A process for manufacturing a MEMS device, wherein a bottom silicon region is formed on a substrate and on an insulating layer; a sacrificial region of dielectric is formed on the bottom region; a membrane region, of semiconductor material, is epitaxially grown on the sacrificial region; the membrane region is dug down to the sacrificial region so as to form through apertures; the side wall and the bottom of the apertures are completely coated in a conformal way with a porous material layer; at least one portion of the sacrificial region is selectively removed through the porous material layer and forms a cavity; and the apertures are filled with filling material so as to form a monolithic membrane suspended above the cavity. Other embodiments are directed to MEMS devices and pressure sensors.