Finite temperature effects on the structural stability of Si-doped HfO${}_2$ using first-principles calculations

The structural stabilities of the monoclinic and tetragonal phases of Si-doped HfO${}_2$ at finite temperatures were analyzed using a computational scheme to assess the effects of impurity doping. The finite temperature effects considered in this work represented lattice vibration and impurity configuration effects. The results show that 6% Si doping stabilizes the tetragonal phase at room temperature, although a higher concentration of Si is required to stabilize the tetragonal phase at zero temperature. These data indicate that lattice vibration and impurity configuration effects are important factors determining structural stability at finite temperatures.