多层MEMS结构的Stoney延伸公式  

Extension of the Stoney formula for multilayer MEMS structure

作　　者：董健[1] 蒋恒[1] 孙笠[1] 

机构地区：[1]浙江工业大学浙江省特种装备制造与先进加工技术教育部重点实验室,浙江杭州310014

出　　处：《浙江工业大学学报》2014年第4期452-457,共6页Journal of Zhejiang University of Technology

基　　金：浙江省自然科学基金资助项目(Y1100707)

摘　　要：利用薄膜—基底结构的曲率来表征薄膜残余应力的方法正在被广泛应用,这种表征方法的理论基础是Stoney公式.然而Stoney公式所采取的假设导致它在应用范围上存在着较大的局限性.提出了一类Stoney延伸公式,利用有限元仿真以及解析计算比较分析证明,这类Stoney延伸公式不仅在一定范围内受薄膜—基底厚度比和杨氏模量比的影响比较小,而且在应用到梯度残余应力下多层MEMS结构时依然能保持较好的准确性.Curvature-based techniques are gaining increasingly widespread application for evaluating the stress status in the film of a film-substrate system,and its theoretical basis is Stoney formula.While the assumptions of Stoney formula significantly limit its application range.A kind of Stoney extended formula is proposed,and comparisons based on the Finite element simulation and analytic calculations show that this kind of Stoney formula is hardly subjected to in a certain range the thickness ratio and Young＇s modulus ratio of a film-substrate system,and while applied to the multilayer MEMS structure with gradient residual stress,high accuracy can be also guaranteed.

关 键 词：梯度残余应力 多层结构 微机电系统 Stoney延伸公式 

分 类 号：O484.5[理学—固体物理]