Hydrogen in Si(100)–SiO2–HfO2 gate stacks: Relevant charge states and their location

Using a density functional approach, we study the energetics of various charged hydrogen states in the Si(100)–SiO2–HfO2 gate stack. We describe the SiO2–HfO2 transition region through model structures of amorphous hafnium silicate HfxSi1−xO2 with different Hf contents x. Hydrogen is found to be amphoteric with a +/− charge transition level lying close to the Si conduction band minimum. This implies that protons are the most stable form of hydrogen for most electron chemical potentials in the Si band gap. Formation energies of the positively charged state across the Si(100)–SiO2–HfO2 stack indicate that protons mainly locate in the Si–SiO2 or SiO2–HfO2 transition regions.