Application of curvature measurement technique for measuring residual stresses in MEMS thin films

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.