An integrated circuit structure vertically isolated electrically from the underlying substrate is formed in/on a single crystal semiconductor substrate, such as a silicon semiconductor wafer, by first implanting the substrate with a sufficient dosage of noble gas atoms to inhibit subsequent recrystallization of the semiconductor lattice in the implanted region during subsequent annealing, resulting in the formation of an isolation layer comprising implanted noble gas atoms enmeshed with semiconductor atoms in the substrate which has sufficient resistivity to act as an isolation layer. The preferred noble gases used to form such isolation layers are neon, argon, krypton, and xenon. When neon atoms are implanted, the minimum dosage should be at least about 6.times.10.sup.15 neon atoms/cm.sup.2 to inhibit subsequent recrystallization of the silicon substrate. When argon atoms are implanted, the minimum dosage should be at least about 2.times.10.sup.15 argon atoms/cm.sup.2. When krypton is implanted, the minimum dosage should be at least about 6.times.10.sup.14 krypton atoms/cm.sup.2. The energy used for the implant should be sufficient to provide an average implant depth sufficient to form, after annealing, the noble gas isolation layer at a depth of at least about 0.5 microns from the surface.