Stabilization of the high-k tetragonal phase in HfO2: The influence of dopants and temperature fromab initiosimulations

By means of ab initio simulations we investigate the influence of dopants (Si, C, Ge, Sn, Ti, and Ce) on the transition from the monoclinic to the tetragonal phase in HfO2. In this study we focus first on the internal energy only, an approach common to ab initio simulations. In the second step we go beyond this approach in considering the Helmholtz free energy by additionally taking into account the contribution of the phonon density of states. Finally we discuss the change in transition temperature in the regime of thin films based on an empirical model. We find that both the contributions of the internal energy and phonons can be understood in terms of a model relying on the ionic radius of the dopants. Among the investigated dopants silicon is identified to promote the tetragonal phase most efficiently. The effectiveness of the various dopants is compared on the basis of a qualitative phase diagram for doping concentrations up to ∼12%.