Compositional and phase dependence of elastic modulus of crystalline and amorphous Hf_1-xZr_xO₂ thin films

The elastic moduli of amorphous and crystalline atomic layer-deposited Hf_1-xZr_xO₂ (HZO, x = 0, 0.31, 0.46, 0.79, 1) films prepared with TaN electrodes on silicon substrates were investigated using picosecond acoustic measurements. The moduli of the amorphous films were observed to increase between 211 ± 6 GPa for pure HfO₂ and 302 ± 9 GPa for pure ZrO₂. In the crystalline films, it was found that the moduli increased upon increasing the zirconium composition from 248 ± 6 GPa for monoclinic HfO₂ to 267 ± 9 GPa for tetragonal ZrO₂. Positive deviations from this increase were observed for the Hf_0.69Zr_0.31O₂ and Hf_0.54Zr_0.46O₂ compositions, which were measured to have moduli of 264 ± 8 GPa and 274 ± 8 GPa, respectively. These two compositions contained the largest fractions of the ferroelectric orthorhombic phase, as assessed from polarization and diffraction data. The biaxial stress states of the crystalline films were characterized through sin²(⁠$ψ$⁠) x-ray diffraction analysis. The in-plane stresses were all found to be tensile and observed to increase with the increasing zirconium composition, between 2.54 ± 0.6 GPa for pure HfO₂ and 5.22 ± 0.5 GPa for pure ZrO₂. The stresses are consistent with large thermal expansion mismatches between the HZO films and silicon substrates. These results demonstrate a device-scale means to quantify biaxial stress for investigation on its effect on the ferroelectric properties of hafnia-based materials.