Integrated circuit structures having source or drain contacts with enhanced contact area, and methods of fabricating integrated circuit structures having source or drain contacts with enhanced contact area, are described. For example, an integrated circuit structure includes a plurality of horizontally stacked nanowires. A gate structure is over the plurality of horizontally stacked nanowires. An epitaxial source or drain structure is at an end of the plurality of horizontally stacked nanowires. A conductive contact structure is vertically over the epitaxial source or drain structure. The conductive contact structure has a lower portion extending over the top and along upper portions of sides of the epitaxial source or drain structure, and has an upper portion on the lower portion. The upper portion has a maximum lateral width less than a maximum lateral width of the lower portion.