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The ferroelectric properties of nanoscale silicon doped HfO$_2$ promise amultitude of applications ranging from ferroelectric memory to energy-relatedapplications. The reason for the unexpected behavior has not been clearlyproven and presumably include contributions from size effects and dopingeffects. Silicon incorporation in HfO$_2$ is investigated computationally byfirst-principles using different density functional theory (DFT) methods.Formation energies of interstitial and substitutional silicon in HfO$_2$ pairedwith and without an oxygen vacancy prove the substitutional defect as the mostlikely. Within the investigated concentration window up to 12.5 formula unit %,silicon doping alone is not sufficient to stabilize the polar and orthorhombiccrystal phase (p-o-phase), which has been identified as the source of theferroelectricity in HfO$_2$. On the other hand, silicon incorporation is one ofthe strongest promoters of the p-o-phase and the tetragonal phase (t-phase)within the group of investigated dopants, confirming the experimentalferroelectric window. Besides silicon, the favoring effects on the energy ofother four-valent dopants, C, Ge, Ti, Sn, Zr and Ce, are examined, revealing Ceas a very promising candidate. The evolution of the volume changes withincreasing doping concentration of these four-valent dopants shows an inversetrend for Ce in comparison to silicon. To complement this study, thegeometrical incorporation of the dopants in the host HfO$_2$ lattice wasanalyzed.

acs applied nano materials

Impact of Four-Valent Doping on the Crystallographic Phase Formation for  Ferroelectric HfO$_2$ from First-Principles: Implications for Ferroelectric  Memory and Energy-Related Applications