One method disclosed herein includes forming a patterned mask layer above a surface of a semiconductor substrate, performing at least one etching process through the patterned mask layer to define a plurality of intersecting ridges that define a ridged surface in the substrate, and forming a Group III-V material on the ridged surface of the substrate. An illustrative device disclosed herein includes a Group IV substrate having a ridged surface comprised of a plurality of intersecting ridges and a Group III-V material layer positioned on the ridged surface of the Group IV substrate.