Methods of making a self-aligned gate contact structure and source/drain metallization structures on integrated circuit products

A method of forming a gate structure in a gate cavity laterally defined by a sidewall spacer and recessing the sidewall spacer so as to form a recessed sidewall spacer with a recessed upper surface is disclosed. In this example, the method also includes performing at least one etching process to form a tapered upper surface on the exposed portion of the gate structure above the recessed upper surface of the spacer and forming a gate cap above the tapered upper surface of the gate structure and above the recessed upper surface of the recessed sidewall spacer.