曲率测量技术在微机电系统薄膜残余应力测量中的应用

APPLICATION OF CURVATURE MEASUREMENT TECHNIQUE FOR MEASURING RESIDUAL STRESSES IN MEMS THIN FILMS

在比较曲率测量技术常用的Stoney公式及其修正式的基础上,利用有限元分析方法,建立薄膜/基底结构的有限元模型,给出一种薄膜残余应力的等效施加方法,从两个方面详细分析并对比这两个公式在微机电系统(Micro electromechanical systems,MEMS)薄膜残余应力测量中的检测精度。仿真及分析结果表明,修正后的Stoney公式在很大程度上提高薄膜残余应力的测量精度,使曲率测量技术的适用范围得到较大扩展。但是当薄膜厚度接近于基底厚度或结构处于大变形状态下,修正式的计算精度也将受到较大影响,此时可以采用有限元分析方法来获得临界状态值,以提高残余应力的检测精度。同时,通过有限元分析,证实曲率测量技术应用中存在的另一个问题,即曲率的空间分布不均匀性现象。

Both the Stoney formula and its extended one are widely used in curvature measurement technique. To investigate in detail the measuring precision of residual stresses in micro electromechanical systems （MEMS） thin films with these two formulas, a finite element model for the thin film/substrate structure is constructed and finite element analysis is performed For introducing residual stresses into MEMS thin films, the method of equivalent thermal loading is employed. Results of simulation and analysis show that the measuring precision of the extended Stoney formula is indeed improved to a great extent, largely expanding the application range of the curvature measurement technique. However, when the thickness ratio of substrate to thin film is less than a certain value or the residual stress reaches a considerable amplitude, which are 6 and 50 MPa here respectively, precision of the extended formula will be degraded greatly. In that case, FEM becomes an effective tool to find out the critical value, and consequently improves the measuring precision. Meanwhile, another problem of the uneven distribution of curvature in space for curvature measurement technique is pointed out and proved by FEM.