Impact of Four-Valent Doping on the Crystallographic Phase Formation for Ferroelectric HfO2 from First-Principles: Implications for Ferroelectric Memory and Energy-Related Applications

The ferroelectric properties of nanoscale silicon-doped HfO2 promise a multitude of applications ranging from ferroelectric memory to energy-related applications. The reason for the unexpected behavior has not been clearly proven and presumably includes contributions from size effects and doping effects. Silicon incorporation in HfO2 is investigated computationally by first principles using different density functional theory (DFT) methods. Formation energies of interstitial and substitutional silicon in HfO2 paired with and without an oxygen vacancy prove the substitutional defect as the most likely. Within the investigated concentration window up to 12.5 formula unit %, silicon doping alone is not sufficient to stabilize the polar and orthorhombic crystal phase (p-o-phase), which has been identified as the source of the ferroelectricity in HfO2. On the other hand, silicon incorporation is one of the strongest promoters of the p-o-phase and the tetragonal phase (t-phase) within the group of investigated dopants, confirming the experimental ferroelectric window. Aside from silicon, the favoring effects on the energy of other four-valent dopants, C, Ge, Ti, Sn, Zr, and Ce, are examined, revealing Ce as a very promising candidate. The evolution of the volume changes with increasing doping concentration of these four-valent dopants shows an inverse trend for Ce in comparison to silicon. To complement this study, the geometrical incorporation of the dopants in the host HfO2 lattice was analyzed.