First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

Crystalline structures, zone-center phonon modes, and the related dielectric response of the three low- pressure phases of HfO2 have been investigated in density-functional theory using ultrasoft pseudopotentials and a plane-wave basis. The structures of low-pressure HfO2 polymorphs are carefully studied with both the local-density approximation ~LDA! and the generalized gradient approximation. The fully relaxed structures obtained with either exchange-correlation scheme agree reasonably well with experiment, although LDA yields better overall agreement. After calculating the Born effective charge tensors and the force-constant matrices by finite-difference methods, the lattice dielectric susceptibility tensors for the three HfO2 phases are computed by decomposing the tensors into the contributions from individual infrared-active phonon modes. have, in a previous paper, 4 investigated the bulk structures and lattice dielectric response of ZrO 2 polymorphs. We found that the dielectric responses vary dramatically with the crystal phase. Specifically, we found that the monoclinic phase has a strongly anisotropic lattice dielectric tensor and a rather small orientationally averaged dielectric constant ow- ing to the fact that the mode effective charges associated with the softest modes are relatively weak. This Brief Report presents the corresponding work on HfO2, providing the first thorough theoretical study of the structural, vibrational, and lattice dielectric properties of the HfO2 phases. Such properties are naturally expected to be similar to those of ZrO2 in view of the chemical similarities mentioned above. We find that this is generally true, although we also find some significant quantitative differences in some of the calculated properties. The calculation of the lattice contributions to the static dielectric tensor e 0 entails the computations of the Born ef- fective charge tensors Z* and the force-constant matrices F. The Z* tensors, defined via DP5(e/V)( iZ iiDui , are ob- tained by finite differences of polarizations ~P! as various sublattice displacements ( u i ) are imposed, with the elec- tronic part of the polarizations computed using the Berry- phase approach. 5,6 Here V is the volume of the unit cell, e is the electron charge, and i labels the atom in the unit cell. We then calculate the force-constant matrix, F ij 52)F i /)u j .2DF i /Du j b by calculating all the Hellmann-Feynman forces Fi caused by making displacements u j of each atom in each Cartesian direction in turn ~Greek indices label the Cartesian coordinates!. The resulting F matrix is symme- trized to clean up numerical errors, the dynamical matrix D ij 5( MiM j) 21/2 F ij is constructed, and the latter is then diagonalized to obtain the eigenvalues v l and eigenvectors j i,lb .