Theoretical investigation of phase transitions in hafnia

Transition metal (TM) oxides find applications in ceramics, catalysis and semiconductor technology. In particular, hafnium dioxide or hafnia will succeed silica as a gate dielectric in advanced CMOS devices. However, the thermodynamics properties of thin TM oxide films are not well understood, despite their technological importance. We study theoretically phase transitions in hafnia using density functional theory. We find that the cubic phase of hafnia transforms without a barrier into a tetragonal phase \textit{via} a soft-phonon mode. The direct calculation of the cubic phase phonon dispersion confirms the existence of a zone edge soft mode in the cubic phase. Using the nudged elastic band method (NEBM) we find a barrierless transition path between the cubic and tetragonal phases which coincides with the same soft-mode path. In addition we identify the pathway for the tetragonal to monoclinic phase transition, and find a 0.045 eV/mol barrier. We construct the effective Hamiltonian for zone center distortions correct to the fourth order including the strain renormalization. The energy surface found correctly explains the symmetry of the phase structure observed at low temperature. We find that there are two sides to the phase transition driving forces. First there are local distortion modes; secondly there is strong coupling between the local modes. The coupling determines the transition temperature. We calculate the coupling and estimate the 3-D cubic to tetragonal transition temperature in fair agreement with experiment.