The work function of a high-k gate electrode structure may be adjusted in a late manufacturing stage on the basis of a lanthanum species in an N-channel transistor, thereby obtaining the desired high work function in combination with a typical conductive barrier material, such as titanium nitride. For this purpose, in some illustrative embodiments, the lanthanum species may be formed directly on the previously provided metal-containing electrode material, while an efficient barrier material may be provided in the P-channel transistor, thereby avoiding undue interaction of the lanthanum species in the P-channel transistor.