One method disclosed includes, among other things, forming a gate structure above an active region of a semiconductor substrate, performing an epitaxial deposition process to form an epi semiconductor material on the active region in the source/drain region of the device, performing an etching process on the epi semiconductor material to remove a portion of the epi semiconductor material so as to define at least one epi recess in the epi semiconductor material, forming a metal silicide layer on the upper surface of the epi semiconductor material and in the at least one epi recess in the epi semiconductor material, and forming a conductive structure that is conductively coupled to the metal silicide layer.