Dipole model explaining high-$k$/metal gate field effect transistor threshold voltage tuning

An interface dipole model explaining threshold voltage $(Vt)$ tuning in HfSiON gated $n$-channel field effect transistors $(nFETs)$ is proposed. $Vt$ tuning depends on rare earth (RE) type and diffusion in $Si∕SiOx∕HfSiON∕REOx$/metal gated $nFETs$ as follows: $Sr<Er<Sc+Er<La<Sc<none$⁠. This $Vt$ ordering is very similar to the trends in dopant electronegativity (EN) (dipole charge transfer) and ionic radius $(r)$ (dipole separation) expected for a interfacial dipole mechanism. The resulting $Vt$ dependence on RE dopant allows distinction between a dipole model (dependent on EN and $r$⁠) and an oxygen vacancy model (dependent on valence).