One method and device disclosed includes, among other things, forming a recessed sacrificial gate electrode having a recessed upper surface, performing at least one second etching process to define recessed sidewall spacers positioned adjacent the recessed sacrificial gate electrode, forming a plurality of sidewall spacers within a gate opening above the recessed sidewall spacers, wherein one of the spacers comprises a low-k insulating material that is positioned laterally between two other spacers and a gate cap layer, removing the recessed sacrificial gate electrode and forming a replacement gate structure in its place.