Investigation of the real shape changes of round thin-film membranes during the bulge testing

We discuss the study of the sphericity of the real shape of round thin-film membranes when it changes during the bulge testing. Membrane structures: SiN$_x$/SiО$_2$/SiN$_x$/SiО$_2$, pSi$^*$/SiN$_x$/SiO$_2$, Al, etc. We described the technique for determining the areas of deviation of the membrane surface shape from a spherical one, estimating the magnitude and peculiarities of the distribution of the radius of curvature along the membrane diameter. It is shown that the shape of the membranes differs from spherical closer to the edge (perimeter), and in many cases also to the area of the top (center) of the membrane. A trend was found: an increase in the radius of curvature as it approaches the center of the membrane. Keywords: thin films, membrane, mechanical characteristics, mechanical stresses, deformation, deflection, strain, microelectromechanical systems, MEMS, circular membrane, silicon substrate, optical profilometry, overpressure, bulge testing, bulging method, surface, topography, radius of curvature, curvature.