Origin of the Flatband-Voltage Roll-Off Phenomenon in Metal/High- $k$ Gate Stacks

The effect of flatband-voltage reduction [roll-off (R-O)], which limits fabrication options for obtaining the needed band-edge threshold voltage values in transistors with highly scaled metal/high-
$k$
dielectric gate stacks, is discussed. The proposed mechanism causing this R-O phenomenon is suggested to be associated with the generation of positively charged oxygen vacancies in the interfacial
$\hbox{SiO}_{2}$
layer next to the Si substrate. The vacancies in the interfacial layer are induced by oxygen outdiffusing into the overlying high-
$k$
dielectric. The model is consistent with the variety of observations of R-O dependence on the electrode and substrate type, high-
$k$
dielectric composition and thickness, temperature, etc. The model's predictions were experimentally verified.