Peculiarities of deformation of round thin-film membranes and experimental determination of their effective characteristics

The features of thin-film membranes, which are formed above round holes in silicon substrates using the Bosch-process are considered. The membrane has a complex shape due to the presence of the stress state of the initial films. The analysis of the dependence of the membrane deflection w on the supplied overpressure $P$ is used to calculate the mechanical characteristics of the membranes. In this case, it is necessary to determine directly on the membrane its diameter, the thickness of the constituent layers, the change in the relief of the membrane surface over its entire area as the excess pressure $P$. Determination of the membrane diameter and the thicknesses of the constituent layers is shown by the example of $p$-Si$^{*}$/SiN$_{x}$/SiO$_{2}$- and SiN$_{x}$/SiО$_{2}$/SiN$_{x}$/SiО$_{2}$ membranes. We used spectral ellipsometry, energy-dispersive X-ray spectroscopy, optical profilometry, optical microscopy. The influence of the peculiarities of the fixing conditions on the stress-strain state of membranes is shown, and the assessment is carried out by means of numerical modeling. A technique has been developed for measuring and calculating the mechanical characteristics of membranes that have an initial deflection. The calculation result is shown on the example of a membrane with an initial deflection of 2 $\mu$m – SiN$_{x}$/SiО$_{2}$/SiN$_{x}$/SiО$_{2}$ and a membrane with an initial deflection of 30 $\mu$m – Al/SiO$_2$/Al.