Disclosed herein are various methods of epitaxially forming materials on transistor devices. In one example, the method includes forming an isolation region in a semiconducting substrate that defines an active area, performing a heating process on the active area to cause an upper surface of the active area to become a curved surface and performing an etching process on the active area to define a recess having a curved bottom surface. The method further includes the steps of forming a channel semiconductor material in the recess with a curved upper surface and forming a gate structure for a transistor above the curved upper surface of the channel semiconductor material.