A manufacturing method includes providing a semiconductor substrate having a pressure sensor structure; and forming, during a BEOL process (BEOL=back-end-of-line), a metal-insulator-stack arrangement on the semiconductor substrate, wherein the metal-insulator-stack arrangement is formed to comprise (1) a cavity adjacent to the pressure sensor structure and extending over the pressure sensor structure, and (2) a pressure port through the metal-insulator-stack arrangement for providing a fluidic connection between the cavity and an environmental atmosphere, wherein the pressure port has a cross-sectional area, which is smaller than 10% of a footprint area of the pressure sensor structure within the cavity.