Piezoelectricity in hafnia

Abstract

Because of its compatibility with semiconductor-based technologies, hafnia (HfO₂) is today's most promising ferroelectric material for applications in electronics. Yet, knowledge on the ferroic and electromechanical response properties of this all-important compound is still lacking. Interestingly, HfO₂ has recently been predicted to display a negative longitudinal piezoelectric effect, which sets it apart from classic ferroelectrics (e.g., perovskite oxides like PbTiO₃) and is reminiscent of the behavior of some organic compounds. The present work corroborates this behavior, by first-principles calculations and an experimental investigation of HfO₂ thin films using piezoresponse force microscopy. Further, the simulations show how the chemical coordination of the active oxygen atoms is responsible for the negative longitudinal piezoelectric effect. Building on these insights, it is predicted that, by controlling the environment of such active oxygens (e.g., by means of an epitaxial strain), it is possible to change the sign of the piezoelectric response of the material.

Fig. 1. Key structural features of HfO₂.

Structure of the cubic paraelectric (a) and orthorhombic ferroelectric (b) polymorphs of HfO₂. In the cubic $Fm\overline{3}m$ phase, all Hf and O atoms are equivalent by symmetry. In the ferroelectric Pca2₁ structure we have two symmetry-inequivalent sets of oxygen atoms –labeled O_I (shown in orange) and O_II (red), respectively–, while all Hf atoms are equivalent. In panel b, the black arrow indicates the positive spontaneous polarization of the structure shown, which is essentially related to the vertical downward shift of the O_I atoms from their high-symmetry position in the cubic phase. In the ferroelectric state, the O_I atoms have three nearest-neighboring Hf cations; the bonding distances are explicitly indicated for the O_I(1) atom, which is a representative case.

Fig. 2. Dynamic measurements of piezoelectricity using piezoresponse force microscopy (PFM).

a–c PFM phase (top panel) and amplitude (bottom panel) loops measured in the IrO₂/PZT/Pt capacitor (a), PVDF film (b), and Pt/Ti/TiN/La:HfO₂/TiN capacitor (c). The loops were obtained in the bias-off mode to minimize the electrostatic contribution to the PFM signal.

Fig. 3. Comparison between PbTiO₃ and HfO₂.

Cubic $Pm\overline{3}m$ paraelectric (a) and tetragonal P4mm ferroelectric (b) phases of PbTiO₃. The tetragonal phase presents two symmetry-inequivalent oxygen anions, colored differently and labeled by O_I and O_II, respectively. In panel b the arrow on the right marks the spontaneous polarization, which is essentially related to the upward displacement of the Pb and Ti cations with respect to the oxygen atoms (the arrows on the atoms mark such displacements). Panel c is a sketch of the tetragonal phase subject to a tensile η₃ > 0 strain (the strain is exaggerated for clarity); the arrows on the atoms indicate how they react in response to the strain, as computed from first principles. Panels d–f are analogous to the previous three panels, but featuring the paraelectric (d) and ferroelectric (e) states of HfO₂, and its longitudinal piezoresponse (f).

Fig. 4. Visualizing Hf–O bonds.

Computed electronic charge density for the unperturbed ferroelectric phase of HfO₂ (panels a and b) as well as for the structures obtained at η_epi = −7 % (c and d) and η_epi = + 4 % (e and f). Panels a, c and e show a contour plot of the charge density within a plane that approximately contains the O_I(1) atom highlighted in Fig. 1 as well as its three nearest-neighboring Hf atoms. Panels b, d and f show the charge density along lines connecting the central oxygen with each of its three nearest-neighboring Hf cations. In panel c, the red globe at the top left of the Hf(2) atom corresponds to a neighboring oxygen anion that gets close to the shown plane.

Fig. 5. Controlling bonds with epitaxial strain.

Lengths of the Hf(1)–O_I(1), Hf(2)–O_I(1) and Hf(3)–O_I(1) bonds defined in Fig. 1, computed as a function of epitaxial strain.

Fig. 6. Computed e₃₃ piezoresponse component as a function of epitaxial strain.

The total e₃₃ (black) is split into frozen-ion (blue) and lattice-mediated (red) contributions.

Fig. 7. Epitaxial strain dependence of the Λ components that control the e₃₃ response (see text).

More precisely, the shown components quantify the third (vertical) component of the force that acts on the Hf, O_I and O_II atoms as a consequence of an applied strain η₃ > 0.