The Effect of Y Doping on Monoclinic, Orthorhombic, and Cubic Polymorphs of HfO₂: A First Principles Study

HfO₂ can assume different crystalline structures, such as monoclinic, orthorhombic, and cubic polymorphs, each one characterized by unical properties. The peculiarities of this material are also strongly related to the presence of doping elements in the unit cell. Thus, the present paper has the main purpose of studying and comparing twelve different systems characterized by diverse polymorphs and doping percentages. In particular, three different crystalline structures were considered: the monoclinic P2, the orthorhombic Pca2, and the cubic Fm3¯m phases of HfO₂. Each one has been studied by using Y as a doping agent with three different contents: 0% Y:HfO₂, 8% Y:HfO₂, 12% Y:HfO₂, and 16% Y:HfO₂. For all the systems, density functional theory (DFT) methods based on PBE/GGA, and on the HSE hybrid functionals were used to optimize the geometry as well as to study their optical properties. Depending on the polymorphs, Y affects the formation energy in different ways and causes changes in the optical properties. When the percentage of Y did not exceed 12%, a stabilization of the cubic phase fraction and an increase of the dielectric constant was observed. Additionally, the calculated optical bandgap energies and the refractive index are examined to provide an overview of the systems and are compared with experimental data. The bandgaps obtained are in perfect agreement with the experimental values and show a slight increase as the doping percentage grows, while only minor differences are found between the three polymorphs in terms of both refractive index and optical band gap. The adopted first principles study generates a reasonable prediction of the physical-chemical properties of all the systems, thus identifying the effects of doping phenomena.