Stability of valence alternation pairs across the substoichiometric region at Ge/GeO2 interfaces

Through hybrid density functional calculations, we compare the Ge–Ge bond energy with the formation energy of a valence alternation pair as the O concentration varies across the Ge/GeO₂ interface. First, hole trapping energies are calculated for three atomistic models with different O concentrations: bulk Ge with isolated O atoms, amorphous GeO, and amorphous GeO₂ with an O vacancy. The reaction is then broken down in three steps involving the breaking of a Ge–Ge bond, charge transfer processes involving dangling bonds, and the formation of a threefold coordinated O atom. The energy of each elemental reaction is estimated through suitable model calculations. The charge transition levels resulting from this analysis agree with those obtained for the atomistic models. Our estimates indicate that hole trapping at low O concentrations occurs at no energy cost for p-type germanium owing to the formation of threefold-coordinated O atoms. Applied to n-type Ge, our analysis indicates that electron trapping in dangling bonds obtained from the breaking of Ge–Ge bonds is unfavorable. The formation energy of a valence alternation pair is evaluated and discussed in relation to previous results.