Structures having raised epitaxy on channel structure transistors are described. In an example, an integrated circuit structure includes a channel structure having multi-layer epitaxial source or drain structures thereon, the multi-layer epitaxial source or drain structures having a recess extending there through. A gate dielectric layer is on a bottom and along sides of the recess and laterally surrounded by the epitaxial source or drain structures. A gate electrode is on and laterally surrounded by the gate dielectric layer. The gate electrode has an uppermost surface below an uppermost surface of the gate dielectric layer.