Investigating Mechanical Strength of Multilayer Membranes for MEMS Converters of Physical Quantities
A key role in the micro electronic and mechanical systems (MEMS) is played by a membrane that consists of one or several layers. Each layer has its own mechanical properties. The performance of MEMS strongly depends on the mechanical properties of materials used. Accurate values of mechanical properties (elastic properties, internal stress, strength, fatigue) are necessary for obtaining the optimum performances. Еlastic properties are necessary for predicting the amount of deflection from an applied force, and material strength sets the device operational limits . For example, during the operation of the X-ray source, a vacuum is created and therefore the membrane must withstand the pressure drop . Also, in view of reliability and life time requirements, mechanical characterization (including mechanical stresses) of MEMS materials becomes increasingly important. Fig. 1 shows the films bent under the action of mechanical stresses.
The small size of MEMS devices often leads to their usage in harsh environments, and good knowledge of mechanical properties may result in elimination of some of the mechanical failure modes through proper material selection, design, fabrication and packaging .
The values of mechanical properties have been determined on the developed stand (see Fig. 2).
The pressure from the compressor is fed to the reducer, which has a maximum pressure limit of 5atm. A receiver has been installed to reduce pressure drop between reducer and crystal. Several manometers are used in the circuit. One manometer is installed between receiver and platform with a crystal for measuring excess pressure on MEMS membrane (the step being 0.05atm and the measurement limit up to 2.5atm). The second manometer shows the pressure from compressor. It appeared that to obtain accurate data, the focal length between the surface and the objective should not exceed 5mm. The platform with a crystal consists of a metal cover, a crystal glued to the textolite (Fig. 2), and a rubber washer. A hole is made in the metal cover and textolite for working with an optical profilometer.
We have used a silicon plate with 150mm diameter and 460um thickness. A membrane has been formed on a Si crystal of square shape with a side of 6mm. The membrane consists of four dielectric layers of silicon oxide and nitride with a total thickness of 1.26um. The topology of a set of membranes is a circle with diameters of 1.0mm, 1.4mm and 1.8mm located in the center of the crystal.
Fig. 3 shows the elastic deformation of a membrane with 1.4mm diameter.
Fig. 4 shows the measurement results for a 1.0mm diameter structure.
The graph shows that the membrane has elastic (reversible) deformations, the critical excess pressure P* being 1.6atm for 1.0mm diameter.
The bulge method of dependence of deflection w on external force (pressure) makes it possible to determine the mechanical properties (biaxial module E/(1 – μ) and critical excess pressure) of the membrane using the formula 1 [1, 3]:
where P is the excess pressure, w is the deflection of the center of the membrane; σo, a, t, E and μ are residual stress, radius, thickness, Young’s modulus and Poisson’s ratio of the circular membrane.
The bulge method is based on the following principle: membrane surface is flat without excess pressure. Applying an external action (in our case, an excessive air pressure by means of a compressor) perpendicular to the plane of the surface of test crystal, it is possible to measure the dependence of deflection of membrane on external force.
The value of residual stresses σ0 has been determined by the method developed earlier by the authors  by means of a profilometer, and it amounted to 200MPa. The magnitude of the biaxial module E/(1 – μ) has been calculated using the formula (1): for ∅1.0mm it is 132GPa; for ∅1.4mm it is 156GPa; for ∅1.8mm it is 143GPa. The value correlates with the experimental result for a membrane consisting of one pair SiO2/Si3N4 — 190GPa . Also, the value of critical excess pressure has been determined: for ∅1.0mm — 1.6atm; for ∅1.4mm — 0.8atm; for ∅1.8mm — 0.5atm. The results confirm that the size effect and technological parameters of the process affect the elasticity characteristics of materials .
It is known from  that Young’s modulus of oxide silicon E(SiO2) is 70GPa, Poisson’s ratio of oxide silicon μ(SiO2) is 0.2, Young’s modulus of nitride silicon E(Si3N4) is 270GPa, Poisson’s ratio of nitride silicon μ(Si3N4) is 0.27.
Then using formula (2) we calculated the value of the Young’s modulus of the membrane Em from the mathematical model presented in :
where HSiO2 is thickness of SiO2, HSi3N4 is thickness of Si3N4.
Similarly, the Poisson’s ratio was calculated. In our case, HSiO2 is 1.0μm, HSi3N4 is 0.26μm, Em is 111GPa, um is 0.21. Therefore, analytical value of biaxial module Em/(1 – μm) of SiO2/Si3N4/SiO2/Si3N4 membrane is 142 GPa. The experimental and analytical value strongly correlate.
As is known, the magnitude of the force F is equal to the product of the pressure by the area (formula 3):
The experiment has shown that circular membranes of different diameters can withstand the same value of external force. The value of external force is 125mN.
We have presented the design of the stand using bulge method. The stand makes it possible to control changes in the deflection of the membrane from excess pressure with 0.05atm step. The experimental value of biaxial module E/(1 – μ) of SiO2/Si3N4/SiO2/Si3N4 membrane is 144±12GPa. It has been established that as the area of the membrane decreases from 2.54mm2 to 0.785mm2, the critical excess pressure P* increases from 0.5 to 1.6atm. The reversible deflection of the membrane from the excess pressure has been shown. The limiting force of the external action on the membrane is independent of the surface area and makes 125mN.
The work was performed using the equipment of MIET R&D Center “Microsystem Technique and the Bases of Electronic Components” supported by the Ministry of Education and Science of the Russian Federation (state contract No. 14.594.21.0012, unique identifier of the project RFMEFI59417X0012).
1. Kenichi Takahata, Micro Electronic and Mechanical Systems, ISBN 978-953-307-027-8, 386 pages, Publisher by InTech, 2009, Chapter 11 Mechanical Properties of MEMS Materials
2. Djuzhev N. A., Makhiboroda M. A., Pre¬ob¬ra¬zhen¬sky R. Y., Demin G. D., Gusev E. E., Dedkova A. A., J. Synch. Investig., 2017, 11: 443. DOI:10.1134/S1027451017020239
3. Benoit Merle, Mechanical Properties of Thin Films Studied by Bulge Testing, Thesis, Ph.D., 2013
4. Djuzhev N. A., Dedkova A. A., Gu¬sev E. E., Makhiboroda M. A., Gla¬go¬lev P. Y. Non-Contact Technique for Determining the Mechanical Stress in Thin Films on Wafers by Profiler. Source of the Document IOP Conference Series: Materials Science and Engineering, 2017, DOI: 10.1088/1757-899X/189/1/012019
5. Martins P. On the Determination of Poisson’s Ratio of Stressed Monolayer and Bilayer Submicron Thick Films, Microsystem Technologies September 2009, Volume 15, Issue 9, pp 1343–1348, DOI: 10.1007/s00542-009-0822-5
6. Laconte J., Flandre D., Raskin J.-P. Micromachined Thin-Film Sensors for SOI-CMOS Co-Integration, Springer, 294 p., 2006.
7. Astashenkova O. N., Physico-technological Basis of Management Mechanical Stresses in Thin Film Compositions of Micromechanics, Thesis, Ph. D., 2015. (In Russian).