Processes are provided for fabricating a substrate having a silicon-on-insulator (SOI) or silicon-on-nothing (SON) architecture, which are applicable to the manufacture of semiconductor devices, especially transistors such as those of the MOS, CMOS, BICMOS, and HCMOS types. In the fabrication processes, a multilayer stack is grown on a substrate by non-selective full-wafer epitaxy. The multilayer stack includes a silicon layer on a Ge or SiGe layer. Active regions are defined and masked, and insulating pads are formed so as to be located around the perimeter of each of the active regions at predetermined intervals and placed against the sidewalls of the active regions. The insulating trenches are etched, and the SiGe or Ge layer is laterally etched so as to form an empty tunnel under the silicon layer. The trenches are filled with a dielectric. In the case of an SOI archiutecture, the tunnel is filled with a dielectric.