An illustrative transistor device disclosed herein includes a gate structure positioned around a portion of a fin defined in a semiconductor substrate and epitaxial semiconductor material positioned on the fin in a source/drain region of the transistor device, wherein the epitaxial semiconductor material has a plurality of lower angled surfaces. In this example, the device further includes a first sidewall spacer positioned adjacent the gate structure, wherein a first portion of the first sidewall spacer is also positioned on and in physical contact with at least a portion of the lower angled surfaces of the epitaxial semiconductor material.