Hafnium dioxide ($\mathrm{Hf}{\mathrm{O}}_2$), commonly known as hafnia, serves as a critical high-$k$ gate dielectric material in complementary metal-oxide-semiconductor (CMOS) devices and is also widely utilized in dynamic random-access memory (DRAM) capacitors. To gain better understanding of their physical properties, crystalline structures and dielectric constants of the three orthorhombic phases (OI-Pbca, OII-Pnma, OIII-$Pca{2}_1$) of $\mathrm{Hf}{\mathrm{O}}_2$ under mechanical strain have been investigated by first-principles calculations. Strain modifies both the mode effective charges and the frequencies of infrared-active (IR-active) phonon modes. The dielectric constant is directly proportional to the former and inversely proportional to the latter. Moreover, lattice-dynamics simulations revealed that large biaxial/triaxial tensile strains induce a phase transition from the ferroelectric phase (OIII-$Pca{2}_1$) to antipolar phase (OVIII-Pbcn), which arises from the coordination number change in half of the oxygen atoms. These results demonstrate strain engineering as a powerful means to control and modulate the dielectric properties and phase stabilities of $\mathrm{Hf}{\mathrm{O}}_2$.

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• Dielectric properties
• Ferroelectricity
• Phase transitions
• Piezoelectricity