Density functional based tight-binding parametrization of hafnium oxide: Simulations of amorphous structures

This work presents both the parametrization procedure of a self-consistent charge density functional based tight-binding scheme (SCC-DFTB) for hafnium oxide and the structural as well as the electronic results of the simulations of amorphous hafnium oxide $a\text{-HfO}{}_2$ using the data resulting during the parametrization. While aiming at describing amorphous hafnium oxide, the created parameters could be successfully compared to ab initio DFT data for hafnium and hafnium oxide crystalline structures. Furthermore the atomic structure and electronic properties obtained in the DFTB simulations of $a\text{-HfO}{}_2$ compare well to other theoretical studies using classical many-body as well as quantum-mechanical approaches.

Figure 1

Structural snapshots of an amorphous $\mathrm{Hf}{\mathrm{O}}_2$ network at $\rho =8.93\mathrm{g}/{\mathrm{cm}}^3$.

Figure 2

Structural snapshots of a classical grown amorphous $\mathrm{Hf}{\mathrm{O}}_2$ network with a resulting density of $\rho =8.50\mathrm{g}/{\mathrm{cm}}^3$.

Figure 3

Band structures for hcp and bcc hafnium. Comparison between PBE (red) and DFTB (black).

Figure 4

Band structures for monoclinic, fcc, and tetragonal hafnium oxide. Comparison between PBE (red) and DFTB (black).

Figure 5

Partial pair distribution functions for the hafnium-hafnium, hafnium-oxygen, and oxygen-oxygen correlation.

Figure 6

Partial pair distribution functions for the hafnium-hafnium, hafnium-oxygen, and oxygen-oxygen correlation in comparison to the two classical models.

Figure 7

Comparison of the coordination numbers for $\rho =7.97\frac{\mathrm{g}}{{\mathrm{cm}}^3}$ (left) and $\rho =10.0\frac{\mathrm{g}}{{\mathrm{cm}}^3}$ (right). Oxygen is colored in red, fourfold hafnium in blue, fivefold in black, sixfold in green, sevenfold in grey, and eightfold in gold.

Figure 8

Angle distributions for the models DFTB-II, BMB-VI, and BMB-VII.

Figure 9

Electronic density of states for the different models.

Figure 10

Density of states for the oxygen vacancy defect in monoclinic hafnia calculated with PBE (top) and DFTB (bottom). The valence-band maximum was shifted to 0 eV in both cases.