Density Functional Theory Calculations of Al doped Hafnia for Different Crystal Symmetry Configurations

Dogan et al.[1], investigated the causes of ferroelectricity in doped hafnia using ab initio methods. Similarly, we investigated the stability of Al doped hafnia using quantum mechanical methods. There are many different phases of Hafnia: monoclinic, tetragonal, cubic and orthorhombic. Starting with the monoclinic phase of Hafnia, Hafnia undergoes phase transitions which result in different space groups. The temperature at which the tetragonal phase is induced is 2000 K and cubic phase is induced at 2900 K[1]. Different dielectric constants vary from phase to phase. The average dielectric constants are highest for the cubic and tetragonal phases. In order to force a high temperature phase to be stable in Hafnia, one would need to introduce cation dopants. The polar orthorhombic phase is well known to exhibit ferroelectricity. Since inducing this phase with about 40 GPa it is more effective to induce a ferroelectric phase in Hafnia via doping methods. Doping methods for Hafnia are well established in [1] and demonstrated for Si, Ge, La and other elements. The rhombohedral phase is of interest and investigated first in [35]. Since ferroelectricity in the rhombohedral phase is difficult to stabilize, dopants are introduced analogously to the orthorhombic case. In this work, we doped the monoclinic, tetragonal, orthorhombic and rhombohedral phase of Hafnia with Al to investigate the effect of dopants on ferroelectricity and relevant EXAFS data was also produced. Using plane wave density functional theory, the tetragonal, orthorhombic, and trigonal phases of aluminum doped hafnia were geometrically optimized. The resulting 3 percent, 6 percent, and 7 percent Al doped hafnia structures were used for generating expected EXAFS spectra for experimental data analysis and validation. Specifically, these DFT calculated structures are going to be used in the non-linear least square EXAFS fits of the thin films HfAlO2