Strongly buckled square micromachined membranes

Abstract

The buckling of compressively prestressed square membranes with built-in edges is investigated experimentally and analyzed theoretically. The buckling depends weakly on Poisson's ratio and essentially is a function of the reduced prestrain, " 0 = " 0 a 2 =h 2 , where " 0 is the physical prestrain, a is the width, and h is the thickness of the membrane. As " 0 becomes increasingly negative, the membrane undergoes two symmetry breaking buckling transitions. Beyond the first transition occurring at " cr1 , the buckling profile has all the reflection and rotation symmetries of a square. The reflection symmetries are lost through a second instability transition at "cr2: The bifurcation points, "cr1 and "cr2; and buckling profiles were calculated using analytical energy minimization and nonlinear finite-element simulation. Both methods agree. The buckling of micromachined plasma-enhanced chemical vapor deposition silicon nitride membranes on a silicon wafer is interpreted in terms of the theoretical results. Good matching between measured and calculated buckling profiles is found. The extracted strain values are consistent irrespective of the size and buckling mode of the membranes. From the average strain across the wafer " 0 = 03:50 2 10 04 and complementary wafer curvature measurements, a Young's modulus of 130 GPa is deduced. Methods for the straightforward extraction of " 0 from experimental center deflections of buckled square membranes are described. [443]

The Mexican hat effect on the delamination buckling of a compressed thin film

“…Here the film in-plane displacement, which can have significant impacts on the film stretching energy in the postbuckling region [6,11], is not included. This study focuses only on the buckling, on which the in-plane displacement is shown to have a minor influence [1].…”

Mechanical characterization of MEMS bi-stable buckled diaphragms.

“…A small pressure was applied to the diaphragm; the thermal loads were then slowly applied; and finally the pressure was slowly removed. This roundabout process bypasses numerical instability in the FEA model [12]. The process in this work follows a similar path and is elaborated in the procedure section.…”

“…The smaller diaphragms show a uniform, parabolic buckled shape for a small value of w, higher-order modes are seen as the diaphragms get larger [12].…”

“…Similar to the process used in this work, they simulated the pre-stress of the diaphragm using a thermal load [12]. Because other thermal effects are not considered throughout the rest of the experiments, an actual coefficient of thermal expansion is not required, and a temperature that results in the measured pre-stress is sufficient.…”

“…The larger diaphragms behave with high-order buckling modes as seen in Figure 5. The diaphragms for the work presented here are not completely homogenous, since polyimide is deposited onto silicon dioxide [12].…”