Disclosed herein are various methods of forming high mobility fin channels on three dimensional semiconductor devices, such as, for example, FinFET semiconductor devices. In one example, the method includes forming a plurality of spaced-apart trenches in a semiconducting substrate, wherein the trenches define an original fin structure for the device, and wherein a portion of a mask layer is positioned above the original fin structure, forming a compressively-stressed material in the trenches and adjacent the portion of mask layer, after forming the compressively-stressed material, removing the portion of the mask layer to thereby expose an upper surface of the original fin structure, and forming a final fin structure above the exposed surface of the original fin structure.