Quantum- well-based semiconductor devices and methods of forming quantum- well-based semiconductor devices are described. A method includes providing a hetero- structure disposed above a substrate and including a quantum-well channel region. The method also includes forming a source and drain material region above the quantum-well channel region. The method also includes forming a trench in the source and drain material region to provide a source region separated from a drain region. The method also includes forming a gate dielectric layer in the trench, between the source and drain regions; and forming a gate electrode in the trench, above the gate dielectric layer.