One illustrative device disclosed herein includes, among other things, a fin defined on a substrate. A gate electrode structure is positioned above the fin in a channel region. A source/drain region is defined in the fin. The source/drain region includes a first epitaxial semiconductor material. The first epitaxial semiconductor material includes a dopant species having a first concentration. A diffusion blocking layer is positioned above the first epitaxial semiconductor material. A second epitaxial semiconductor material is positioned above the diffusion blocking layer. The second epitaxial semiconductor material includes the dopant species having a second concentration greater than the first concentration.