Understanding and tuning negative longitudinal piezoelectricity in hafnia

Most piezoelectric materials exhibit a positive longitudinal piezoelectric effect (PLPE), while a negative longitudinal piezoelectric effect (NLPE) is rarely reported or paid much attention. Here, utilizing first-principles calculations, we unveil the origin of negative longitudinal piezoelectricity in ferroelectric hafnia by introducing the concept of weighted projected bond strength around cation in the c direction (WPBc), which is proposed to quantitatively characterize the asymmetric bonding stiffness along the strain direction. When the WPBc is anti-parallel to the direction of bulk spontaneous polarization, the polarization decreases with respect to tensile strain and leads to a negative piezoelectricity. Furthermore, to confirm the influence of WPBc on the piezoelectric effect and understand how the value of WPBc influences the piezoelectric coefficient e33, we acquire both the piezoelectric coefficient of doped hafnia and the corresponding bonding environment around each cation. The finding reveals that the more negative piezoelectric coefficient can be achieved through a concurrent achievement of the more negative average WPBc and the lower standard deviation (STD) of WPBc. In addition, the Sn-doped hafnia with the lowest average WPBc and smaller STD-WPBc is identified to have the highest piezoelectric coefficient (-2.04 C/m²) compared to other dopants, showing great potential in next-generation electromechanical devices.