Technique for investigation of the shape changes of wafers and thin-film membranes by using geomorphometric approaches

We discuss a technique for investigating changes in complex topography and shape of structures using geomorphometric methods to study surfaces of wafers and membranes formed by the Bosch process. The wafers were analyzed before and after the deposition of the SiO$_2$ layer. The membranes were analyzed during the bulge testing. The study was carried out using maps of the catchment area and principal curvatures taking into account artifacts of the approximation of experimental data. We found a correspondence between the distribution of lines connecting the highest surface areas before and after the deposition of the SiO$_2$ layer on the wafers. For membranes with structure: Al(0.8 $\mu$m)/SiO$_2$(0.6 $\mu$m)/Al(1.1 $\mu$m), pSi$^*$ (0.8 $\mu$m)/SiN$_x$(0.13 $\mu$m)/SiO$_2$, Al(0.6 $\mu$m) we also found that features of membrane boundaries are mainly caused by their initial shape rather than change under the action of an applied pressure. The advantages of geomorphometric methods for studying changes in the shape of wafers and thin-film membranes in technological processes for the manufacturing of microelectronic devices are shown in comparison with traditional methods for analyzing surface topography maps.