Amorphous (a)-${\mathrm{HfO}}_2$ is a prototype high dielectric constant insulator with wide technological applications. Using ab initio calculations we show that excess electrons and holes can trap in a-${\mathrm{HfO}}_2$ in energetically much deeper polaron states than in the crystalline monoclinic phase. The electrons and holes localize at precursor sites, such as elongated Hf-O bonds or undercoordinated Hf and O atoms, and the polaronic relaxation is amplified by the local disorder of amorphous network. Single electron polarons produce states in the gap at $\sim 2$ eV below the bottom of the conduction band with average trapping energies of 1.0 eV. Two electrons can form even deeper bipolaron states on the same site. Holes are typically localized on undercoordinated O ions with average trapping energies of 1.4 eV. These results advance our general understanding of charge trapping in amorphous oxides by demonstrating that deep polaron states are inherent and do not require any bond rupture to form precursor sites.

We used density functional theory (DFT) calculations to study the interaction of hydrogen with amorphous hafnia ($\mathrm{a}\text{−}{\mathrm{HfO}}_2$) using a hybrid exchange-correlation functional. Injection of atomic hydrogen, its diffusion towards electrodes, and ionization can be seen as key processes underlying charge instability of high-permittivity amorphous hafnia layers in many applications. Hydrogen in many wide band gap crystalline oxides exhibits negative-U behavior (+1 and $-1$ charged states are thermodynamically more stable than the neutral state) . Our results show that in $\mathrm{a}\text{−}{\mathrm{HfO}}_2$ hydrogen is also negative-U, with charged states being the most thermodynamically stable at all Fermi level positions. However, metastable atomic hydrogen can share an electron with intrinsic electron trapping precursor sites [ Phys. Rev. B 94, 020103 (2016).] forming a $[e_{tr}^{-}+\mathrm{O}–\mathrm{H}]$ center, which is lower in energy on average by about 0.2 eV. These electron trapping sites can affect both the dynamics and thermodynamics of the interaction of hydrogen with $\mathrm{a}\text{−}{\mathrm{HfO}}_2$ and the electrical behavior of amorphous hafnia films in CMOS devices.

We demonstrate that electron trapping at intrinsic precursor sites is endemic in non-glass-forming amorphous oxide films. The energy distributions of trapped electron states in ultra-pure prototype amorphous (a)-HfO2 insulator obtained from exhaustive photo-depopulation experiments demonstrate electron states in the energy range of 2-3 eV below the oxide conduction band. These energy distributions are compared to the results of density functional calculations of a-HfO2 models of realistic density. The experimental results can be explained by the presence of intrinsic charge trapping sites formed by under-coordinated Hf cations and elongated Hf-O bonds in a-HfO2. These charge trapping states can capture up to two electrons, forming polarons and bi-polarons. The corresponding trapping sites are different from the dangling-bond type defects responsible for trapping in glass-forming oxides, such as SiO2, in that the traps are formed without bonds being broken. Furthermore, introduction of hydrogen causes formation of somewhat energetically deeper electron traps when a proton is immobilized next to the trapped electron bi-polaron. The proposed novel mechanism of intrinsic charge trapping in a-HfO2 represents a new paradigm for charge trapping in a broad class of non-glass-forming amorphous insulators.

DOI: http://dx.doi.org/10.1103/PhysRevB.89.079905Published 27 February 2014Received 20 February 2014©2014 American Physical Society