A transistor includes a body of semiconductor material, where the body has laterally opposed body sidewalls and a top surface. A gate structure contacts the top surface of the body. A source region contacts a first one of the laterally opposed body sidewalls and a drain region contacts a second one of the laterally opposed body sidewalls. A first isolation region is under the source region and has a top surface in contact with a bottom surface of the source region. A second isolation region is under the drain region and has a top surface in contact with a bottom surface of the drain region. Depending on the transistor configuration, a major portion of the inner-facing sidewalls of the first and second isolation regions contact respective sidewalls of either a subfin structure (e.g., FinFET transistor configurations) or a lower portion of a gate structure (e.g., gate-all-around transistor configuration).