
基金资助:
浙江省自然科学基金资助项目(Y1100707)

Gradient Residual Stress Induced Elastic Deformation of Multilayer Structures

Dong Jian;Jiang Heng

Zhejiang Provincial Key Laboratory of Special Purpose Equipment and Advanced Manufacturing Technology, Zhejiang University of Technology,Hangzhou,310014

Online:2014-07-25 Published:2014-08-25
Supported by:
Zhejiang Provincial Natural Science Foundation of China（No. Y1100707）

摘要/Abstract

摘要：

提出了一类Stoney延伸公式来表征多层MEMS膜结构的曲率和其各层膜内沿厚度任意分布的残余应力之间的关系。推导出三层结构下的Stoney延伸公式,并利用它解决了残余应力沿厚度方向梯度分布的三层悬臂梁结构的变形问题。制造了一个Si3N4/p+Si/Si三层悬臂梁微结构,并测得其弯曲曲率,在p+硅层残余应力梯度分布和均匀分布两种情况下分别对该结构进行了仿真和解析计算。结果表明：所提出的Stoney延伸公式能比较准确地表征多层膜结构的弹性变形和其各层膜内任意分布的残余应力之间的关系；用平均残余应力代替实际的梯度残余应力，会对结构变形的预测带来更大的误差。

关键词: Stoney延伸公式, 微机电系统, 梯度残余应力, 多层膜结构, 弹性变形, 三层悬臂梁

Abstract:

A kind of Stoney extended formula was proposed to characterize the relation among the deformation of the multilayer structures and the gradient residual stress in each layers. The Stoney extended formula of trilayer structures was deduced herein, which was used to arrive at the solutions for a trilayer cantilever with gradient residual stress distributions throughout the thickness. A Si3N4/p+ Si/Si multilayer cantilever structure was fabricated and the measurement of its bending curvature was also conducted. Analytical calculation and finite element simulation were carried out considering a p+Si layer with gradient residual stress and mean residual stress,respectively. The presented results herein show that this approach is a precise way to characterize the relation between the elastic deformation of multilayer MEMS structures and arbitrary residual stress distributions throughout the thickness in each layer. The results also show that there will be a larger deviation of displacement if the gradient residual stress is replaced by mean residual stress.

Key words: Stoney extended formula, microelectromechanical system(MEMS), gradient residual stress, multilayer structure, elastic deformation, trilayer cantilever

中图分类号:

O484.5

董健, 蒋恒. 梯度残余应力下多层膜结构的弹性变形[J]. 中国机械工程, 2014, 25(14): 1867-1871.

Dong Jian, Jiang Heng. Gradient Residual Stress Induced Elastic Deformation of Multilayer Structures[J]. China Mechanical Engineering, 2014, 25(14): 1867-1871.

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