Abstract
A new analysis of the deflection of square and rectangular membranes of varying aspect ratio under the influence of a uniform pressure is presented. The influence of residual stresses on the deflection of membranes is examined. Expressions have been developed that allow one to measure residual stresses and Young's moduli. By testing both square and rectangular membranes of the same film, it is possible to determine Poisson's ratio of the film. Using standard micromachining techniques, free-standing films of LPCVD silicon nitride were fabricated and tested as a model system. The deflection of the silicon nitride films as a function of film aspect ratio is very well predicted by the new analysis. Young's modulus of the silicon nitride films is 222 ± 3 GPa and Poisson's ratio is 0.28 ± 0.05. The residual stress varies between 120 and 150 MPa. Young's modulus and hardness of the films were also measured by means of nanoindentation, yielding values of 216 ± 10 GPa and 21.0 ± 0.9 GPa, respectively.
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