Fast Multi-parametric Method for Mechanical Properties Estimation of Clamped—Clamped Perforated Membranes
The knowledge of material properties like Young’s modulus and residual stress is crucial for a reliable design of devices with optimized performance. Several works discussed on the determination of the mechanical properties of thin/thick films and microstructures from deflection measurements by a profiler. This work provides an approximate solution for the load-deflection response of perforated membranes clamped on two opposite edges subjected to quasi-point pressure loads applied by a profilometer. SixNy/a-Si/SixNy thin film membranes of different sizes and porosities were fabricated by unconventional 100 °C PECVD process using surface micromachining approach. Tri-layer thin films were mechanically characterized by nanoindentation tests and residual stress measurements based on the wafer curvature method. Load-deflection measurements were done by applying quasi-point loads in the range 4.9–9.8 μN. Finite Element Analysis was used to model the mechanical behavior of the membrane, in agreement with the deflection data measured by profilometer. The elastic modulus measured by nanoindentation was used as reference for the perforated membranes load-deflection analytical function identification. An approximate analytical law was developed, which explicates the maximum deflection amplitude as a function of geometric features (sizes and thickness) and mechanical properties (Young’s modulus and residual stress). It was validated numerically and experimentally; it was able to provide an estimation of the residual stress of CCFF perforated membranes, starting from measured data of deflection, for single or multiple loads; also, it can be used in a complementary way to calculate the Young’s modulus from deflection data and residual stress information.
KeywordsLoad-deflection model Perforated clamped-clamped membrane Finite element analysis Young’s modulus Residual stress
- 1.Pan, J.Y., Lin, P., Maseeh, F., Senturia, S.D.: Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films. In: Technical Digest IEEE Solid State Sensor and Actuators Workshop, Hilton Head Island, SC, 73, 70–73 (1990)Google Scholar
- 4.Timoshenko, S., Woinowsky-Krieger, S.: Theory of Plates and Shells, 2nd edn. McGraw-Hill, Inc. (1959)Google Scholar
- 5.Eaton, W.P., Bitsie, F., Smith, J.H., Plummer, D.W.: A new analytical solution for diaphragm deflection and its application to a surface-micromachined pressure sensor. In: Technical Proceedings of the 1999 International Conference on Modeling and Simulation of Microsystems, Chapter 17, 640–643 (1999)Google Scholar
- 8.Ugural, A.C.: Stress in Plates and Shells. McGraw-Hill, Boston (1999)Google Scholar
- 10.Rabinovich, V.L., Gupta, R.K., Senturia, S.D.: The effect of release-etch holes on the electromechanical behavior of MEMS structures. In: International Conference on Solid State Sensors and Actuators, TRANSDUCERS Chicago, IL, 2, 1125–1128 (1997)Google Scholar