Postbuckled Square Thin Film Membranes Under Differential Pressure
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Postbuckled Square Thin Film Membranes Under Differential Pressure Torsten Kramer, Oliver Paul IMTEK, Microsystem Materials Laboratory, University of Freiburg Georges-Köhler-Allee 103, D-79110 Freiburg, Germany [email protected] ABSTRACT We report quantitative results on the load-deflection response of compressively prestressed square membranes under differential pressure. The membranes consist of 0.485 µm and 1.9 µm thick silicon nitride films. For these square membranes we observed a new symmetry transition of the deflection profile between a state without reflection symmetries at small loads to a state with reflection symmetries at sufficiently large loads. The load-deflection response was modeled by finite element simulations covering a wide range of prestrains ε0 and pressures using various geometries. From the symmetry transition process, Young's modulus E = (150±5) GPa and the prestrain ε0 = −(1.6±0.1)×10−3 of the membrane material was extracted. INTRODUCTION The buckling behavior of microstructures has been commonly analyzed to extract thin film material parameters such as prestrain ε0, prestress σ0, and elastic properties like Young's modulus E and Poisson's number ν. The microstructures can be membranes [1,2] as well as surface micromachined structures such as beams [3], bridges [4], rings [5] and annuli [6]. In the case of membranes the bulge test has been a well-known method for extracting mechanical parameters from prestressed thin films [1,2,7]. So far, its applicability to compressively prestressed materials was limited to long membranes, due to the absence of validated mechanical models for other geometries, in particular compact square membranes. In this paper we report experimental results on the load-deflection of such compressively prestressed square membranes and their successful modeling using the finite element method. We observed a new symmetry transition of the deflection profile between a state without reflection symmetries at small loads, to a state with reflection symmetries at sufficiently large loads. This behavior is shown in Fig. 1 for a membrane with side length a = 1040 µm and thickness h = 1.9 µm. This transition and the corresponding deflection profiles are used to extract Young’s modulus E or the prestrain ε0. FABRICATION Two types of membranes, A and B, were fabricated. For both types, 525 µm thick doublesided polished 4'' n-Si wafer were used as substrate material. In the case of type A membranes (see Table I) the silicon nitride layer was deposited from SiH4 (20 sccm), NH3 (20 sccm) and N2 (1500 sccm) by plasma enhanced chemical vapor deposition (PECVD) at 300 °C in a Multiplex CVD chamber of STS, UK. The type B membranes consist of a silicon nitride layer, which was deposited from SiH4 (40 sccm), NH3 (40 sccm) and N2 (1960 sccm) by PECVD at 300 °C in an STS PECVD chamber MPX 310 PC using a mixed frequency process. The film thicknesses were L3.4.1
27 µ m
30 µ m
y
x B
A a
0 mbar
(a)
400 mbar 0 µm
(b)
0 µm
(c)
Figure 1. Optical micrograph of a compressive
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