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 (WPB_c), which is proposed to quantitatively characterize the asymmetric bonding stiffness along the strain direction. When the WPB_c 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 WPB_c on the piezoelectric effect and understand how the value of WPB_c 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 WPB_c and the lower standard deviation (STD) of WPB_c. In addition, the Sn-doped hafnia with the lowest average WPB_c and smaller STD-WPB_c is identified to have the highest piezoelectric coefficient (−2.04 C/m²) compared to other dopants, showing great potential in next-generation electromechanical devices.