Theoretical calculation of ferroelectric Hf1−xZrxO2 by first-principle molecular dynamic simulation

Abstract

The origin of the ferroelectricity in HfO2 is considered to be the formation of a non-centrosymmetric polar orthorhombic phase. The phase stability and the ferroelectricity of orthorhombic Hf1−xZrxO2 ferroelectric material are theoretically investigated with the density functional computations. The percentage of each phase is estimated based on the Maxwell–Boltzmann distribution, and the orthorhombic phase has the largest distribution when Zr/Hf = 1. The double-well landscape of the energy as a function of the polarization for the orthorhombic Hf1−xZrxO2 is obtained. Our calculation shows that the orthorhombic HfO2 has the ferroelectricity with a saturated polarization of 66.25 μC cm−2 and the barrier height of 77.4 meV atom−1. To consider the phase distribution for different Zr content, the calculated remnant polarization of Hf0.5Zr0.5O2 has the largest value of 21.5 μC cm−2. The metastable life time from zero polarization to saturated polarization is 0.19 ps and 0.17 ps for orthorhombic HfO2 and ZrO2, respectively, and depend on the Zr/Hf ratio.